71 lines
2.2 KiB
Python
71 lines
2.2 KiB
Python
|
from . import tau, unwarp
|
||
|
|
|
||
|
|
import numpy as np
|
||
|
|
|
||
|
|
# via http://nbviewer.ipython.org/urls/music-synthesizer-for-android.googlecode.com/git/lab/Second%20order%20sections%20in%20matrix%20form.ipynb
|
||
|
|
def svf_core(w0, Q, m, shelfA=1, gain=1):
|
||
|
|
# TODO: implement constant gain parameter
|
||
|
|
g = unwarp(w0)*shelfA
|
||
|
|
a1 = 1/(1 + g*(g + 1/Q))
|
||
|
|
a2 = g*a1
|
||
|
|
a3 = g*a2
|
||
|
|
A = np.array([[2*a1 - 1, -2*a2], [2*a2, 1 - 2*a3]])
|
||
|
|
B = np.array([2*a2, 2*a3])
|
||
|
|
v0 = np.array([1, 0, 0])
|
||
|
|
v1 = np.array([a2, a1, -a2])
|
||
|
|
v2 = np.array([a3, a2, 1 - a3])
|
||
|
|
C = v0*m[0] + v1*m[1] + v2*m[2]
|
||
|
|
return A, B, C
|
||
|
|
|
||
|
|
LP2S = lambda A, Q: (Q, [0, 0, 1], 1)
|
||
|
|
BP2S = lambda A, Q: (Q, [0, 1, 0], 1)
|
||
|
|
HP2S = lambda A, Q: (Q, [1, -1/Q, -1], 1)
|
||
|
|
#AP2S = lambda A, Q:
|
||
|
|
#BP2aS = lambda A, Q:
|
||
|
|
#BP2bS = lambda A, Q:
|
||
|
|
NO2S = lambda A, Q: (Q, [1, -1/Q, 0], 1)
|
||
|
|
PE2S = lambda A, Q: (Q*A, [1, (A*A - 1)/A/Q, 0], 1)
|
||
|
|
LS2S = lambda A, Q: (Q, [1, (A - 1)/Q, A*A - 1], 1/np.sqrt(A))
|
||
|
|
HS2S = lambda A, Q: (Q, [A*A, (1 - A)*A/Q, 1 - A*A], np.sqrt(A))
|
||
|
|
|
||
|
|
# actual peaking filter (not a bell?)
|
||
|
|
#PE2S = lambda A, Q: ([1, -1/Q, -2], 1)
|
||
|
|
# original uncompensated
|
||
|
|
#PE2S = lambda A, Q: (Q, [1, (A*A - 1)/Q, 0], 1)
|
||
|
|
#LS2S = lambda A, Q: (Q, [1, (A - 1)/Q, A*A - 1], 1/np.sqrt(A))
|
||
|
|
#HS2S = lambda A, Q: (Q, [A*A, (A - A*A)/Q, 1 - A*A], 1/np.sqrt(A))
|
||
|
|
|
||
|
|
gen_filters_svf = lambda cascade, srate: [
|
||
|
|
svf_core(tau*f[0]/srate, *f[1], gain=10**(f[2]/20)) for f in cascade
|
||
|
|
]
|
||
|
|
|
||
|
|
def svf_run(svf, xs):
|
||
|
|
A, B, C = svf
|
||
|
|
result = []
|
||
|
|
y = np.zeros(2) # filter memory
|
||
|
|
for x in xs:
|
||
|
|
result.append(np.dot(C, np.concatenate([[x], y])))
|
||
|
|
y = B*x + np.dot(A, y)
|
||
|
|
return np.array(result)
|
||
|
|
|
||
|
|
def svf_mat(svf):
|
||
|
|
A, B, C = svf
|
||
|
|
AA = np.dot(A, A)
|
||
|
|
AB = np.dot(A, B)
|
||
|
|
CA = np.dot(C[1:], A)
|
||
|
|
cb = np.dot(C[1:], B)
|
||
|
|
return np.array([[ C[0], 0, C[1], C[2]],
|
||
|
|
[ cb, C[0], CA[0], CA[1]],
|
||
|
|
[AB[0], B[0], AA[0][0], AA[0][1]],
|
||
|
|
[AB[1], B[1], AA[1][0], AA[1][1]]])
|
||
|
|
|
||
|
|
def svf_run4(mat, xs):
|
||
|
|
assert(len(xs) % 2 == 0)
|
||
|
|
out = np.zeros(len(xs))
|
||
|
|
y = np.zeros(4) # filter memory
|
||
|
|
for i in range(0, len(xs), 2):
|
||
|
|
y[0:2] = xs[i:i+2]
|
||
|
|
y = np.dot(mat, y)
|
||
|
|
out[i:i+2] = y[0:2]
|
||
|
|
return out
|