wirtz
/
OpenAudio_ArduinoLibrary
mirror of https://github.com/chipaudette/OpenAudio_ArduinoLibrary.git
1
0
Fork 0
Code Issues Releases Wiki Activity

Add AudioFilter 90Deg and RadioIQMixer plus support for these.

Browse Source
pull/11/head
boblark 4 years ago
parent 825f50668b
commit ae99656d29
14 changed files with 1816 additions and 0 deletions
Show all changes Ignore whitespace when comparing lines Ignore changes in amount of whitespace Ignore changes in whitespace at EOL
Show Stats Download Patch File Download Diff File
  1. 235
      AudioEffectDelay_OA_F32.cpp
  2. 152
      AudioEffectDelay_OA_F32.h
  3. 95
      AudioFilter90Deg_F32.cpp
  4. 153
      AudioFilter90Deg_F32.h
  5. 3
      OpenAudio_ArduinoLibrary.h
  6. 106
      RadioIQMixer_F32.cpp
  7. 138
      RadioIQMixer_F32.h
  8. 290
      examples/FineFreqShift_OA/FineFreqShift_OA.ino
  9. 123
      examples/FineFreqShift_OA/hilbert121A.h
  10. 253
      examples/FineFreqShift_OA/hilbert251A.h
  11. 114
      mathDSP_F32.cpp
  12. 50
      mathDSP_F32.h
  13. 6
      readme.md
  14. 98
      sinTable512_f32.h

235
AudioEffectDelay_OA_F32.cpp
Unescape View File

@ -0,0 +1,235 @@
/*
*
*
* Audio Library for Teensy 3.X
* Copyright (c) 2014, Paul Stoffregen, paul@pjrc.com
* Extended by Chip Audette, Open Audio, April 2018
*
* Development of this audio library was funded by PJRC.COM, LLC by sales of
* Teensy and Audio Adaptor boards. Please support PJRC's efforts to develop
* open source software by purchasing Teensy or other PJRC products.
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice, development funding notice, and this permission
* notice shall be included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
* THE SOFTWARE.
*/
#include <Arduino.h>
#include "AudioEffectDelay_OA_F32.h"
void AudioEffectDelay_OA_F32::update(void)
{
//Serial.println("AudioEffectDelay_OA_F32: update()...");
receiveIncomingData(); //put the in-coming audio data into the queue
discardUnneededBlocksFromQueue(); //clear out queued data this is no longer needed
transmitOutgoingData(); //put the queued data into the output
return;
}
void AudioEffectDelay_OA_F32::receiveIncomingData(void) {
//Serial.println("AudioEffectDelay_OA_F32::receiveIncomingData: starting...");
//prepare the receiving queue
uint16_t head = headindex; //what block to write to
uint16_t tail = tailindex; //what block to read from
if (queue[head] == NULL) {
//if (!Serial) Serial.println("AudioEffectDelay_OA_F32::receiveIncomingData: Allocating queue[head].");
queue[head] = allocate_f32();
if (queue[head] == NULL) {
//if (!Serial) Serial.println("AudioEffectDelay_OA_F32::receiveIncomingData: Null memory 1. Returning.");
return;
}
}
//prepare target memory nto which we'll copy the incoming data into the queue
int dest_ind = writeposition; //inclusive
if (dest_ind >= (queue[head]->full_length)) {
head++; dest_ind = 0;
if (head >= DELAY_QUEUE_SIZE) head = 0;
if (queue[head] != NULL) {
if (head==tail) {tail++; if (tail >= DELAY_QUEUE_SIZE) tail = 0; }
AudioStream_F32::release(queue[head]);
queue[head]=NULL;
}
}
if (queue[head]==NULL) {
queue[head] = allocate_f32();
if (queue[head] == NULL) {
if (!Serial) Serial.println("AudioEffectDelay_OA_F32::receiveIncomingData: Null memory 2. Returning.");
return;
}
}
//receive the in-coming audio data block
audio_block_f32_t *input = receiveReadOnly_f32();
if (input == NULL) {
//if (!Serial) Serial.println("AudioEffectDelay_OA_F32::receiveIncomingData: Input data is NULL. Returning.");
return;
}
int n_copy = input->length;
last_received_block_id = input->id;
// Now we'll loop over the individual samples of the in-coming data
float32_t *dest = queue[head]->data;
float32_t *source = input->data;
int end_write = dest_ind + n_copy; //this may go past the end of the destination array
int end_loop = min(end_write,(int)(queue[head]->full_length)); //limit to the end of the array
int src_count=0, dest_count=dest_ind;
for (int i=dest_ind; i<end_loop; i++) dest[dest_count++] = source[src_count++];
//finish writing taking data from the next queue buffer
if (src_count < n_copy) { // there's still more input data to copy...but we need to roll-over to a new input queue
head++; dest_ind = 0;
if (head >= DELAY_QUEUE_SIZE) head = 0;
if (queue[head] != NULL) {
if (head==tail) {tail++; if (tail >= DELAY_QUEUE_SIZE) tail = 0; }
AudioStream_F32::release(queue[head]);
queue[head]=NULL;
}
if (queue[head]==NULL) {
queue[head] = allocate_f32();
if (queue[head] == NULL) {
Serial.println("AudioEffectDelay_OA_F32::receiveIncomingData: Null memory 3. Returning.");
AudioStream_F32::release(input);
return;
}
}
float32_t *dest = queue[head]->data;
end_loop = end_write - (queue[head]->full_length);
dest_count = dest_ind;
for (int i=dest_ind; i < end_loop; i++) dest[dest_count++]=source[src_count++];
}
AudioStream_F32::release(input);
writeposition = dest_count;
headindex = head;
tailindex = tail;
return;
}
void AudioEffectDelay_OA_F32::discardUnneededBlocksFromQueue(void) {
uint16_t head = headindex; //what block to write to
uint16_t tail = tailindex; //last useful block of data
uint32_t count;
// discard unneeded blocks from the queue
if (head >= tail) {
count = head - tail;
} else {
count = DELAY_QUEUE_SIZE + head - tail;
}
/* if (head>0) {
Serial.print("AudioEffectDelay_OA_F32::discardUnneededBlocksFromQueue: head, tail, count, maxblocks, DELAY_QUEUE_SIZE: ");
Serial.print(head); Serial.print(", ");
Serial.print(tail); Serial.print(", ");
Serial.print(count); Serial.print(", ");
Serial.print(maxblocks); Serial.print(", ");
Serial.print(DELAY_QUEUE_SIZE); Serial.print(", ");
Serial.println();
} */
if (count > maxblocks) {
count -= maxblocks;
do {
if (queue[tail] != NULL) {
AudioStream_F32::release(queue[tail]);
queue[tail] = NULL;
}
if (++tail >= DELAY_QUEUE_SIZE) tail = 0;
} while (--count > 0);
}
tailindex = tail;
}
void AudioEffectDelay_OA_F32::transmitOutgoingData(void) {
uint16_t head = headindex; //what block to write to
//uint16_t tail = tailindex; //last useful block of data
audio_block_f32_t *output;
int channel; //, index, prev, offset;
//const float32_t *src, *end;
//float32_t *dst;
// transmit the delayed outputs using queue data
for (channel = 0; channel < 8; channel++) {
if (!(activemask & (1<<channel))) continue;
output = allocate_f32();
if (!output) continue;
//figure out where to start pulling the data samples from
uint32_t ref_samp_long = (head*AUDIO_BLOCK_SIZE_F32) + writeposition; //note that writepoisition has already been
//incremented by the block length by the
//receiveIncomingData method. We'll adjust it next
uint32_t offset_samp = delay_samps[channel]+output->length;
if (ref_samp_long < offset_samp) { //when (ref_samp_long - offset_samp) goes negative, the uint32_t will fail, so we do this logic check
ref_samp_long = ref_samp_long + (((uint32_t)(DELAY_QUEUE_SIZE))*((uint32_t)AUDIO_BLOCK_SIZE_F32));
}
ref_samp_long = ref_samp_long - offset_samp;
uint16_t source_queue_ind = (uint16_t)(ref_samp_long / ((uint32_t)AUDIO_BLOCK_SIZE_F32));
int source_samp = (int)(ref_samp_long - (((uint32_t)source_queue_ind)*((uint32_t)AUDIO_BLOCK_SIZE_F32)));
//pull the data from the first source data block
int dest_counter=0;
int n_output = output->length;
float32_t *dest = output->data;
audio_block_f32_t *source_block = queue[source_queue_ind];
if (source_block == NULL) {
//fill destination with zeros for this source block
int Iend = min(source_samp+n_output,AUDIO_BLOCK_SIZE_F32);
for (int Isource = source_samp; Isource < Iend; Isource++) {
dest[dest_counter++]=0.0;
}
} else {
//fill destination with this source block's values
float32_t *source = source_block->data;
int Iend = min(source_samp+n_output,AUDIO_BLOCK_SIZE_F32);
for (int Isource = source_samp; Isource < Iend; Isource++) {
dest[dest_counter++]=source[Isource];
}
}
//pull the data from the second source data block, if needed
if (dest_counter < n_output) {
//yes, we need to keep filling the output
int Iend = n_output - dest_counter; //how many more data points do we need
source_queue_ind++; source_samp = 0; //which source block will we draw from (and reset the source sample counter)
if (source_queue_ind >= DELAY_QUEUE_SIZE) source_queue_ind = 0; //wrap around on our source black.
source_block = queue[source_queue_ind]; //get the source block
if (source_block == NULL) { //does it have data?
//no, it doesn't have data. fill destination with zeros
for (int Isource = source_samp; Isource < Iend; Isource++) {
dest[dest_counter++] = 0.0;
}
} else {
//source block does have data. use this block's values
float32_t *source = source_block->data;
for (int Isource = source_samp; Isource < Iend; Isource++) {
dest[dest_counter++]=source[Isource];
}
}
}
//add the id of the last received audio block
output->id = last_received_block_id;
//transmit and release
AudioStream_F32::transmit(output, channel);
AudioStream_F32::release(output);
}
}

152
AudioEffectDelay_OA_F32.h
Unescape View File

@ -0,0 +1,152 @@
/*
* AudioEffectDelay_OA_F32.h
*
* Audio Library for Teensy 3.X
* Copyright (c) 2014, Paul Stoffregen, paul@pjrc.com
* Extended by Chip Audette, Open Audio, Apr 2018
* Isolated names for Open Audio (F32) RSL June 2020
*
* Development of this audio library was funded by PJRC.COM, LLC by sales of
* Teensy and Audio Adaptor boards. Please support PJRC's efforts to develop
* open source software by purchasing Teensy or other PJRC products.
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice, development funding notice, and this permission
* notice shall be included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
* THE SOFTWARE.
*/
#ifndef AudioEffecDelay_OA_F32_h_
#define AudioEffecDelay_OA_F32_h_
#include "Arduino.h"
#include "AudioStream_F32.h"
#include "utility/dspinst.h"
#define AUDIO_BLOCK_SIZE_F32 AUDIO_BLOCK_SAMPLES //what is the maximum length of the F32 audio blocks
// Are these too big??? I think the same as I16---half as much? <<<<<<<<<<<<<<<<
#if defined(__IMXRT1062__)
// 4.00 second maximum on Teensy 4.0
#define DELAY_QUEUE_SIZE (176512 / AUDIO_BLOCK_SAMPLES)
#elif defined(__MK66FX1M0__)
// 2.41 second maximum on Teensy 3.6
#define DELAY_QUEUE_SIZE (106496 / AUDIO_BLOCK_SIZE_F32)
#elif defined(__MK64FX512__)
// 1.67 second maximum on Teensy 3.5
#define DELAY_QUEUE_SIZE (73728 / AUDIO_BLOCK_SIZE_F32)
#elif defined(__MK20DX256__)
// 0.45 second maximum on Teensy 3.1 & 3.2
#define DELAY_QUEUE_SIZE (19826 / AUDIO_BLOCK_SIZE_F32)
#else
// 0.14 second maximum on Teensy 3.0
#define DELAY_QUEUE_SIZE (6144 / AUDIO_BLOCK_SIZE_F32)
#endif
class AudioEffectDelay_OA_F32 : public AudioStream_F32
{
//GUI: inputs:1, outputs:1 //this line used for automatic generation of GUI node
//GUI: shortName:delay
public:
AudioEffectDelay_OA_F32() : AudioStream_F32(1, inputQueueArray) {
activemask = 0;
headindex = 0;
tailindex = 0;
maxblocks = 0;
memset(queue, 0, sizeof(queue));
}
AudioEffectDelay_OA_F32(const AudioSettings_F32 &settings) :
AudioStream_F32(1,inputQueueArray) {
activemask = 0;
headindex = 0;
tailindex = 0;
maxblocks = 0;
memset(queue, 0, sizeof(queue));
setSampleRate_Hz(settings.sample_rate_Hz);
}
void setSampleRate_Hz(float _fs_Hz) {
//Serial.print("AudioEffectDelay_OA_F32: setSampleRate_Hz to ");
//Serial.println(_fs_Hz);
sampleRate_Hz = _fs_Hz;
//audio_block_len_samples = block_size; //this is the actual size that is being used in each audio_block_f32
}
void delay(uint8_t channel, float milliseconds) {
if (channel >= 8) return;
if (milliseconds < 0.0) milliseconds = 0.0;
uint32_t n = (milliseconds*(sampleRate_Hz/1000.0))+0.5;
uint32_t nmax = AUDIO_BLOCK_SIZE_F32 * (DELAY_QUEUE_SIZE-1);
if (n > nmax) n = nmax;
uint32_t blks = (n + (AUDIO_BLOCK_SIZE_F32-1)) / AUDIO_BLOCK_SIZE_F32 + 1;
if (!(activemask & (1<<channel))) {
// enabling a previously disabled channel
delay_samps[channel] = n;
if (blks > maxblocks) maxblocks = blks;
activemask |= (1<<channel);
} else {
if (n > delay_samps[channel]) {
// new delay is greater than previous setting
if (blks > maxblocks) maxblocks = blks;
delay_samps[channel] = n;
} else {
// new delay is less than previous setting
delay_samps[channel] = n;
recompute_maxblocks();
}
}
}
void disable(uint8_t channel) {
if (channel >= 8) return;
// diable this channel
activemask &= ~(1<<channel);
// recompute maxblocks for remaining enabled channels
recompute_maxblocks();
}
virtual void update(void);
private:
void recompute_maxblocks(void) {
uint32_t max=0;
uint32_t channel = 0;
do {
if (activemask & (1<<channel)) {
uint32_t n = delay_samps[channel];
n = (n + (AUDIO_BLOCK_SIZE_F32-1)) / AUDIO_BLOCK_SIZE_F32 + 1;
if (n > max) max = n;
}
} while(++channel < 8);
maxblocks = max;
}
uint8_t activemask; // which output channels are active
uint16_t headindex; // head index (incoming) data in queue
uint16_t tailindex; // tail index (outgoing) data from queue
uint16_t maxblocks; // number of blocks needed in queue
//#if DELAY_QUEUE_SIZE * AUDIO_BLOCK_SAMPLES < 65535
// uint16_t writeposition;
// uint16_t delay_samps[8]; // # of samples to delay for each channel
//#else
int writeposition; //position within current head buffer in the queue
uint32_t delay_samps[8]; // # of samples to delay for each channel
//#endif
audio_block_f32_t *queue[DELAY_QUEUE_SIZE];
audio_block_f32_t *inputQueueArray[1];
float sampleRate_Hz = AUDIO_SAMPLE_RATE_EXACT; //default. from AudioStream.h??
//int audio_block_len_samples = AUDIO_BLOCK_SAMPLES;
void receiveIncomingData(void);
void discardUnneededBlocksFromQueue(void);
void transmitOutgoingData(void);
unsigned long last_received_block_id = 0;
};
#endif

95
AudioFilter90Deg_F32.cpp
Unescape View File

@ -0,0 +1,95 @@
/*
* AudioFilter90Deg_F32.cpp
*
* 22 March 2020
* Bob Larkin, in support of the library:
* Chip Audette, OpenAudio, Apr 2017
* -------------------
* There are two channels that update synchronously, but operate
* independently. The I-channel, coresponding to a "Left"
* audio channel, is filtered with an N coefficient
* Hilbert Transform in FIR form.
* The Q-channel, or "Right" channel, is simply
* delayed by the (N-1)/2 sample periods. The phase between
* the two outputs is 90-Degrees. The amplitude response cuts off low
* frequencies and depends on N.
*
* The I-channel FIR is a Hilbert Transform and this has every other term 0.
* These need not be multiplied-and-accumulated, but for now, we do. By the
* time the indexes are calculated, it may be quicker to process everything.
* Additionally, to not require a half-sample delay, the number of terms in
* the Hilbert FIR needs to be odd.
*
* MIT License, Use at your own risk.
*/
#include "AudioFilter90Deg_F32.h"
void AudioFilter90Deg_F32::update(void)
{
audio_block_f32_t *block_i, *block_q, *blockOut_i=NULL;
uint16_t i;
// Get first input, i, that will be filtered
block_i = AudioStream_F32::receiveWritable_f32(0);
if (!block_i) {
if(errorPrint) Serial.println("FIL90-ERR: No i input memory");
return;
}
// Get second input, q, that will be delayed
block_q = AudioStream_F32::receiveWritable_f32(1);
if (!block_q){
if(errorPrint) Serial.println("FIL90-ERR: No q input memory");
AudioStream_F32::release(block_i);
return;
}
// If there's no coefficient table, give up.
if (coeff_p == NULL) {
if(errorPrint) Serial.println("FIL90-ERR: No Hilbert FIR coefficients");
AudioStream_F32::release(block_i);
AudioStream_F32::release(block_q);
return;
}
// Try to get a block for the FIR output
blockOut_i = AudioStream_F32::allocate_f32();
if (!blockOut_i){ // Didn't have any
if(errorPrint) Serial.println("FIL90-ERR: No out 0 block");
AudioStream_F32::release(block_i);
AudioStream_F32::release(block_q);
return;
}
// Apply the Hilbert transform FIR. This includes multiplies by zero.
// Is there any way to play with the indexes and not multiply by zero
// without spending more time than is saved? How about something like
// pick right nn, then for(j=0; j<fir_length; j+=2) {sum += coef[j] * data[j+nn];}
arm_fir_f32(&Ph90Deg_inst, block_i->data, blockOut_i->data, block_i->length);
AudioStream_F32::release(block_i); // Not needed further
// Now enter block_size points to the delay loop and move earlier points to re-used block
float32_t *pin, *pout;
pin = &(block_q->data[0]); // point to beginning of block_q
for(i=0; i<block_size; i++) { // Let it wrap around at 256
in_index++;
in_index = delayBufferMask & in_index; // Index into delay buffer, wrapping
delayData[in_index] = *pin++; // Put ith q data to circular delay buffer
}
// And similarly, output with a delay, i.e., a buffer offset
pout = &(block_q->data[0]); // Re-use the input block
for(i=0; i<block_size; i++) {
out_index++;
out_index = delayBufferMask & out_index; // Index into delay buffer, wrapping
*pout++ = delayData[out_index];
}
//transmit the data
AudioStream_F32::transmit(blockOut_i, 0); // send the FIR outputs
AudioStream_F32::release (blockOut_i);
AudioStream_F32::transmit(block_q, 1); // and the delayed outputs
AudioStream_F32::release (block_q);
}

153
AudioFilter90Deg_F32.h
Unescape View File

@ -0,0 +1,153 @@
/*
* AudioFilter90Deg_F32.h
* 22 March 2020 Bob Larkin
* Parts are based on Open Audio FIR filter by Chip Audette:
*
* Chip Audette (OpenAudio) Feb 2017
* - Building from AudioFilterFIR from Teensy Audio Library
* (AudioFilterFIR credited to Pete (El Supremo))
* Copyright (c) 2020 Bob Larkin
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice, development funding notice, and this permission
* notice shall be included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
* THE SOFTWARE.
*/
/*
* This consists of two uncoupled paths that almost have the same amplitude gain
* but differ in phase by exactly 90 degrees. See AudioFilter90Deg_F32.cpp
* The number of coefficients is an odd number for the FIR Hilbert transform
* as that produces an easily achievable integer sample period delay. In
* float, the ARM FIR library routine will handle odd numbers.\, so no zero padding
* is needed.
*
* No default Hilbert Transform is provided, as it is highly application dependent.
* The number of coefficients is an odd number with a maximum of 250. The Iowa
* Hills program can design a Hilbert Transform filter. Use begin(*pCoeff, nCoeff)
* in the .INO to initialize this block.
*
* Status: Tested T3.6 and T4.0. No known bugs.
* Functions:
* begin(*pCoeff, nCoeff); Initializes this block, with:
* pCoeff = pointer to array of F32 Hilbert Transform coefficients
* nCoeff = uint16_t number of Hilbert transform coefficients
* showError(e); Turns error printing in update() on (e=1) and off (e=0). For debug.
* Examples:
* ReceiverPart1.ino
* ReceiverPart2.ino
* Time: Depends on size of Hilbert FIR. Time for main body of update() including
* Hilbert FIR and compensating delay, 128 data block, running on Teensy 3.6 is:
* 19 tap Hilbert (including 0's) 74 microseconds
* 121 tap Hilbert (including 0's) 324 microseconds
* 251 tap Hilbert (including 0's) 646 microseconds
* Same 121 tap Hilbert on T4.0 is 57 microseconds per update()
* Same 251 tap Hilbert on T4.0 is 114 microseconds per update()
*/
#ifndef _filter_90deg_f32_h
#define _filter_90deg_f32_h
#include "AudioStream_F32.h"
#include "arm_math.h"
#define TEST_TIME_90D 1
// Following supports a maximum FIR Hilbert Transform of 251
#define HILBERT_MAX_COEFFS 251
class AudioFilter90Deg_F32 : public AudioStream_F32 {
//GUI: inputs:2, outputs:2 //this line used for automatic generation of GUI node
//GUI: shortName: 90DegPhase
public:
// Option of AudioSettings_F32 change to block size (no sample rate dependent variables here):
AudioFilter90Deg_F32(void) : AudioStream_F32(2, inputQueueArray_f32) {
block_size = AUDIO_BLOCK_SAMPLES;
}
AudioFilter90Deg_F32(const AudioSettings_F32 &settings) : AudioStream_F32(2, inputQueueArray_f32) {
block_size = settings.audio_block_samples;
}
// Initialize the 90Deg by giving it the filter coefficients and number of coefficients
// Then the delay line for the q (Right) channel is initialized
void begin(const float32_t *cp, const int _n_coeffs) {
coeff_p = cp;
n_coeffs = _n_coeffs;
// Initialize FIR instance (ARM DSP Math Library) (for f32 the return is always void)
if (coeff_p!=NULL && n_coeffs<252) {
arm_fir_init_f32(&Ph90Deg_inst, n_coeffs, (float32_t *)coeff_p, &StateF32[0], block_size);
}
else {
coeff_p = NULL; // Stops further FIR filtering for Hilbert
// Serial.println("Hilbert: Missing FIR Coefficients or number > 251");
}
// For the equalizing delay in q, if n_coeffs==19, n_delay=9
// Max of 251 coeffs needs a delay of 125 sample periods.
n_delay = (uint8_t)((n_coeffs-1)/2);
in_index = n_delay;
out_index = 0;
for (uint16_t i=0; i<256; i++){
delayData[i] = 0.0F;
}
} // End of begin()
void showError(uint16_t e) {
errorPrint = e;
}
void update(void);
private:
uint16_t block_size = AUDIO_BLOCK_SAMPLES;
// Two input data pointers
audio_block_f32_t *inputQueueArray_f32[2];
// One output pointer
audio_block_f32_t *blockOut_i;
#if TEST_TIME_90D
// *Temporary* - allows measuring time in microseconds for each part of the update()
elapsedMicros tElapse;
int32_t iitt = 999000; // count up to a million during startup
#endif
// Control error printing in update() 0=No print
uint16_t errorPrint = 0;
//float32_t tmpHil[5]={0.0, 1.0, 0.0, -1.0, 0.0}; coeff_p = &tmpHil[0];
// pointer to current coefficients or NULL
const float32_t *coeff_p = NULL;
uint16_t n_coeffs = 0;
// Variables for the delayed q-channel:
// For the q-channel, we need a delay of ((Ncoeff - 1) / 2) samples. This
// is 9 delay for 19 coefficient FIR. This can be implemented as a simple circular
// buffer if we make the buffer a power of 2 in length and binary-truncate the index.
// Choose 2^8 = 256. For a 251 long Hilbert this wastes 256-128-125 = 3, but
// more for shorter Hilberts.
float32_t delayData[256]; // The circular delay line
uint16_t in_index;
uint16_t out_index;
// And a mask to make the circular buffer limit to a power of 2
uint16_t delayBufferMask = 0X00FF;
uint16_t n_delay;
// ARM DSP Math library filter instance
arm_fir_instance_f32 Ph90Deg_inst;
float32_t StateF32[AUDIO_BLOCK_SAMPLES + HILBERT_MAX_COEFFS];
};
#endif

3
OpenAudio_ArduinoLibrary.h
Unescape View File

@ -32,3 +32,6 @@
#include "AudioSwitch_OA_F32.h"
#include "FFT_Overlapped_OA_F32.h"
#include "AudioEffectFreqShiftFD_OA_F32.h"
#include "AudioEffectDelay_OA_F32.h"
#include "RadioIQMixer_F32.h"
#include "AudioFilter90Deg_F32.h"

106
RadioIQMixer_F32.cpp
Unescape View File

@ -0,0 +1,106 @@
/*
* RadioIQMixer_F32.cpp
*
* 22 March 2020
* Bob Larkin, in support of the library:
* Chip Audette, OpenAudio, Apr 2017
* -------------------
* A single signal channel comes in and is multiplied (mixed) with a sin
* and cos of the same frequency. The pair of mixer outputs are
* referred to as i and q. The conversion in frequency is either
* up or down, and a pair of filters on i and q determine which is allow
* to pass to the output.
*
* The sin/cos LO is from synth_sin_cos_f32.cpp See that for details.
*
* There are two then two outputs.
*
* MIT License, Use at your own risk.
*/
#include "RadioIQMixer_F32.h"
// 513 values of the sine wave in a float array:
#include "sinTable512_f32.h"
void RadioIQMixer_F32::update(void) {
audio_block_f32_t *blockIn, *blockOut_i=NULL, *blockOut_q=NULL;
uint16_t index, i;
float32_t a, b, deltaPhase, phaseC;
// Get first input, i, that will be filtered
blockIn = AudioStream_F32::receiveWritable_f32(0);
if (!blockIn) {
if(errorPrintIQM) Serial.println("IQMIXER-ERR: No input memory");
return;
}
// Try to get a pair of blocks for the IQ output
blockOut_i = AudioStream_F32::allocate_f32();
if (!blockOut_i){ // Didn't have any
if(errorPrintIQM) Serial.println("IQMIXER-ERR: No I output memory");
AudioStream_F32::release(blockIn);
return;
}
blockOut_q = AudioStream_F32::allocate_f32();
if (!blockOut_q){
if(errorPrintIQM) Serial.println("IQMIXER-ERR: No Q output memory");
AudioStream_F32::release(blockIn);
AudioStream_F32::release(blockOut_i);
return;
}
// doSimple has amplitude (-1, 1) and sin/cos differ by 90.00 degrees.
if (doSimple) {
for (i=0; i < block_size; i++) {
phaseS += phaseIncrement;
if (phaseS > 512.0f)
phaseS -= 512.0f;
index = (uint16_t) phaseS;
deltaPhase = phaseS -(float32_t) index;
/* Read two nearest values of input value from the sin table */
a = sinTable512_f32[index];
b = sinTable512_f32[index+1];
// Linear interpolation and multiplying (DBMixer) with input
blockOut_i->data[i] = blockIn->data[i] * (a + 0.001953125*(b-a)*deltaPhase);
/* Repeat for cosine by adding 90 degrees phase */
index = (index + 128) & 0x01ff;
/* Read two nearest values of input value from the sin table */
a = sinTable512_f32[index];
b = sinTable512_f32[index+1];
/* deltaPhase will be the same as used for sin */
blockOut_q->data[i] = blockIn->data[i]*(a + 0.001953125*(b-a)*deltaPhase);
}
}
else { // Do a more flexible update, i.e., not doSimple
for (i=0; i < block_size; i++) {
phaseS += phaseIncrement;
if (phaseS > 512.0f) phaseS -= 512.0f;
index = (uint16_t) phaseS;
deltaPhase = phaseS -(float32_t) index;
/* Read two nearest values of input value from the sin table */
a = sinTable512_f32[index];
b = sinTable512_f32[index+1];
// We now have a sine value, so multiply with the input data and save
// Linear interpolate sine and multiply with the input and amplitude (about 1.0)
blockOut_i->data[i] = amplitude_pk * blockIn->data[i] * (a + 0.001953125*(b-a)*deltaPhase);
/* Shift forward phaseS_C and get cos. First, the calculation of index of the table */
phaseC = phaseS + phaseS_C;
if (phaseC > 512.0f) phaseC -= 512.0f;
index = (uint16_t) phaseC;
deltaPhase = phaseC -(float32_t) index;
/* Read two nearest values of input value from the sin table */
a = sinTable512_f32[index];
b = sinTable512_f32[index+1];
// Same as sin, but leave amplitude of LO at +/- 1.0
blockOut_q->data[i] = blockIn->data[i] * (a + 0.001953125*(b-a)*deltaPhase);
}
}
AudioStream_F32::release(blockIn); // Done with this
//transmit the data
AudioStream_F32::transmit(blockOut_i, 0); // send the I outputs
AudioStream_F32::release(blockOut_i);
AudioStream_F32::transmit(blockOut_q, 1); // and the Q outputs
AudioStream_F32::release(blockOut_q);
}

138
RadioIQMixer_F32.h
Unescape View File

@ -0,0 +1,138 @@
/*
* RadioIQMixer_F32
* 8 April 2020 Bob Larkin
* With much credit to:
* Chip Audette (OpenAudio) Feb 2017
* and of course, to PJRC for the Teensy and Teensy Audio Library
*
* A basic building block is a pair of mixers fed in parallel with the
* LO going to the mixers at the same frequency, but differing in phase
* by 90 degrees. This provides two outputs I and Q that are offset in
* frequency but also 90 degrees apart in phase. The LO are included
* in the block, but there are no post-mixing filters.
*
* The frequency is set by .frequency(float freq_Hz)
* Particularly for use in transmitting, there is provision for varying
* the phase between the sine and cosine oscillators. Technically this is no
* longer sin and cos, but that is what real hardware needs.
*
* The output levels are 0.5 times the input level.
*
* Status: Tested in doSimple==1
* Tested in FineFreqShift_OA.ino, T3.6 and T4.0
*
* Inputs: 0 is signal
* Outputs: 0 is I 1 is Q
*
* Functions, available during operation:
* void frequency(float32_t fr) Sets BFO frequency Hz
* void iqmPhaseS(float32_t ps) Sets Phase of Sine in radians
* void phaseS_C_r(float32_t pc) Sets relative phase of Cosine in radians, approximately pi/2
* void amplitudeC(float32_t a) Sets relative amplitude of Sine, approximately 1.0
* void useSimple(bool s) Faster if 1, but no phase/amplitude adjustment
* void setSampleRate_Hz(float32_t fs_Hz) Allows dynamic sample rate change for this function
*
* Time: T3.6 For an update of a 128 sample block, doSimple=1, 46 microseconds
* T4.0 For an update of a 128 sample block, doSimple=1, 20 microseconds
*/
#ifndef _radioIQMixer_f32_h
#define _radioIQMixer_f32_h
#include "AudioStream_F32.h"
#include "arm_math.h"
#include "mathDSP_F32.h"
class RadioIQMixer_F32 : public AudioStream_F32 {
//GUI: inputs:2, outputs:2 //this line used for automatic generation of GUI node
//GUI: shortName: IQMixer
public:
// Option of AudioSettings_F32 change to block size or sample rate:
RadioIQMixer_F32(void) : AudioStream_F32(1, inputQueueArray_f32) {
// Defaults
}
RadioIQMixer_F32(const AudioSettings_F32 &settings) : AudioStream_F32(1, inputQueueArray_f32) {
setSampleRate_Hz(settings.sample_rate_Hz);
block_size = settings.audio_block_samples;
}
void frequency(float32_t fr) { // Frequency in Hz
freq = fr;
if (freq < 0.0f) freq = 0.0f;
else if (freq > sample_rate_Hz/2.0f) freq = sample_rate_Hz/2.0f;
phaseIncrement = 512.0f * freq / sample_rate_Hz;
}
/* Externally, phase comes in the range (0,2*M_PI) keeping with C math functions
* Internally, the full circle is represented as (0.0, 512.0). This is
* convenient for finding the entry to the sine table.
*/
void iqmPhaseS(float32_t a) {
while (a < 0.0f) a += MF_TWOPI;
while (a > MF_TWOPI) a -= MF_TWOPI;
phaseS = 512.0f * a / MF_TWOPI;
doSimple = false;
return;
}
// phaseS_C_r is the number of radians that the cosine output leads the
// sine output. The default is M_PI_2 = pi/2 = 1.57079633 radians,
// corresponding to 90.00 degrees cosine leading sine.
void iqmPhaseS_C(float32_t a) {
while (a < 0.0f) a += MF_TWOPI;
while (a > MF_TWOPI) a -= MF_TWOPI;
// Internally a full circle is 512.00 of phase
phaseS_C = 512.0f * a / MF_TWOPI;
doSimple = false;
return;
}
// The amplitude, a, is the peak, as in zero-to-peak. This produces outputs
// ranging from -a to +a. Both outputs are the same amplitude.
void iqmAmplitude(float32_t a) {
amplitude_pk = a;
doSimple = false;
return;
}
// Speed up calculations by setting phaseS_C=90deg, amplitude=1
void useSimple(bool s) {
doSimple = s;
if(doSimple) {
phaseS_C = 128.0f;
amplitude_pk = 1.0f;
}
return;
}
void setSampleRate_Hz(float32_t fs_Hz) {
// Check freq range
if (freq > sample_rate_Hz/2.0f) freq = sample_rate_Hz/2.f;
// update phase increment for new frequency
phaseIncrement = 512.0f * freq / fs_Hz;
}
void showError(uint16_t e) { // Serial.print errors in update()
errorPrintIQM = e;
}
virtual void update(void);
private:
audio_block_f32_t *inputQueueArray_f32[1];
float32_t freq = 1000.0f;
float32_t phaseS = 0.0f;
float32_t phaseS_C = 128.00; // 512.00 is 360 degrees
float32_t amplitude_pk = 1.0f;
float32_t sample_rate_Hz = AUDIO_SAMPLE_RATE_EXACT;
float32_t phaseIncrement = 512.00f * freq /sample_rate_Hz;
uint16_t block_size = AUDIO_BLOCK_SAMPLES;
uint16_t errorPrintIQM = 0; // Normally off
// if only freq() is used, the complexities of phase, phaseS_C,
// and amplitude are not used, speeding up the sin and cos:
bool doSimple = true;
};
#endif

290
examples/FineFreqShift_OA/FineFreqShift_OA.ino
Unescape View File

@ -0,0 +1,290 @@
/* FineFreqShift_OA.ino
*
* 1 Hz Resolution Frequency Shift and Synthetic Stereo
*
* Written for Open Audio Bob Larkin June 2020
*
* This sketch demonstrates the use of dual multipliers along with broad-band 90-degree
* phase shifters (Hilbert transforms) and sine/cosine generator to shift all frequencies
* by a fixed amount. The shift amount is set by a digital oscillator frequency
* and can be made arbitrarily precise. Thus the name "Fine Frequency Shifter."
*
* Two blocks do most of the work of shifting the frequency band. The RadioIQMixer_F32
* has a pair of multipliers that have one of their inputs from an oscillator that produces
* a sine and a cosine waveform of the same frequency. This oscillator phase difference
* is transferred to the output producing phase differences of 90-degrees. The multipliers,
* called double-balanced mixers in the analog world, produce sum and difference frequencies
* but the original input frequencies are suppressed. In the analog case, this suppression
* is limited by circuit balance, but for digital multipliers, the suppression is
* close-to-perfect. Thus the outputs of the I-Q Mixers is a pair of frequency sum and
* difference signals. Since the oscillator can be a low frequency, such as 100 Hz,
* the frequency band of sum and difference signals will include much overlap.
*
* The next block, the "AudioFilter90Deg_F32" applies a constant phase difference between
* the two inputs, which are then added or subtracted. That turns out to cause either the
* frequency sum or difference to be cancelled out. At that point only one audio signal
* remains and it is frequency shifted by the oscillator frequency.
*
* This INO also demonstrates the conversion of monaural to stereo sound by
* delaying one channel. This technique has been used for many years to de-correlate
* monaural noise before sending it to both ears. This can engage the the human brain
* to hear correlated signals better. It also adds a stereo presence to monaural voice
* that is pleasant to hear. It is tossed in here for experimentation. In general,
* delays up to 20 msec give the illusion of presence, whereas larger delays start to
* sound like loud echos! Play with it. Headphones vs. speakers change the perception.
*
* Control is done over the "USB Serial" using the Serial Monitor of the Arduino
* IDE. The commands control most functions and a list can be seen by typing
* "h<enter>", or looking in the listing below, at printHelp().
*
* Refs - The phasing method of SSB generation goes way back.
* https://en.wikipedia.org/wiki/Single-sideband_modulation#Hartley_modulator
* The precision of DSP makes it practical for overlapping input and output bands.
* I first encountered this in conversation with friend Johan Forrer:
* https://www.arrl.org/files/file/Technology/tis/info/pdf/9609x008.pdf
* I need to find the German description of delay stereo from the 1980's. Both audio
* shifting and delay stereo were put into the DSP-10 audio processor:
* http://www.janbob.com/electron/dsp10/dsp10.htm
*
* Tested OK for Teensy 3.6 and 4.0.
* For settings:
* sample rate (Hz) = 44117.00
* block size (samples) = 128
* N_FFT = 512
* Hilbert 251 taps
* CPU Cur/Peak, Teensy 3.6: 27.28%/27.49%
* CPU Cur/Peak, Teensy 4.0: 5.82%/5.84%
* Memory useage is 4 for I16 Memory
* Memory for F32 is 6 plus 1 more for every 2.9 mSec of Stereo Delay.
*
* This INO sketch is in the public domain.
*/
#include "Audio.h"
#include "AudioStream_F32.h"
#include "OpenAudio_ArduinoLibrary.h"
//set the sample rate and block size
const float sample_rate_Hz = 44117.f;
const int audio_block_samples = 128;
AudioSettings_F32 audio_settings(sample_rate_Hz, audio_block_samples);
//create audio library objects for handling the audio
AudioInputI2S i2sIn; // This I16 input/output is T4.x compatible
AudioConvert_I16toF32 cnvrt1; // Convert to float
RadioIQMixer_F32 iqmixer1;
AudioFilter90Deg_F32 hilbert1;
AudioMixer4_F32 sum1; // Summing node for the SSB receiver
AudioFilterFIR_F32 fir1; // Low Pass Filter to frequency limit the SSB
AudioEffectDelay_OA_F32 delay1; // Pleasant and useful sound between L & R
AudioConvert_F32toI16 cnvrt2;
AudioConvert_F32toI16 cnvrt3;
AudioOutputI2S i2sOut;
AudioControlSGTL5000 codec;
//Make all of the audio connections
AudioConnection patchCord0(i2sIn, 0, cnvrt1, 0); // connect to Left codec, 16-bit
AudioConnection_F32 patchCord1(cnvrt1, 0, iqmixer1, 0); // Input to 2 mixers
AudioConnection_F32 patchCord2(cnvrt1, 0, iqmixer1, 1);
AudioConnection_F32 patchCord3(iqmixer1, 0, hilbert1, 0); // Broadband 90 deg phase
AudioConnection_F32 patchCord4(iqmixer1, 1, hilbert1, 1);
AudioConnection_F32 patchCord5(hilbert1, 0, sum1, 0); // Sideband select
AudioConnection_F32 patchCord6(hilbert1, 1, sum1, 1);
AudioConnection_F32 patchCord7(sum1, 0, delay1, 0); // delay channel 0
AudioConnection_F32 patchCord9(sum1, 0, cnvrt2, 0); // connect to the left output
AudioConnection_F32 patchCordA(delay1, 0, cnvrt3, 0); // right output
AudioConnection patchCordB(cnvrt2, 0, i2sOut, 0);
AudioConnection patchCordC(cnvrt3, 0, i2sOut, 1);
//control display and serial interaction
bool enable_printCPUandMemory = false;
void togglePrintMemoryAndCPU(void) { enable_printCPUandMemory = !enable_printCPUandMemory; };
// Filter for AudioFilter90Deg_F32 hilbert1
#include "hilbert251A.h"
//inputs and levels
float gain_dB = -15.0f;
float gain = 0.177828f; // Same as -15 dB
float sign = 1.0f;
float deltaGain_dB = 2.5f;
float frequencyLO = 100.0f;
float delayms = 1.0f;
// *************** SETUP **********************************
void setup() {
Serial.begin(1); delay(1000);
Serial.println("*** Fine Frequency Shifter - June 2020 ***");
Serial.print("Sample Rate in Hz = ");
Serial.println(audio_settings.sample_rate_Hz, 0);
Serial.print("Block size, samples = ");
Serial.println(audio_settings.audio_block_samples);
AudioMemory(10); // I16 type
AudioMemory_F32(200, audio_settings);
//Enable the codec to start the audio flowing!
codec.enable();
codec.adcHighPassFilterEnable();
codec.inputSelect(AUDIO_INPUT_LINEIN);
iqmixer1.frequency(frequencyLO); // Frequency shift, Hz
deltaFrequency(0.0f); // Print freq
hilbert1.begin(hilbert251A, 251); // Set the Hilbert transform FIR filter
sum1.gain(0, gain*sign); // Set gains
sum1.gain(1, gain);
delay1.delay(0, delayms); // Delay right channel
deltaDelay(0.0f); // Print delay
//finish the setup by printing the help menu to the serial connections
printHelp();
}
// ************************* LOOP ****************************
void loop() {
//respond to Serial commands
while (Serial.available()) respondToByte((char)Serial.read());
//check to see whether to print the CPU and Memory Usage
if (enable_printCPUandMemory) printCPUandMemory(millis(), 3000); //print every 3000 msec
} //end loop();
//This routine prints the current and maximum CPU usage and the current usage of the AudioMemory that has been allocated
void printCPUandMemory(unsigned long curTime_millis, unsigned long updatePeriod_millis) {
//static unsigned long updatePeriod_millis = 3000; //how many milliseconds between updating gain reading?
static unsigned long lastUpdate_millis = 0;
//has enough time passed to update everything?
if (curTime_millis < lastUpdate_millis) lastUpdate_millis = 0; //handle wrap-around of the clock
if ((curTime_millis - lastUpdate_millis) > updatePeriod_millis) { //is it time to update the user interface?
Serial.print("CPU Cur/Peak: ");
Serial.print(audio_settings.processorUsage());
Serial.print("%/");
Serial.print(audio_settings.processorUsageMax());
Serial.println("%");
Serial.print(" Audio MEM Float32 Cur/Peak: ");
Serial.print(AudioMemoryUsage_F32());
Serial.print("/");
Serial.println(AudioMemoryUsageMax_F32());
Serial.print(" Audio MEM Int16 Cur/Peak: ");
Serial.print(AudioMemoryUsage());
Serial.print("/");
Serial.println(AudioMemoryUsageMax());
lastUpdate_millis = curTime_millis; //we will use this value the next time around.
}
}
void incrementGain(float increment_dB) {
gain_dB += increment_dB;
// gain is set in the "mixer" block, including sign for raise/lower freq
gain = powf(10.0f, 0.05f * gain_dB);
sum1.gain(0, gain*sign);
sum1.gain(1, gain);
printGainSettings();
}
void printGainSettings(void) {
Serial.print("Gain in dB = "); Serial.println(gain_dB, 1);
}
void deltaFrequency(float dfr) {
frequencyLO += dfr;
Serial.print("Frequency shift in Hz = ");
Serial.println(frequencyLO, 1);
if(frequencyLO < 0.0f)
sign = 1.0f;
else
sign = -1.0f;
iqmixer1.frequency(fabsf(frequencyLO));
incrementGain(0.0f);
}
void deltaDelay(float dtau) {
delayms += dtau;
if (delayms < 0.0f)
delayms = 0.0f;
delay1.delay(0, delayms); // Delay right channel
Serial.print("Delay in milliseconds = ");
Serial.println(delayms, 1);
}
//switch yard to determine the desired action
void respondToByte(char c) {
char s[2];
s[0] = c; s[1] = 0;
if( !isalpha((int)c) && c!='?') return;
switch (c) {
case 'h': case '?':
printHelp();
break;
case 'g': case 'G':
printGainSettings();
break;
case 'k':
incrementGain(deltaGain_dB);
break;
case 'K': // which is "shift k"
incrementGain(-deltaGain_dB);
break;
case 'C': case 'c':
Serial.println("Toggle printing of memory and CPU usage.");
togglePrintMemoryAndCPU();
break;
case 'd':
deltaFrequency(1.0f);
break;
case 'D':
deltaFrequency(-1.0f);
break;
case 'e':
deltaFrequency(10.0f);
break;
case 'E':
deltaFrequency(-10.0f);
break;
case 'f':
deltaFrequency(100.0f);
break;
case 'F':
deltaFrequency(-100.0f);
break;
case 't':
deltaDelay(1.0f);
break;
case 'T':
deltaDelay(-1.0f);
break;
case 'u':
deltaDelay(10.0f);
break;
case 'U':
deltaDelay(-10.0f);
break;
default:
Serial.print("You typed "); Serial.print(s);
Serial.println(". What command?");
}
}
void printHelp(void) {
Serial.println();
Serial.println("Help: Available Commands:");
Serial.println(" h: Print this help");
Serial.println(" g: Print the gain settings of the device.");
Serial.println(" C: Toggle printing of CPU and Memory usage");
Serial.print( " k: Increase the gain of both channels by ");
Serial.print(deltaGain_dB); Serial.println(" dB");
Serial.print( " K: Decrease the gain of both channels by ");
Serial.print(-deltaGain_dB); Serial.println(" dB");
Serial.println(" d: Raise frequency by 1 Hz");
Serial.println(" D: Lower frequency by 1 Hz");
Serial.println(" e: Raise frequency by 10 Hz");
Serial.println(" E: Lower frequency by 10 Hz");
Serial.println(" f: Raise frequency by 100 Hz");
Serial.println(" F: Lower frequency by 100 Hz");
Serial.println(" t: Raise stereo delay by 1 msec");
Serial.println(" T: Lower stereo delay by 1 msec");
Serial.println(" u: Raise stereo delay by 10 msec");
Serial.println(" U: Lower stereo delay by 10 msec");
}

123
examples/FineFreqShift_OA/hilbert121A.h
Unescape View File

@ -0,0 +1,123 @@
// Following is 121 term Hilbert FIR filter
float32_t hilbert121A[121] = {
0.000000000000000000,
0.000773378567767513,
0.000000000000000000,
0.001046207887980644,
0.000000000000000000,
0.001368896533613985,
0.000000000000000000,
0.001746769975247667,
0.000000000000000000,
0.002185555845922462,
0.000000000000000000,
0.002691457154069645,
0.000000000000000000,
0.003271251311125927,
0.000000000000000000,
0.003932423233774751,
0.000000000000000000,
0.004683343721596901,
0.000000000000000000,
0.005533508538632429,
0.000000000000000000,
0.006493859804516438,
0.000000000000000000,
0.007577220484233372,
0.000000000000000000,
0.008798886675905997,
0.000000000000000000,
0.010177443901536392,
0.000000000000000000,
0.011735907609641917,
0.000000000000000000,
0.013503343224246872,
0.000000000000000000,
0.015517212970554440,
0.000000000000000000,
0.017826854793349920,
0.000000000000000000,
0.020498780519188083,
0.000000000000000000,
0.023625003856774591,
0.000000000000000000,
0.027336628208641155,
0.000000000000000000,
0.031827023036304102,
0.000000000000000000,
0.037393534868609392,
0.000000000000000000,
0.044517689704988733,
0.000000000000000000,
0.054032871748808158,
0.000000000000000000,
0.067515548043274365,
0.000000000000000000,
0.088347125250410385,
0.000000000000000000,
0.125324201622410869,
0.000000000000000000,
0.210709715079613419,
0.000000000000000000,
0.634897508268964295,
0.000000000000000000,
-0.634897508268964295,
0.000000000000000000,
-0.210709715079613419,
0.000000000000000000,
-0.125324201622410869,
0.000000000000000000,
-0.088347125250410385,
0.000000000000000000,
-0.067515548043274365,
0.000000000000000000,
-0.054032871748808158,
0.000000000000000000,
-0.044517689704988733,
0.000000000000000000,
-0.037393534868609392,
0.000000000000000000,
-0.031827023036304102,
0.000000000000000000,
-0.027336628208641155,
0.000000000000000000,
-0.023625003856774591,
0.000000000000000000,
-0.020498780519188083,
0.000000000000000000,
-0.017826854793349920,
0.000000000000000000,
-0.015517212970554440,
0.000000000000000000,
-0.013503343224246872,
0.000000000000000000,
-0.011735907609641917,
0.000000000000000000,
-0.010177443901536392,
0.000000000000000000,
-0.008798886675905997,
0.000000000000000000,
-0.007577220484233372,
0.000000000000000000,
-0.006493859804516438,
0.000000000000000000,
-0.005533508538632429,
0.000000000000000000,
-0.004683343721596901,
0.000000000000000000,
-0.003932423233774751,
0.000000000000000000,
-0.003271251311125927,
0.000000000000000000,
-0.002691457154069645,
0.000000000000000000,
-0.002185555845922462,
0.000000000000000000,
-0.001746769975247667,
0.000000000000000000,
-0.001368896533613985,
0.000000000000000000,
-0.001046207887980644,
0.000000000000000000,
-0.000773378567767513,
0.000000000000000000};

253
examples/FineFreqShift_OA/hilbert251A.h
Unescape View File

@ -0,0 +1,253 @@
// Following is 251 term Hilbert FIR filter
float32_t hilbert251A[]={
0.0000003255,
0.0000000000,
0.0000030702,
0.0000000000,
0.0000089286,
0.0000000000,
0.0000183061,
0.0000000000,
0.0000316287,
0.0000000000,
0.0000493436,
0.0000000000,
0.0000719193,
0.0000000000,
0.0000998451,
0.0000000000,
0.0001336320,
0.0000000000,
0.0001738120,
0.0000000000,
0.0002209393,
0.0000000000,
0.0002755899,
0.0000000000,
0.0003383625,
0.0000000000,
0.0004098790,
0.0000000000,
0.0004907853,
0.0000000000,
0.0005817525,
0.0000000000,
0.0006834782,
0.0000000000,
0.0007966881,
0.0000000000,
0.0009221383,
0.0000000000,
0.0010606178,
0.0000000000,
0.0012129515,
0.0000000000,
0.0013800041,
0.0000000000,
0.0015626848,
0.0000000000,
0.0017619529,
0.0000000000,
0.0019788241,
0.0000000000,
0.0022143787,
0.0000000000,
0.0024697715,
0.0000000000,
0.0027462425,
0.0000000000,
0.0030451312,
0.0000000000,
0.0033678928,
0.0000000000,
0.0037161183,
0.0000000000,
0.0040915578,
0.0000000000,
0.0044961498,
0.0000000000,
0.0049320558,
0.0000000000,
0.0054017033,
0.0000000000,
0.0059078375,
0.0000000000,
0.0064535860,
0.0000000000,
0.0070425380,
0.0000000000,
0.0076788436,
0.0000000000,
0.0083673390,
0.0000000000,
0.0091137048,
0.0000000000,
0.0099246683,
0.0000000000,
0.0108082660,
0.0000000000,
0.0117741868,
0.0000000000,
0.0128342256,
0.0000000000,
0.0140028938,
0.0000000000,
0.0152982506,
0.0000000000,
0.0167430570,
0.0000000000,
0.0183664064,
0.0000000000,
0.0202060801,
0.0000000000,
0.0223120327,
0.0000000000,
0.0247516963,
0.0000000000,
0.0276183140,
0.0000000000,
0.0310445375,
0.0000000000,
0.0352256211,
0.0000000000,
0.0404611696,
0.0000000000,
0.0472354231,
0.0000000000,
0.0563851215,
0.0000000000,
0.0694911881,
0.0000000000,
0.0899418673,
0.0000000000,
0.1265473875,
0.0000000000,
0.2116132716,
0.0000000000,
0.6358933477,
0.0000000000,
-0.6358933478,
0.0000000000,
-0.2116132717,
0.0000000000,
-0.1265473876,
0.0000000000,
-0.0899418674,
0.0000000000,
-0.0694911882,
0.0000000000,
-0.0563851216,
0.0000000000,
-0.0472354232,
0.0000000000,
-0.0404611697,
0.0000000000,
-0.0352256212,
0.0000000000,
-0.0310445376,
0.0000000000,
-0.0276183141,
0.0000000000,
-0.0247516964,
0.0000000000,
-0.0223120328,
0.0000000000,
-0.0202060802,
0.0000000000,
-0.0183664065,
0.0000000000,
-0.0167430571,
0.0000000000,
-0.0152982507,
0.0000000000,
-0.0140028939,
0.0000000000,
-0.0128342257,
0.0000000000,
-0.0117741869,
0.0000000000,
-0.0108082661,
0.0000000000,
-0.0099246684,
0.0000000000,
-0.0091137049,
0.0000000000,
-0.0083673391,
0.0000000000,
-0.0076788437,
0.0000000000,
-0.0070425381,
0.0000000000,
-0.0064535861,
0.0000000000,
-0.0059078376,
0.0000000000,
-0.0054017034,
0.0000000000,
-0.0049320559,
0.0000000000,
-0.0044961499,
0.0000000000,
-0.0040915579,
0.0000000000,
-0.0037161184,
0.0000000000,
-0.0033678929,
0.0000000000,
-0.0030451313,
0.0000000000,
-0.0027462426,
0.0000000000,
-0.0024697716,
0.0000000000,
-0.0022143788,
0.0000000000,
-0.0019788242,
0.0000000000,
-0.0017619530,
0.0000000000,
-0.0015626849,
0.0000000000,
-0.0013800042,
0.0000000000,
-0.0012129516,
0.0000000000,
-0.0010606179,
0.0000000000,
-0.0009221384,
0.0000000000,
-0.0007966882,
0.0000000000,
-0.0006834783,
0.0000000000,
-0.0005817526,
0.0000000000,
-0.0004907854,
0.0000000000,
-0.0004098791,
0.0000000000,
-0.0003383626,
0.0000000000,
-0.0002755900,
0.0000000000,
-0.0002209394,
0.0000000000,
-0.0001738121,
0.0000000000,
-0.0001336321,
0.0000000000,
-0.0000998452,
0.0000000000,
-0.0000719194,
0.0000000000,
-0.0000493437,
0.0000000000,
-0.0000316288,
0.0000000000,
-0.0000183062,
0.0000000000,
-0.0000089287,
0.0000000000,
-0.0000030703,
0.0000000000,
-0.0000003256};

114
mathDSP_F32.cpp
Unescape View File

@ -0,0 +1,114 @@
#include "mathDSP_F32.h"
#include <math.h>
/* acos_f32(x) Bob Larkin 2020
* This acos(x) approximation is intended as being fast, resonably accurate, and
* with continuous function and derivative (slope) between -1 and 1 x value.
* It is the result of a "Chebychev-zero" fit to the true values, and is a 7th
* order polynomial for the full (-1.0, 1.0) range.
* Max error from -0.99 to 0.99 is < 0.018/Pi (1.0 deg)
* Error at -1 or +1 is 0.112/Pi (6.4 deg)
* For acos, speed and accuracy are in conflict near x = +/- 1, but that
* is not where communications phase detectors are normally used.
* Using T3.6 this function, by itself, measures as 0.18 uSec
*
* Thanks to Bob K3KHF for ideas on minimizing errors with acos().
* RSL 5 April 2020.
*/
float mathDSP_F32::acos_f32(float x) {
float w;
// These next two error checks use 0.056 uSec per call
if(x > 1.00000) return 0.0f;
if(x < -1.00000) return MF_PI;
w = x * x;
return 1.5707963268f+(x*((-0.97090f)+w*((-0.529008f)+w*(1.00279f-w*0.961446))));
}
/* *** Not currently used, but possible substitute for acosf(x) ***
* Apparently based on Handbook of Mathematical Functions
* M. Abramowitz and I.A. Stegun, Ed. Check before using.
* https://developer.download.nvidia.com/cg/acos.html
* Absolute error <= 6.7e-5, good, but not as good as acosf()
* T3.6 this measures 0.51 uSec (0.23 uSec from sqrtf() ),
* better than acosf(x) by a factor of 2.
*/
float mathDSP_F32::approxAcos(float x) {
if(x > 0.999999) return 0.0f;
if(x < -0.999999) return M_PI; // 3.14159265358979f;
float negate = float(x < 0);
x = fabsf(x);
float ret = -0.0187293f;
ret = ret * x;
ret = ret + 0.0742610f;
ret = ret * x;
ret = ret - 0.2121144f;
ret = ret * x;
ret = ret + 1.5707288f;
ret = ret * sqrtf(1.0f-x);
ret = ret - 2 * negate * ret;
return negate * MF_PI + ret;
}
/* Polynomial approximating arctangenet on iput range (-1, 1)
* giving result in a range of approximately (-pi/4, pi/4)
* Max error < 0.005 radians (or 0.29 degrees)
*
* Directly from www.dsprelated.com/showarticle/1052.php
* Thank you Nic Taylor---nice work.
*/
float mathDSP_F32::fastAtan2(float y, float x) {
if (x != 0.0f) {
if (fabsf(x) > fabsf(y)) {
const float z = y / x;
if (x > 0.0)
// atan2(y,x) = atan(y/x) if x > 0
return _Atan(z);
else if (y >= 0.0)
// atan2(y,x) = atan(y/x) + PI if x < 0, y >= 0
return _Atan(z) + M_PI;
else
// atan2(y,x) = atan(y/x) - PI if x < 0, y < 0
return _Atan(z) - M_PI;
}
else { // Use property atan(y/x) = PI/2-atan(x/y) if |y/x| > 1.
const float z = x / y;
if (y > 0.0)
// atan2(y,x) = PI/2 - atan(x/y) if |y/x| > 1, y > 0
return -_Atan(z) + M_PI_2;
else
// atan2(y,x) = -PI/2 - atan(x/y) if |y/x| > 1, y < 0
return -_Atan(z) - M_PI_2;
}
}
else {
if (y > 0.0f) // x = 0, y > 0
return M_PI_2;
else if (y < 0.0f) // x = 0, y < 0
return -M_PI_2;
}
return 0.0f; // x,y = 0. Undefined, stay finite.
}
/* float i0f(float x) Returns the modified Bessel function Io(x).
* Algorithm is based on Abromowitz and Stegun, Handbook of Mathematical
* Functions, and Press, et. al., Numerical Recepies in C.
* All in 32-bit floating point
*/
float mathDSP_F32::i0f(float x) {
float af, bf, cf;
if( (af=fabsf(x)) < 3.75f ) {
cf = x/3.75f;
cf = cf*cf;
bf=1.0f+cf*(3.515623f+cf*(3.089943f+cf*(1.20675f+cf*(0.265973f+
cf*(0.0360768f+cf*0.0045813f)))));
}
else {
cf = 3.75f/af;
bf=(expf(af)/sqrtf(af))*(0.3989423f+cf*(0.0132859f+cf*(0.0022532f+
cf*(-0.0015756f+cf*(0.0091628f+cf*(-0.0205771f+cf*(0.0263554f+
cf*(-0.0164763f+cf*0.0039238f))))))));
}
return bf;
}

50
mathDSP_F32.h
Unescape View File

@ -0,0 +1,50 @@
/*
mathDSP.h - Definitions and functions to support OpenAudio_ArduinoLibrary_F32
Created by Bob Larkin 15 April 2020.
*/
#ifndef mathDSP_F32_h
#define mathDSP_F32_h
#ifndef M_PI_2
#define M_PI_2 1.57079632679489661923
#endif
#ifndef M_PI
#define M_PI 3.14159265358979323846
#endif
#ifndef M_TWOPI
#define M_TWOPI 6.28318530717958647692
#endif
#ifndef MF_PI_2
#define MF_PI_2 1.5707963f
#endif
#ifndef MF_PI
#define MF_PI 3.14159265f
#endif
#ifndef MF_TWOPI
#define MF_TWOPI 6.2831853f
#endif
class mathDSP_F32
{
public:
float acos_f32(float x);
float approxAcos(float x);
float fastAtan2(float y, float x);
float i0f(float x);
private:
// Support for FastAtan2(x,y)
float _Atan(float z) {
const float n1 = 0.97239411f;
const float n2 = -0.19194795f;
return (n1 + n2 * z * z) * z;
}
};
#endif

6
readme.md
Unescape View File

@ -20,6 +20,12 @@ OpenAudio Library for Teensy
15-Moved Overlapped FFT AudioFormantShifter INO and related from Tympan to _OA Open Audio. Tested 3.6 and 4.0.
16-Moved AudioFrequencyShifter INO and related from Tympan to _OA Open Audio. Tested 3.6 and 4.0.
17-Working on SdFatWriter and related SdFat files. DO NOT USE.
18-Modified AudioEffectDelay for T4.0.
19-Moved in radio function AudioFilter90Deg_F32.
20-Moved in radio function RadioIQMixer_F32.
21-Added Example INO, FineFreqShift_OA.ino with Hilbert shifter and delay stereo.
22-Brought in support stuff mathDSP_F32 and sinTable512_F32.h.
**Purpose**: The purpose of this library is to build upon the [Teensy Audio Library](http://www.pjrc.com/teensy/td_libs_Audio.html) to enable new functionality for real-time audio processing.

98
sinTable512_f32.h
Unescape View File

@ -0,0 +1,98 @@
// This comes from the ARM Cortex M3, M4 sin(). Linear interpolation between points
// gives the 24-bit accuracy of float32_t
const float32_t sinTable512_f32[513] = {
0.00000000f, 0.01227154f, 0.02454123f, 0.03680722f, 0.04906767f, 0.06132074f,
0.07356456f, 0.08579731f, 0.09801714f, 0.11022221f, 0.12241068f, 0.13458071f,
0.14673047f, 0.15885814f, 0.17096189f, 0.18303989f, 0.19509032f, 0.20711138f,
0.21910124f, 0.23105811f, 0.24298018f, 0.25486566f, 0.26671276f, 0.27851969f,
0.29028468f, 0.30200595f, 0.31368174f, 0.32531029f, 0.33688985f, 0.34841868f,
0.35989504f, 0.37131719f, 0.38268343f, 0.39399204f, 0.40524131f, 0.41642956f,
0.42755509f, 0.43861624f, 0.44961133f, 0.46053871f, 0.47139674f, 0.48218377f,
0.49289819f, 0.50353838f, 0.51410274f, 0.52458968f, 0.53499762f, 0.54532499f,
0.55557023f, 0.56573181f, 0.57580819f, 0.58579786f, 0.59569930f, 0.60551104f,
0.61523159f, 0.62485949f, 0.63439328f, 0.64383154f, 0.65317284f, 0.66241578f,
0.67155895f, 0.68060100f, 0.68954054f, 0.69837625f, 0.70710678f, 0.71573083f,
0.72424708f, 0.73265427f, 0.74095113f, 0.74913639f, 0.75720885f, 0.76516727f,
0.77301045f, 0.78073723f, 0.78834643f, 0.79583690f, 0.80320753f, 0.81045720f,
0.81758481f, 0.82458930f, 0.83146961f, 0.83822471f, 0.84485357f, 0.85135519f,
0.85772861f, 0.86397286f, 0.87008699f, 0.87607009f, 0.88192126f, 0.88763962f,
0.89322430f, 0.89867447f, 0.90398929f, 0.90916798f, 0.91420976f, 0.91911385f,
0.92387953f, 0.92850608f, 0.93299280f, 0.93733901f, 0.94154407f, 0.94560733f,
0.94952818f, 0.95330604f, 0.95694034f, 0.96043052f, 0.96377607f, 0.96697647f,
0.97003125f, 0.97293995f, 0.97570213f, 0.97831737f, 0.98078528f, 0.98310549f,
0.98527764f, 0.98730142f, 0.98917651f, 0.99090264f, 0.99247953f, 0.99390697f,
0.99518473f, 0.99631261f, 0.99729046f, 0.99811811f, 0.99879546f, 0.99932238f,
0.99969882f, 0.99992470f, 1.00000000f, 0.99992470f, 0.99969882f, 0.99932238f,
0.99879546f, 0.99811811f, 0.99729046f, 0.99631261f, 0.99518473f, 0.99390697f,
0.99247953f, 0.99090264f, 0.98917651f, 0.98730142f, 0.98527764f, 0.98310549f,
0.98078528f, 0.97831737f, 0.97570213f, 0.97293995f, 0.97003125f, 0.96697647f,
0.96377607f, 0.96043052f, 0.95694034f, 0.95330604f, 0.94952818f, 0.94560733f,
0.94154407f, 0.93733901f, 0.93299280f, 0.92850608f, 0.92387953f, 0.91911385f,
0.91420976f, 0.90916798f, 0.90398929f, 0.89867447f, 0.89322430f, 0.88763962f,
0.88192126f, 0.87607009f, 0.87008699f, 0.86397286f, 0.85772861f, 0.85135519f,
0.84485357f, 0.83822471f, 0.83146961f, 0.82458930f, 0.81758481f, 0.81045720f,
0.80320753f, 0.79583690f, 0.78834643f, 0.78073723f, 0.77301045f, 0.76516727f,
0.75720885f, 0.74913639f, 0.74095113f, 0.73265427f, 0.72424708f, 0.71573083f,
0.70710678f, 0.69837625f, 0.68954054f, 0.68060100f, 0.67155895f, 0.66241578f,
0.65317284f, 0.64383154f, 0.63439328f, 0.62485949f, 0.61523159f, 0.60551104f,
0.59569930f, 0.58579786f, 0.57580819f, 0.56573181f, 0.55557023f, 0.54532499f,
0.53499762f, 0.52458968f, 0.51410274f, 0.50353838f, 0.49289819f, 0.48218377f,
0.47139674f, 0.46053871f, 0.44961133f, 0.43861624f, 0.42755509f, 0.41642956f,
0.40524131f, 0.39399204f, 0.38268343f, 0.37131719f, 0.35989504f, 0.34841868f,
0.33688985f, 0.32531029f, 0.31368174f, 0.30200595f, 0.29028468f, 0.27851969f,
0.26671276f, 0.25486566f, 0.24298018f, 0.23105811f, 0.21910124f, 0.20711138f,
0.19509032f, 0.18303989f, 0.17096189f, 0.15885814f, 0.14673047f, 0.13458071f,
0.12241068f, 0.11022221f, 0.09801714f, 0.08579731f, 0.07356456f, 0.06132074f,
0.04906767f, 0.03680722f, 0.02454123f, 0.01227154f, 0.00000000f, -0.01227154f,
-0.02454123f, -0.03680722f, -0.04906767f, -0.06132074f, -0.07356456f,
-0.08579731f, -0.09801714f, -0.11022221f, -0.12241068f, -0.13458071f,
-0.14673047f, -0.15885814f, -0.17096189f, -0.18303989f, -0.19509032f,
-0.20711138f, -0.21910124f, -0.23105811f, -0.24298018f, -0.25486566f,
-0.26671276f, -0.27851969f, -0.29028468f, -0.30200595f, -0.31368174f,
-0.32531029f, -0.33688985f, -0.34841868f, -0.35989504f, -0.37131719f,
-0.38268343f, -0.39399204f, -0.40524131f, -0.41642956f, -0.42755509f,
-0.43861624f, -0.44961133f, -0.46053871f, -0.47139674f, -0.48218377f,
-0.49289819f, -0.50353838f, -0.51410274f, -0.52458968f, -0.53499762f,
-0.54532499f, -0.55557023f, -0.56573181f, -0.57580819f, -0.58579786f,
-0.59569930f, -0.60551104f, -0.61523159f, -0.62485949f, -0.63439328f,
-0.64383154f, -0.65317284f, -0.66241578f, -0.67155895f, -0.68060100f,
-0.68954054f, -0.69837625f, -0.70710678f, -0.71573083f, -0.72424708f,
-0.73265427f, -0.74095113f, -0.74913639f, -0.75720885f, -0.76516727f,
-0.77301045f, -0.78073723f, -0.78834643f, -0.79583690f, -0.80320753f,
-0.81045720f, -0.81758481f, -0.82458930f, -0.83146961f, -0.83822471f,
-0.84485357f, -0.85135519f, -0.85772861f, -0.86397286f, -0.87008699f,
-0.87607009f, -0.88192126f, -0.88763962f, -0.89322430f, -0.89867447f,
-0.90398929f, -0.90916798f, -0.91420976f, -0.91911385f, -0.92387953f,
-0.92850608f, -0.93299280f, -0.93733901f, -0.94154407f, -0.94560733f,
-0.94952818f, -0.95330604f, -0.95694034f, -0.96043052f, -0.96377607f,
-0.96697647f, -0.97003125f, -0.97293995f, -0.97570213f, -0.97831737f,
-0.98078528f, -0.98310549f, -0.98527764f, -0.98730142f, -0.98917651f,
-0.99090264f, -0.99247953f, -0.99390697f, -0.99518473f, -0.99631261f,
-0.99729046f, -0.99811811f, -0.99879546f, -0.99932238f, -0.99969882f,
-0.99992470f, -1.00000000f, -0.99992470f, -0.99969882f, -0.99932238f,
-0.99879546f, -0.99811811f, -0.99729046f, -0.99631261f, -0.99518473f,
-0.99390697f, -0.99247953f, -0.99090264f, -0.98917651f, -0.98730142f,
-0.98527764f, -0.98310549f, -0.98078528f, -0.97831737f, -0.97570213f,
-0.97293995f, -0.97003125f, -0.96697647f, -0.96377607f, -0.96043052f,
-0.95694034f, -0.95330604f, -0.94952818f, -0.94560733f, -0.94154407f,
-0.93733901f, -0.93299280f, -0.92850608f, -0.92387953f, -0.91911385f,
-0.91420976f, -0.90916798f, -0.90398929f, -0.89867447f, -0.89322430f,
-0.88763962f, -0.88192126f, -0.87607009f, -0.87008699f, -0.86397286f,
-0.85772861f, -0.85135519f, -0.84485357f, -0.83822471f, -0.83146961f,
-0.82458930f, -0.81758481f, -0.81045720f, -0.80320753f, -0.79583690f,
-0.78834643f, -0.78073723f, -0.77301045f, -0.76516727f, -0.75720885f,
-0.74913639f, -0.74095113f, -0.73265427f, -0.72424708f, -0.71573083f,
-0.70710678f, -0.69837625f, -0.68954054f, -0.68060100f, -0.67155895f,
-0.66241578f, -0.65317284f, -0.64383154f, -0.63439328f, -0.62485949f,
-0.61523159f, -0.60551104f, -0.59569930f, -0.58579786f, -0.57580819f,
-0.56573181f, -0.55557023f, -0.54532499f, -0.53499762f, -0.52458968f,
-0.51410274f, -0.50353838f, -0.49289819f, -0.48218377f, -0.47139674f,
-0.46053871f, -0.44961133f, -0.43861624f, -0.42755509f, -0.41642956f,
-0.40524131f, -0.39399204f, -0.38268343f, -0.37131719f, -0.35989504f,
-0.34841868f, -0.33688985f, -0.32531029f, -0.31368174f, -0.30200595f,
-0.29028468f, -0.27851969f, -0.26671276f, -0.25486566f, -0.24298018f,
-0.23105811f, -0.21910124f, -0.20711138f, -0.19509032f, -0.18303989f,
-0.17096189f, -0.15885814f, -0.14673047f, -0.13458071f, -0.12241068f,
-0.11022221f, -0.09801714f, -0.08579731f, -0.07356456f, -0.06132074f,
-0.04906767f, -0.03680722f, -0.02454123f, -0.01227154f, -0.00000000f};
Write Preview
Loading…
Cancel
Save