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384 lines
8.5 KiB
384 lines
8.5 KiB
12 years ago
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import argparse
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import struct
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import numpy as np
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from math import *
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samplerate = 44100 * 1
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# generate a saw matching the parameters of "fun with sigmoids"
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def sawperiod():
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result = []
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f0 = 63. * 2 * pi / samplerate
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for i in range(samplerate / 63):
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y = 0
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x0 = i * f0
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for partial in range(1, 351):
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gain = 1.0 / partial
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if partial > 300:
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gain *= (351 - partial) * (1.0 / (351 - 300))
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y += gain * sin(partial * x0)
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result.append(y)
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return result
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def saw(n):
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return sawperiod() * (n / (samplerate / 63))
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def sinsweep(n):
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fmax = 22000 * pi * 2 / samplerate
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scale = fmax * .5 / n
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return [sin(i * i * scale) for i in range(n)]
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def sweep(n):
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n2 = n / 2
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lamin = log(20 * 2 * pi / samplerate)
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lamax = log(14000 * 2 * pi / samplerate)
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result = []
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slope = (lamax - lamin) / n2
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for i in range(n2):
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a = exp(lamin + slope * i)
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result.append(a)
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return result + result[-1::-1]
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# Based on code by mystran (Teemu Voipio)
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# See http://www.kvraudio.com/forum/viewtopic.php?t=349859
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def tanhXdx(x):
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a = x * x
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return ((a + 105.0)* a + 945.0) / ((15.0 * a + 420.0) * a + 945.0)
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def tpt_nl(xs, aas, k):
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z1 = 0
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s = [0] * 4
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r = k
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result = []
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for i in range(len(xs)):
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xin = xs[i]
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a = aas[i]
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f = tan(a * .5)
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ih = .5 * (xin + z1)
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z1 = xin
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t0 = tanhXdx(ih - r * s[3])
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t1 = tanhXdx(s[0])
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t2 = tanhXdx(s[1])
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t3 = tanhXdx(s[2])
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t4 = tanhXdx(s[3])
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g0 = 1 / (1 + f * t1)
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g1 = 1 / (1 + f * t2)
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g2 = 1 / (1 + f * t3)
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g3 = 1 / (1 + f * t4)
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f3 = f * t3 * g3
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f2 = f * t2 * g2 * f3
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f1 = f * t1 * g1 * f2
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f0 = f * t0 * g0 * f1
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y3 = (g3*s[3] + f3*g2*s[2] + f2*g1*s[1] + f1*g0*s[0] + f0*xin)/(1 + r * f0)
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xx = t0 * (xin - r * y3)
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y0 = t1 * g0 * (s[0] + f * xx)
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y1 = t2 * g1 * (s[1] + f * y0)
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y2 = t3 * g2 * (s[2] + f * y1)
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s[0] += 2 * f * (xx - y0)
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s[1] += 2 * f * (y0 - y1)
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s[2] += 2 * f * (y1 - y2)
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s[3] += 2 * f * (y2 - t4 * y3)
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result.append(y3)
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return result
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def antti_nl(xs, aas, k, tanhfunc = tanh):
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y0 = 0
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y1 = 0
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y2 = 0
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y3 = 0
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ty0 = 0
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ty1 = 0
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ty2 = 0
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ty3 = 0
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yy = 0
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result = []
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for i in range(len(xs)):
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xin = xs[i]
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a = aas[i]
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tx = tanhfunc(xin - k * (y3 + yy) * .5)
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y0 += a * (tx - ty0)
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yy = y3
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ty0 = tanhfunc(y0)
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y1 += a * (ty0 - ty1)
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ty1 = tanhfunc(y1)
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y2 += a * (ty1 - ty2)
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ty2 = tanhfunc(y2)
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y3 += a * (ty2 - ty3)
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ty3 = tanhfunc(y3)
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x = 0
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result.append(y3)
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return result
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def expm_series(A, n = 16):
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B = np.identity(len(A))
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C = np.identity(len(A))
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for i in range(1, n):
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C = A * C / i
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B = B + C
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return B
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def expm_hyb(A, n1 = 8, n2 = 8):
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A = expm_series(A / (1 << n2), n1)
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for i in range(n2):
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A = A * A
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return A
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def mkjacobian(a, k):
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return np.matrix([[0, 0, 0, 0, 0],
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[a, -a, 0, 0, -k * a],
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[0, a, -a, 0, 0],
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[0, 0, a, -a, 0],
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[0, 0, 0, a, -a]])
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def expm_nl(xs, aas, k, tanhfunc = tanh, every = 64):
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kk = k
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y = np.zeros([4, 1])
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ty = y
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result = []
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for i in range(len(xs)):
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if i % every == 0:
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a = aas[i]
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A = expm_hyb(mkjacobian(a, k))
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B = A[1:, 0]
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A = A[1:, 1:]
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AM = A - np.identity(4)
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for j in range(4):
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AM[j, 3] += B[j, 0] * kk
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x = xs[i]
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tx = tanhfunc(x - kk * y[3, 0])
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y += B * tx + AM * ty
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ty = np.matrix([tanhfunc(x[0]) for x in y]).T
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result.append(y[3, 0])
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return result
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def invsqrt(x):
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return x / sqrt(1 + x ** 2)
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def clip(x):
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return min(1, max(-1, x))
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fir = map(float, '''-0.00000152158394097619
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-0.00000932875737718674
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-0.00001008290833020705
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0.00000728628960094510
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0.00002272556429291851
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-0.00000017886444625648
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-0.00004038828866646377
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-0.00002127235603321839
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0.00005623314602326363
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0.00006233931357689778
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-0.00005884569707596701
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-0.00012410666372671377
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0.00003231781361429016
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0.00019973378481126099
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0.00004097428652472217
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-0.00027125558280978066
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-0.00017513777576291543
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0.00030833229435342778
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0.00037363561338823163
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-0.00027028256701905416
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-0.00062153272838533420
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0.00011242294792251808
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0.00087909017443692499
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0.00020309303892565388
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-0.00107928469499717137
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-0.00069305675670084180
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0.00113148992142813524
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0.00133794323705832747
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-0.00093286682198106608
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-0.00206892788224323455
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0.00038777937772768273
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0.00276141532345176117
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0.00056670689248167661
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-0.00323852878331680298
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-0.00193259906597622396
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0.00328731491441583683
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0.00362542589345449945
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-0.00268785554870503091
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-0.00545702740033716938
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0.00125317559909794512
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0.00713205061850966104
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0.00112492149537589880
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-0.00826148096867550946
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-0.00443085208574918715
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0.00839336065985300112
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0.00848839486761648020
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-0.00705662837862476577
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-0.01293781936476604867
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0.00380913247729417143
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0.01722862947876550518
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0.00172513205576642695
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-0.02062091118580804822
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-0.00985374287540894019
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0.02217056516274141381
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0.02089533076058044253
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-0.02062760756367006815
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-0.03546365160613443313
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0.01401630243169032369
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0.05541063386809867708
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0.00212045427486363437
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-0.08794052708207862612
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-0.04526389505656687462
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0.18221762668014460096
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0.41075960732889965632
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0.41075960732889965632
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0.18221762668014460096
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-0.04526389505656687462
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-0.08794052708207862612
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0.00212045427486363437
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0.05541063386809867708
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0.01401630243169032369
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-0.03546365160613443313
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-0.02062760756367006815
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0.02089533076058044253
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0.02217056516274141381
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-0.00985374287540894019
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-0.02062091118580804822
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0.00172513205576642695
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0.01722862947876550518
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0.00380913247729417143
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-0.01293781936476604867
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-0.00705662837862476577
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0.00848839486761648020
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0.00839336065985300112
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-0.00443085208574918715
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-0.00826148096867550946
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0.00112492149537589880
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0.00713205061850966104
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0.00125317559909794512
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-0.00545702740033716938
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-0.00268785554870503091
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0.00362542589345449945
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0.00328731491441583683
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-0.00193259906597622396
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-0.00323852878331680298
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0.00056670689248167661
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0.00276141532345176117
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0.00038777937772768273
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-0.00206892788224323455
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-0.00093286682198106608
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0.00133794323705832747
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0.00113148992142813524
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-0.00069305675670084180
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-0.00107928469499717137
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0.00020309303892565388
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0.00087909017443692499
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0.00011242294792251808
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-0.00062153272838533420
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-0.00027028256701905416
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0.00037363561338823163
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0.00030833229435342778
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-0.00017513777576291543
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-0.00027125558280978066
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0.00004097428652472217
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0.00019973378481126099
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0.00003231781361429016
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-0.00012410666372671377
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-0.00005884569707596701
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0.00006233931357689778
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0.00005623314602326363
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-0.00002127235603321839
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-0.00004038828866646377
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-0.00000017886444625648
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0.00002272556429291851
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0.00000728628960094510
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-0.00001008290833020705
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-0.00000932875737718674
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-0.00000152158394097619
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'''.split())
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fir_n = len(fir)
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# would probably be faster to use numpy.convolve and slice, but oh well
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def downsample(data):
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result = []
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buf = [0] * fir_n
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i = 0
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for x in data:
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buf[i] = x
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i = (i + 1) & (fir_n - 1)
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if (i & 1) == 0:
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y = 0
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for j in range(len(fir)):
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y += fir[j] * buf[(i + j) & (fir_n - 1)]
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result.append(y)
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return result
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def wavwrite(seq, fn, sr = 44100):
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f = file(fn, 'wb')
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n_samples = len(seq)
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f.write(struct.pack('<4sI4s4sIHHIIHH4sI',
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'RIFF',
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36 + 2 * n_samples,
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'WAVE',
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'fmt ',
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16,
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1, 1,
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sr,
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2 * sr,
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2, 16,
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'data',
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2 * n_samples))
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for x in seq:
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f.write(struct.pack('<h', min(32767, max(-32767, int(16384 * x)))))
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def main():
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parser = argparse.ArgumentParser()
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parser.add_argument("--oversample", help="oversample factor")
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parser.add_argument("--signal", help="saw or sinsweep")
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parser.add_argument("--k", help="resonance, 4 = oscillate")
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parser.add_argument("--filter", help="tpt, antti, or expm")
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parser.add_argument("--tanhfunc", help="tanh or invsqrt")
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parser.add_argument("--cutoff")
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parser.add_argument("--gain", help="gain in dB")
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parser.add_argument("--ogain", help="outputgain in dB")
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parser.add_argument("--out", help="output wav file")
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args = parser.parse_args()
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oversample = 1
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if args.oversample:
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oversample = int(args.oversample)
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k = 0
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if args.k:
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k = float(args.k)
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signal = 'saw'
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|
if args.signal:
|
||
|
|
signal = args.signal
|
||
|
|
global samplerate
|
||
|
|
samplerate *= oversample
|
||
|
|
n = 6 * samplerate
|
||
|
|
if signal == 'saw':
|
||
|
|
input = saw(n)
|
||
|
|
aas = sweep(n)
|
||
|
|
elif signal == 'sinsweep':
|
||
|
|
input = sinsweep(n)
|
||
|
|
aas = [1000./samplerate * 2 * pi] * n
|
||
|
|
gain = 1
|
||
|
|
if args.gain:
|
||
|
|
gain = 10 ** (float(args.gain)/20)
|
||
|
|
input = [y * gain for y in input]
|
||
|
|
tanhfunc = tanh
|
||
|
|
if args.tanhfunc == 'invsqrt':
|
||
|
|
tanhfunc = invsqrt
|
||
|
|
if args.filter == 'tpt':
|
||
|
|
result = tpt_nl(input, aas, k)
|
||
|
|
elif args.filter == 'antti':
|
||
|
|
result = antti_nl(input, aas, k, tanhfunc = tanhfunc)
|
||
|
|
else:
|
||
|
|
result = expm_nl(input, aas, k, tanhfunc = tanhfunc)
|
||
|
|
while oversample > 1:
|
||
|
|
result = downsample(result)
|
||
|
|
oversample /= 2
|
||
|
|
ogain = 1
|
||
|
|
if args.ogain:
|
||
|
|
ogain = 10 ** (float(args.ogain)/20)
|
||
|
|
if args.out:
|
||
|
|
wavwrite(result, args.out)
|
||
|
|
|
||
|
|
main()
|