def test_q0_equiv(self):
fir = np.asarray([
1.00000000e+00, -7.63387347e-01, -4.02004111e-01, -1.53885083e-01,
-2.76434316e-04, 7.91252937e-02, 1.03165832e-01, 8.83276154e-02,
4.92894661e-02
])
hz = (np.asarray([-1., -1., -1.]),
np.asarray([
0.99382681 + 0.01056265j, 0.98780284 + 0.j,
0.99382681 - 0.01056265j
]), 2.2820568419526305e-07)
gain1 = quantization_noise_gain((fir, np.hstack((1, np.zeros(8)))), hz)
q0 = q0_weighting(8, hz)
Q = la.toeplitz(q0)
fir_coeff = fir.reshape((1, 9))
gain2 = fir_coeff.dot(Q).dot(fir_coeff.T)
np.testing.assert_allclose(gain2, gain1)
def test_q0_butt_lp3(self):
# Generate filter.
# 3rd order lowpass filter
# Freq. passed to butterworth is normalized between 0 and 1
# where 1 is the Nyquist frequency
B = 400.
OSR = 256
fphi = B * OSR * 2
w0 = 2 * B / fphi
hz = signal.butter(3, w0, 'lowpass', output='zpk')
# Order
P = 12
# Compute q0 in two ways
ir = impulse_response(hz, db=80)
q0_ir = q0_from_filter_ir(P, ir)
q0_mr = q0_weighting(P, hz)
np.testing.assert_allclose(q0_ir, q0_mr, atol=1E-7, rtol=1E-5)
def test_q0_butt_bp8(self):
# Generate filter.
# 8th order bandpass filter
# Freq. passed to butterworth is normalized between 0 and 1
# where 1 is the Nyquist frequency
fsig = 1000.
B = 400.
OSR = 64
fphi = B * OSR * 2
w0 = 2 * fsig / fphi
B0 = 2 * B / fphi
w1 = (np.sqrt(B0**2 + 4 * w0**2) - B0) / 2
w2 = (np.sqrt(B0**2 + 4 * w0**2) + B0) / 2
hz = signal.butter(4, [w1, w2], 'bandpass', output='zpk')
# Order
P = 20
# Compute q0 in two ways
ir = impulse_response(hz, db=80)
q0_ir = q0_from_filter_ir(P, ir)
q0_mr = q0_weighting(P, hz)
np.testing.assert_allclose(q0_ir, q0_mr, atol=1E-7, rtol=1E-5)