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_nabsH(self):
"""Test function for nabsH()"""
H = ([1, 2], [2, 0, .25], 1)
N = 129
w = np.linspace(0, 2 * np.pi, num=N, endpoint=True)
z = np.exp(1j * w)
r1 = -np.abs(ds.evalTF(H, z))
r2 = ds.nabsH(w, H)
self.assertTrue(np.allclose(r1, r2, atol=1e-8, rtol=1e-5))
def test_nabsH(self):
"""Test function for nabsH()"""
H = ([1, 2], [2, 0, .25], 1)
N = 129
w = np.linspace(0, 2*np.pi, num=N, endpoint=True)
z = np.exp(1j*w)
r1 = -np.abs(ds.evalTF(H, z))
r2 = ds.nabsH(w, H)
self.assertTrue(np.allclose(r1, r2, atol=1e-8, rtol=1e-5))
def setUp(self):
num = np.poly([3, 0.3, 1])
den = np.poly([2, 0.5, .25])
H = (num, den)
tstr1 = empty()
(tstr1.form, tstr1.num, tstr1.den) = ('coeff', num, den)
tstr2 = empty()
tstr2.form = 'zp'
(tstr2.zeros, tstr2.poles, tstr2.gain) = tf2zpk(num, den)
z = np.exp(1j * np.linspace(0, 2*np.pi, num=129, endpoint=True))
self.h1 = ds.evalTF(tstr1, z)
self.h2 = ds.evalTF(tstr2, z)
self.h3 = ds.evalTF(H, z)
self.h4 = ds.evalTF(lti(tstr2.zeros, tstr2.poles, tstr2.gain), z)
h5tf = lti(tstr2.zeros, tstr2.poles, tstr2.gain).to_ss()
self.h5 = ds.evalTF((h5tf.A, h5tf.B, h5tf.C, h5tf.D), z)
h6tf = np.vstack((np.hstack((h5tf.A, h5tf.B)),
np.hstack((h5tf.C, np.atleast_2d(h5tf.D)))))
self.h6 = ds.evalTF(h6tf, z)
def setUp(self):
num = np.poly([3, 0.3, 1])
den = np.poly([2, 0.5, .25])
H = (num, den)
tstr1 = empty()
(tstr1.form, tstr1.num, tstr1.den) = ('coeff', num, den)
tstr2 = empty()
tstr2.form = 'zp'
(tstr2.zeros, tstr2.poles, tstr2.gain) = tf2zpk(num, den)
z = np.exp(1j * np.linspace(0, 2*np.pi, num=129, endpoint=True))
self.h1 = ds.evalTF(tstr1, z)
self.h2 = ds.evalTF(tstr2, z)
self.h3 = ds.evalTF(H, z)
self.h4 = ds.evalTF(lti(tstr2.zeros, tstr2.poles, tstr2.gain), z)
h5tf = lti(tstr2.zeros, tstr2.poles, tstr2.gain)
self.h5 = ds.evalTF((h5tf.A, h5tf.B, h5tf.C, h5tf.D), z)
h6tf = np.vstack((np.hstack((h5tf.A, h5tf.B)),
np.hstack((h5tf.C, np.atleast_2d(h5tf.D)))))
self.h6 = ds.evalTF(h6tf, z)
def test_evalTF_sixth(self):
"""Test unknown forms error"""
with self.assertRaises(TypeError):
ds.evalTF(empty(), [1, 2, 3])
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_evalTF_sixth(self):
"""Test unknown forms error"""
ds.evalTF(empty(), [1, 2, 3])
def test_evalTF_sixth(self):
"""Test unknown forms error"""
ds.evalTF(empty(), [1, 2, 3])
def test_sim_noiseshaper(self):
fmt = Q(8, 18)
input = fmt.Signal()
dut = Noiseshaper(input, order=8, n_lev=64)
sim = Simulator(dut)
sim.add_clock(1 / 100e6)
input_hist = []
output_hist = []
integrators_hist = [[] for _ in dut.stages]
n = 8192
f_nyquist = int(np.ceil(n / (2. * dut.osr)))
f_test = np.floor(2. / 3. * f_nyquist)
u = dut.n_lev * 0.5 * np.sin(2 * np.pi * f_test / n * np.arange(n))
def testbench():
for x in u:
yield input.eq(x)
input_hist.append(fmt.to_float((yield input.value)))
output_hist.append(
fmt.to_float((yield dut.quantized_value.value)))
for i, integrator in enumerate(dut.stages):
integrators_hist[i].append(
fmt.to_float((yield integrator.value)))
yield
sim.add_sync_process(testbench)
sim.run()
from matplotlib import pyplot as plt
plt.plot(np.arange(n), output_hist, linewidth=1, label="output")
plt.plot(np.arange(n), input_hist, label="input")
plt.legend()
plt.show()
for i, integrator_hist in reversed(list(enumerate(integrators_hist))):
plt.plot(np.arange(n),
integrator_hist,
linewidth=1,
label="integrator {}".format(i))
plt.legend()
plt.show()
import deltasigma as ds
f = np.linspace(0, 0.5, int(n / 2. + 1))
v, xn, xmax, y = ds.simulateDSM(u,
dut.h,
nlev=len(dut.quantization_values))
spec = np.fft.fft(v * ds.ds_hann(n)) / (n / 4)
plt.plot(f, ds.dbv(spec[:int(n / 2. + 1)]), 'b', label='Simulation DS')
spec = np.fft.fft(output_hist * ds.ds_hann(n)) / (n / 4)
plt.plot(f,
ds.dbv(spec[:int(n / 2. + 1)]),
'g',
label='Simulation HW',
alpha=0.7)
ds.figureMagic([0, 0.5], 0.05, None, [-160, 0], 20, None, (16, 6),
'Output Spectrum')
plt.xlabel('Normalized Frequency')
plt.ylabel('dBFS')
snr = ds.calculateSNR(spec[2:f_nyquist + 1], f_test - 2)
plt.text(0.05,
-10,
'SNR = %4.1fdB @ OSR = %d' % (snr, dut.osr),
verticalalignment='center')
NBW = 1.5 / n
Sqq = 4 * ds.evalTF(dut.h, np.exp(2j * np.pi * f))**2 / 3.
plt.plot(f, ds.dbp(Sqq * NBW), 'm', linewidth=2, label='Expected PSD')
plt.text(0.49,
-90,
'NBW = %4.1E x $f_s$' % NBW,
horizontalalignment='right')
plt.legend(loc=4)
plt.show()
pwm_out = py_pwm.modulate(np.array(output_hist) + 32,
n_bits=6,
oversampling_ratio=1)
n = n * 64
f = np.linspace(0, 0.5, int(n / 2. + 1))
spec = np.fft.fft(pwm_out * ds.ds_hann(n)) / (n / 4)
plt.plot(f, ds.dbv(spec[:int(n / 2. + 1)]), 'b', label='PWM')
ds.figureMagic([0, 0.5], 0.05, None, [-160, 0], 20, None, (16, 6),
'Output Spectrum')
plt.xlabel('Normalized Frequency')
plt.ylabel('dBFS')
snr = ds.calculateSNR(spec[2:f_nyquist + 1], f_test - 2)
plt.text(0.05,
-10,
'SNR = %4.1fdB @ OSR = %d' % (snr, dut.osr),
verticalalignment='center')
plt.legend(loc=4)
plt.show()
