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@merryhime
Created June 3, 2019 09:51
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import math
import numpy
import matplotlib.pyplot as plt
def IdealH(f):
T = 1. / 441000. # we use the tenfold sampling frequency
OmegaU = 1. / 15e-6
OmegaL = 15. / 50. * OmegaU
# Calculate filter coefficients
V0 = OmegaL / OmegaU
H0 = V0 - 1.
B = V0 * numpy.tan(OmegaU * T / 2.)
A1 = (B - 1.) / (B + 1.)
B0 = (1. + (1. - A1) * H0 / 2.)
B1 = (A1 + (A1 - 1.) * H0 / 2.)
# helper variables
D = B1 / B0
O = 2 * math.pi * T
# Ideal transfer function
return B0*numpy.sqrt((1 + 2*numpy.cos(f*O)*D + D*D)/(1 + 2*numpy.cos(f*O)*A1 + A1*A1))
def plot(a0, a1, a2, b1, b2):
sampF = 44100.
o = 2 * math.pi * (1. / sampF)
f = numpy.arange(0, sampF / 2, sampF / 1000)
#
H = numpy.sqrt((a0*a0 + a1*a1 + a2*a2 + 2.*(a0*a1 + a1*a2)*numpy.cos(f*o) + 2.*(a0*a2)*numpy.cos(2.*f*o)) / (1. + b1*b1 + b2*b2 + 2.*(b1 + b1*b2)*numpy.cos(f*o) + 2.*b2*numpy.cos(2.*f*o)))
IH = IdealH(f)
#
H = -20. * numpy.log10(H)
IH = -20. * numpy.log10(IH)
#
plt.semilogx(f, H, 'r--')
plt.semilogx(f, IH, 'g--')
plt.show()
def foo(gain, cutoffFrequency):
samplingFrequency = 44100.
#
v = math.pow(10., abs(gain) / 20.0)
k = math.tan(math.pi * cutoffFrequency / samplingFrequency)
n = 0.0
#
if gain >= 0:
n = 1. / (1. + math.sqrt(2.) * k + k * k)
a0 = (v + math.sqrt(2. * v) * k + k * k) * n
a1 = 2 * (k * k - v) * n
a2 = (v - math.sqrt(2. * v) * k + k * k) * n
b1 = 2 * (k * k - 1) * n
b2 = (1 - math.sqrt(2.) * k + k * k) * n
else:
n = 1. / (v + math.sqrt(2 * v) * k + k * k)
a0 = (1 + math.sqrt(2) * k + k * k) * n
a1 = 2 * (k * k - 1) * n
a2 = (1 - math.sqrt(2) * k + k * k) * n
b1 = 2 * (k * k - v) * n
b2 = (v - math.sqrt(2 * v) * k + k * k) * n
#
plot(a0, a1, a2, b1, b2)
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