def test_logsmooth(self):
"""Test function for logsmooth()"""
f0 = 1./8
OSR = 64
order = 8
N = 8192
H = synthesizeNTF(order, OSR, 1, 1.5, f0)
# fB = int(np.ceil(N/(2. * OSR)))
quadrature = False
M = 1
f1, f2 = ds_f1f2(OSR, f0, quadrature)
Amp = undbv(-3)
f = .3
fin = np.round(((1 - f)/2*f1 + (f + 1)/2 * f2) * N)
t = np.arange(0, N).reshape((1, -1))
u = Amp * M * np.cos((2*np.pi/N)*fin*t)
v, _, _, _ = simulateDSM(u, H, M + 1)
window = ds_hann(N)
# NBW = 1.5/N
spec0 = fft(v * window) / (M*N/4)
### -1 is really important THIS IS NOT MATLAB!!
fl, pl = logsmooth(spec0, fin - 1)
fname = pkg_resources.resource_filename(__name__,
"test_data/test_logsmooth.mat")
data = scipy.io.loadmat(fname)
self.assertTrue(np.allclose(fl, data['fl'], atol=1e-8, rtol=1e-5))
self.assertTrue(np.allclose(pl, data['pl'], atol=1e-8, rtol=1e-5))
def test_logsmooth(self):
"""Test function for logsmooth()"""
f0 = 1. / 8
OSR = 64
order = 8
N = 8192
H = synthesizeNTF(order, OSR, 1, 1.5, f0)
# fB = int(np.ceil(N/(2. * OSR)))
quadrature = False
M = 1
f1, f2 = ds_f1f2(OSR, f0, quadrature)
Amp = undbv(-3)
f = .3
fin = np.round(((1 - f) / 2 * f1 + (f + 1) / 2 * f2) * N)
t = np.arange(0, N).reshape((1, -1))
u = Amp * M * np.cos((2 * np.pi / N) * fin * t)
v, _, _, _ = simulateDSM(u, H, M + 1)
window = ds_hann(N)
# NBW = 1.5/N
spec0 = fft(v * window) / (M * N / 4)
### -1 is really important THIS IS NOT MATLAB!!
fl, pl = logsmooth(spec0, fin - 1)
fname = pkg_resources.resource_filename(
__name__, "test_data/test_logsmooth.mat")
data = scipy.io.loadmat(fname)
self.assertTrue(np.allclose(fl, data['fl'], atol=1e-8, rtol=1e-5))
self.assertTrue(np.allclose(pl, data['pl'], atol=1e-8, rtol=1e-5))
def test_plotSpectrum(self):
"""Test function for plotSpectrum()"""
f0 = 0
osr = 32
quadrature = False
Hinf = 1.5
order = 3
ntf = ds.synthesizeNTF(order, osr, 0, Hinf, f0)
f1, f2 = ds.ds_f1f2(osr, f0, quadrature)
delta = 2
Amp = ds.undbv(-3)
f = 0.3
N = 2**12
f1_bin = np.round(f1*N)
f2_bin = np.round(f2*N)
fin = np.round(((1 - f)/2*f1 + (f + 1)/2*f2) * N)
t = np.arange(0, N)
u = Amp*np.cos((2*np.pi/N)*fin*t)
v, xn, xmax, y = ds.simulateDSM(u, ntf, 2)
window = ds.ds_hann(N)
NBW = 1.5/N
spec0 = fft(v * window)/(N/4)
freq = np.linspace(0, 0.5, N/2 + 1)
# plotting
plt.subplot(211)
plt.plot(freq, ds.dbv(spec0[:N/2 + 1]), 'c', linewidth=1, label='$S$')
plt.hold(True)
spec_smoothed = ds.circ_smooth(np.abs(spec0)**2., 16)
plt.plot(freq, ds.dbp(spec_smoothed[:N/2 + 1]), 'b--', linewidth=2,
label='$\\mathrm{circ\\_smooth}(S)$')
ds.plotSpectrum(spec0, fin, 'r', linewidth=2,
label='$\\mathrm{plotSpectrum}(S)$')
Snn = np.abs(ds.evalTF(ntf, np.exp(2j*np.pi*freq)))**2 * 2/12*(delta)**2
plt.plot(freq, ds.dbp(Snn*NBW), 'm', linewidth=1.5,
label='$\mathrm{from\\ NTF}$')
plt.text(0.5, -3, 'NBW = %.1e ' % NBW, horizontalalignment='right',
verticalalignment='top')
ds.figureMagic((0, 0.5), None, None, (-140, 0), 20, None)
plt.ylabel('Spectrum [dB]')
ax = plt.gca()
ax.set_title('Smoothing and plotting for LOG and LIN axes')
plt.legend(loc=4)
plt.subplot(212)
plt.plot(freq, ds.dbv(spec0[:N/2 + 1]), 'c', linewidth=1, label='$S$')
plt.hold(True)
ds.plotSpectrum(spec0, fin, '--r', linewidth=2,
label='$\\mathrm{plotSpectrum}(S)$')
plt.plot(freq, ds.dbp(spec_smoothed[:N/2 + 1]), 'b', linewidth=2,
label='$\\mathrm{circ\\_smooth}(S)$')
plt.plot(freq, ds.dbp(Snn*NBW), 'm', linewidth=1.5,
label='$\mathrm{from\\ NTF}$')
plt.text(0.5, -3, 'NBW = %.1e ' % NBW, horizontalalignment='right',
verticalalignment='top')
ds.figureMagic((0, 0.5), None, None, (-140, 0), 20, None)
ax = plt.gca()
ax.set_xscale('linear')
plt.ylabel('Spectrum [dB]')
plt.xlabel('Normalized frequency ($f_s \\rightarrow 1$)')
plt.legend(loc=4)
def testMultipleQ2(self):
"""Test function for DS simulation with nq>1 2/2"""
# filtering and simulation
filtM1 = [0., 0., 0., 2., -1.]
filtM2 = [1., -2., 1.]
ntf_eq = zpk_multiply(self.ntfs[1, 1], self.ntfs[1, 1])
M = self.nlev[0] - 1
osr = 64
f0 = 0.
f1, f2 = ds.ds_f1f2(OSR=64, f0=0., complex_flag=False)
delta = 2
Amp = ds.undbv(-3) # Test tone amplitude, relative to full-scale.
f = 0.3 # will be adjusted to a bin
N = 2**12
f1_bin = int(np.round(f1 * N))
f2_bin = int(np.round(f2 * N))
fin = np.round(((1 - f) / 2 * f1 + (f + 1) / 2 * f2) * N)
# input sine
t = np.arange(0, N).reshape((1, -1))
u = Amp * M * np.cos((2 * np.pi / N) * fin * t)
vx, _, xmax, y = ds.simulateDSM(u, self.ABCD, nlev=self.nlev)
# separate output #1 and output #2
v1 = vx[0, :]
v2 = vx[1, :]
# filter and combine
vf = lfilter(filtM1, [1.], v1) + lfilter(filtM2, [1.], v2)
# compute the spectra
window = ds.ds_hann(N)
NBW = 1.5 / N
spec0 = np.fft.fft(vf * window) / (M * N / 2) / ds.undbv(-6)
spec1 = np.fft.fft(v1 * window) / (M * N / 2) / ds.undbv(-6)
spec2 = np.fft.fft(v1 * window) / (M * N / 2) / ds.undbv(-6)
freq = np.linspace(0, 0.5, N // 2 + 1)
# smooth, calculate the theorethical response and the SNR for VF
spec0_smoothed = ds.circ_smooth(np.abs(spec0)**2., 16)
Snn0 = np.abs(ds.evalTF(ntf_eq, np.exp(
2j * np.pi * freq)))**2 * 2 / 12 * (delta / M)**2
snr0 = ds.calculateSNR(spec0[f1_bin:f2_bin + 1], fin - f1_bin)
# smooth, calculate the theorethical response and the SNR for V1
spec1_smoothed = ds.circ_smooth(np.abs(spec1)**2., 16)
Snn1 = np.abs(ds.evalTF(self.ntfs[0, 0], np.exp(
2j * np.pi * freq)))**2 * 2 / 12 * (delta / M)**2
snr1 = ds.calculateSNR(spec1[f1_bin:f2_bin + 1], fin - f1_bin)
assert snr0 > 40
assert snr1 > 40
assert snr0 - snr1 > 40
def testMultipleQ2(self):
"""Test function for DS simulation with nq>1 2/2"""
# filtering and simulation
filtM1 = [0., 0., 0., 2., -1.]
filtM2 = [1., -2., 1.]
ntf_eq = zpk_multiply(self.ntfs[1, 1], self.ntfs[1, 1])
M = self.nlev[0] - 1
osr = 64
f0 = 0.
f1, f2 = ds.ds_f1f2(OSR=64, f0=0., complex_flag=False)
delta = 2
Amp = ds.undbv(-3) # Test tone amplitude, relative to full-scale.
f = 0.3 # will be adjusted to a bin
N = 2**12
f1_bin = np.round(f1*N)
f2_bin = np.round(f2*N)
fin = np.round(((1 - f)/2*f1 + (f + 1)/2*f2) * N)
# input sine
t = np.arange(0, N).reshape((1, -1))
u = Amp*M*np.cos((2*np.pi/N)*fin*t)
vx, _, xmax, y = ds.simulateDSM(u, self.ABCD, nlev=self.nlev)
# separate output #1 and output #2
v1 = vx[0, :]
v2 = vx[1, :]
# filter and combine
vf = lfilter(filtM1, [1.], v1) + lfilter(filtM2, [1.], v2)
# compute the spectra
window = ds.ds_hann(N)
NBW = 1.5/N
spec0 = np.fft.fft(vf*window)/(M*N/2)/ds.undbv(-6)
spec1 = np.fft.fft(v1*window)/(M*N/2)/ds.undbv(-6)
spec2 = np.fft.fft(v1*window)/(M*N/2)/ds.undbv(-6)
freq = np.linspace(0, 0.5, N/2 + 1)
# smooth, calculate the theorethical response and the SNR for VF
spec0_smoothed = ds.circ_smooth(np.abs(spec0)**2., 16)
Snn0 = np.abs(ds.evalTF(ntf_eq, np.exp(2j*np.pi*freq)))**2 * 2/12*(delta/M)**2
snr0 = ds.calculateSNR(spec0[f1_bin:f2_bin + 1], fin - f1_bin)
# smooth, calculate the theorethical response and the SNR for V1
spec1_smoothed = ds.circ_smooth(np.abs(spec1)**2., 16)
Snn1 = np.abs(ds.evalTF(self.ntfs[0, 0], np.exp(2j*np.pi*freq)))**2 * 2/12*(delta/M)**2
snr1 = ds.calculateSNR(spec1[f1_bin:f2_bin + 1], fin - f1_bin)
assert snr0 > 40
assert snr1 > 40
assert snr0-snr1 > 40
def test_plotSpectrum(self):
"""Test function for plotSpectrum()"""
f0 = 0
osr = 32
quadrature = False
Hinf = 1.5
order = 3
ntf = ds.synthesizeNTF(order, osr, 0, Hinf, f0)
f1, f2 = ds.ds_f1f2(osr, f0, quadrature)
delta = 2
Amp = ds.undbv(-3)
f = 0.3
N = 2**12
f1_bin = np.round(f1 * N)
f2_bin = np.round(f2 * N)
fin = np.round(((1 - f) / 2 * f1 + (f + 1) / 2 * f2) * N)
t = np.arange(0, N)
u = Amp * np.cos((2 * np.pi / N) * fin * t)
v, xn, xmax, y = ds.simulateDSM(u, ntf, 2)
window = ds.ds_hann(N)
NBW = 1.5 / N
spec0 = fft(v * window) / (N / 4)
freq = np.linspace(0, 0.5, N // 2 + 1)
# plotting
plt.subplot(211)
plt.plot(freq,
ds.dbv(spec0[:N // 2 + 1]),
'c',
linewidth=1,
label='$S$')
#plt.hold(True)
spec_smoothed = ds.circ_smooth(np.abs(spec0)**2., 16)
plt.plot(freq,
ds.dbp(spec_smoothed[:N // 2 + 1]),
'b--',
linewidth=2,
label='$\\mathrm{circ\\_smooth}(S)$')
ds.plotSpectrum(spec0,
fin,
'r',
linewidth=2,
label='$\\mathrm{plotSpectrum}(S)$')
Snn = np.abs(ds.evalTF(ntf, np.exp(
2j * np.pi * freq)))**2 * 2 / 12 * (delta)**2
plt.plot(freq,
ds.dbp(Snn * NBW),
'm',
linewidth=1.5,
label='$\\mathrm{from\\ NTF}$')
plt.text(0.5,
-3,
'NBW = %.1e ' % NBW,
horizontalalignment='right',
verticalalignment='top')
ds.figureMagic((0, 0.5), None, None, (-140, 0), 20, None)
plt.ylabel('Spectrum [dB]')
ax = plt.gca()
ax.set_title('Smoothing and plotting for LOG and LIN axes')
plt.legend(loc=4)
plt.subplot(212)
plt.plot(freq,
ds.dbv(spec0[:N // 2 + 1]),
'c',
linewidth=1,
label='$S$')
#plt.hold(True)
ds.plotSpectrum(spec0,
fin,
'--r',
linewidth=2,
label='$\\mathrm{plotSpectrum}(S)$')
plt.plot(freq,
ds.dbp(spec_smoothed[:N // 2 + 1]),
'b',
linewidth=2,
label='$\\mathrm{circ\\_smooth}(S)$')
plt.plot(freq,
ds.dbp(Snn * NBW),
'm',
linewidth=1.5,
label='$\\mathrm{from\\ NTF}$')
plt.text(0.5,
-3,
'NBW = %.1e ' % NBW,
horizontalalignment='right',
verticalalignment='top')
ds.figureMagic((0, 0.5), None, None, (-140, 0), 20, None)
ax = plt.gca()
ax.set_xscale('linear')
plt.ylabel('Spectrum [dB]')
plt.xlabel('Normalized frequency ($f_s \\rightarrow 1$)')
plt.legend(loc=4)
def test_ds_f1f2_3(self):
"""Test function for ds_f1f2() 3/3"""
t3f1, t3f2 = ds.ds_f1f2(self.OSR, .24/self.OSR, self.cf)
self.assertTrue((t3f1, t3f2) == (0., 0.5/self.OSR))
def test_ds_f1f2_2(self):
"""Test function for ds_f1f2() 2/3"""
t2f1, t2f2 = ds.ds_f1f2(self.OSR, self.f0, not self.cf)
self.assertTrue((t2f1, t2f2) == (self.f0 - 0.5/self.OSR, self.f0 + 0.5/self.OSR))
def test_ds_f1f2_1(self):
"""Test function for ds_f1f2() 1/3"""
t1f1, t1f2 = ds.ds_f1f2(self.OSR, self.f0, self.cf)
self.assertTrue((t1f1, t1f2) == (self.f0 - 0.25/self.OSR, self.f0 + 0.25/self.OSR))
def test_ds_f1f2_3(self):
"""Test function for ds_f1f2() 3/3"""
t3f1, t3f2 = ds.ds_f1f2(self.OSR, .24 / self.OSR, self.cf)
self.assertTrue((t3f1, t3f2) == (0., 0.5 / self.OSR))
def test_ds_f1f2_2(self):
"""Test function for ds_f1f2() 2/3"""
t2f1, t2f2 = ds.ds_f1f2(self.OSR, self.f0, not self.cf)
self.assertTrue((t2f1, t2f2) == (self.f0 - 0.5 / self.OSR,
self.f0 + 0.5 / self.OSR))
def test_ds_f1f2_1(self):
"""Test function for ds_f1f2() 1/3"""
t1f1, t1f2 = ds.ds_f1f2(self.OSR, self.f0, self.cf)
self.assertTrue((t1f1, t1f2) == (self.f0 - 0.25 / self.OSR,
self.f0 + 0.25 / self.OSR))