dsp/lib/svf.py

from . import tau, unwarp

import numpy as np


def svf_core(w0, Q, m, shelfA=1, gain=1):
    # via:
    # http://nbviewer.ipython.org/urls/music-synthesizer-for-android.googlecode.com/git/lab/Second%20order%20sections%20in%20matrix%20form.ipynb
    # 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


def LP2S(A, Q):
    return (Q, [0, 0, 1], 1)


def BP2S(A, Q):
    return (Q, [0, 1, 0], 1)


def HP2S(A, Q):
    return (Q, [1, -1/Q, -1], 1)


# TODO: AP2S
# TODO: BP2aS
# TODO: BP2bS


def NO2S(A, Q):
    return (Q, [1, -1/Q, 0], 1)


def PE2S(A, Q):
    return (Q*A, [1, (A*A - 1)/A/Q, 0], 1)


def LS2S(A, Q):
    return (Q, [1, (A - 1)/Q, A*A - 1], 1/np.sqrt(A))


def HS2S(A, Q):
    return (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))

def gen_filters_svf(cascade, srate):
    return [
        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