88 lines
2.2 KiB
Python
88 lines
2.2 KiB
Python
import numpy as np
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def LPB(n):
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# crap ripped from https://github.com/vinniefalco/DSPFilters/blob/master/shared/DSPFilters/source
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"""n-th degree butterworth low-pass filter cascade
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-3 dB at center frequency."""
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series = []
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pi2 = np.pi/2
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pairs = int(n/2)
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for i in range(pairs):
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# magnitude = 1
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theta = pi2*(1 + (2*i + 1)/n)
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real = np.cos(theta)
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imag = np.sin(theta)
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num = (0, 0, 1)
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den = (1, -2*real, real*real + imag*imag)
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series += [(num, den)]
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if n % 2:
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num = (0, 1)
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den = (1, 1)
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series += [(num, den)]
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return series
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def LPC(n, ripple, type=1):
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# crap ripped from https://github.com/vinniefalco/DSPFilters/blob/master/shared/DSPFilters/source
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# FIXME: type 2 has wrong center frequency?
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"""n-th degree chebyshev low-pass filter cascade
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0 dB at center frequency for type 1.
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-ripple dB at center frequency for type 2.
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when ripple=0 and type=1, acts as butterworth."""
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series = []
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ripple = np.abs(ripple)
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lin = np.exp(ripple*0.1*np.log(10))
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if ripple != 0:
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if type == 2:
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eps = np.sqrt(1/(lin - 1))
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else:
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eps = np.sqrt(lin - 1)
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v0 = np.arcsinh(1/eps)/n
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else:
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if type == 2:
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v0 = 0 # allpass?
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else:
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v0 = 1 # butterworth
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sinh_v0 = -np.sinh(v0)
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cosh_v0 = np.cosh(v0)
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fn = np.pi/(2*n)
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pairs = int(n/2)
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for i in range(pairs):
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k = 2*i + 1
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theta = (k - n)*fn
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real = sinh_v0*np.cos(theta)
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imag = cosh_v0*np.sin(theta)
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if type == 2:
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d2 = real*real + imag*imag
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im = 1/np.cos(k*fn)
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real = real/d2
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imag = imag/d2
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num = (1, 0, im*im)
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else:
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num = (0, 0, 1)
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den = (1, -2*real, real*real + imag*imag)
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# normalize such that 0 Hz is 0 dB
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den = np.array(den)
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gain = den[2]/num[2]
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den /= gain
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series += [(num, den)]
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if n % 2:
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real = sinh_v0
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if type == 2:
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real = 1/real
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num = (0, 1)
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den = (1/-real, 1)
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series += [(num, den)]
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return series
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