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