51 lines
1.4 KiB
Python
51 lines
1.4 KiB
Python
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#based on https://github.com/gnuradio/gnuradio/blob/master/gr-analog/python/analog/fm_emph.py
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import math
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import cmath
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import numpy as np
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import scipy.signal as signal
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import pylab as pl
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tau = 750e-6
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fs = 8000
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fh = 2700
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# Digital corner frequencies
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w_cl = 1.0 / tau
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w_ch = 2.0 * math.pi * fh
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# Prewarped analog corner frequencies
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w_cla = 2.0 * fs * math.tan(w_cl / (2.0 * fs))
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w_cha = 2.0 * fs * math.tan(w_ch / (2.0 * fs))
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# Resulting digital pole, zero, and gain term from the bilinear
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# transformation of H(s) = (s + w_cla) / (s + w_cha) to
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# H(z) = b0 (1 - z1 z^-1)/(1 - p1 z^-1)
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kl = -w_cla / (2.0 * fs)
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kh = -w_cha / (2.0 * fs)
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z1 = (1.0 + kl) / (1.0 - kl)
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p1 = (1.0 + kh) / (1.0 - kh)
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b0 = (1.0 - kl) / (1.0 - kh)
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# Since H(s = infinity) = 1.0, then H(z = -1) = 1.0 and
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# this filter has 0 dB gain at fs/2.0.
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# That isn't what users are going to expect, so adjust with a
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# gain, g, so that H(z = 1) = 1.0 for 0 dB gain at DC.
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w_0dB = 2.0 * math.pi * 0.0
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g = abs(1.0 - p1 * cmath.rect(1.0, -w_0dB)) \
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/ (b0 * abs(1.0 - z1 * cmath.rect(1.0, -w_0dB)))
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btaps = [ g * b0 * 1.0, g * b0 * -z1, 0]
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ataps = [ 1.0, -p1, 0]
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taps = np.concatenate((btaps, ataps), axis=0)
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print("Taps")
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print(*taps, "", sep=",", end="\n")
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f,h = signal.freqz(btaps,ataps, fs=fs)
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pl.plot(f, 20*np.log10(np.abs(h)))
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pl.xlabel('frequency/Hz')
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pl.ylabel('gain/dB')
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pl.ylim(top=30,bottom=0)
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pl.xlim(left=0, right=fh*2.5)
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pl.show()
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