In [1]:
%pylab inline

Populating the interactive namespace from numpy and matplotlib

In [2]:
from __future__ import division
from IPython.display import Image
from deltasigma import *
import warnings
warnings.filterwarnings('ignore')

In [3]:
np.set_printoptions(suppress=True, precision=3)

In [4]:
order = 8
osr = 32
nlev = 2
f0 = 0.125
Hinf = 1.5
form = 'CRFB'

In [5]:
ntf = synthesizeNTF(order, osr, 2, Hinf, f0)            # Optimized zero placement
print "Synthesized a %d-order NTF, with roots:\n" % order
print " Zeros:\t\t\t Poles:"
for z, p in zip(ntf[0], ntf[1]):
print "(%f, %fj)\t(%f, %fj)" % (np.real(z), np.imag(z), np.real(p), np.imag(p))
print ""

Synthesized a 8-order NTF, with roots:

Zeros:			 Poles:
(0.677171, -0.735825j)	(0.574412, -0.755247j)
(0.677171, 0.735825j)	(0.574412, 0.755247j)
(0.707107, -0.707107j)	(0.576806, -0.657630j)
(0.707107, 0.707107j)	(0.576806, 0.657630j)
(0.707107, -0.707107j)	(0.637688, -0.578575j)
(0.707107, 0.707107j)	(0.637688, 0.578575j)
(0.735825, -0.677171j)	(0.751098, -0.551585j)
(0.735825, 0.677171j)	(0.751098, 0.551585j)


In [6]:
plotPZ(ntf, showlist=True)
a, g, b, c = realizeNTF(ntf, form)

In [7]:
Image(url='http://python-deltasigma.readthedocs.org/en/latest/_images/CRFB.png', retina=True)

Out[7]:
In [8]:
b = np.hstack(( # Use a single feed-in for the input
np.atleast_1d(b[0]),
np.zeros((b.shape[0] - 1, ))
))
ABCD = stuffABCD(a, g, b, c, form)
print "ABCD Matrix:"
print ABCD

ABCD Matrix:
[[ 1.    -0.528  0.     0.     0.     0.     0.     0.     0.001 -0.001]
[ 1.     0.472  0.     0.     0.     0.     0.     0.     0.001  0.001]
[ 0.     1.     1.    -0.586  0.     0.     0.     0.     0.     0.008]
[ 0.     1.     1.     0.414  0.     0.     0.     0.     0.     0.028]
[ 0.     0.     0.     1.     1.    -0.586  0.     0.     0.     0.126]
[ 0.     0.     0.     1.     1.     0.414  0.     0.     0.     0.048]
[ 0.     0.     0.     0.     0.     1.     1.    -0.646  0.    -0.018]
[ 0.     0.     0.     0.     0.     1.     1.     0.354  0.    -0.574]
[ 0.     0.     0.     0.     0.     0.     0.     1.     0.     0.   ]]

In [9]:
DocumentNTF(ABCD, osr, f0)
f = gcf()
f.set_size_inches((15, 6))

In [10]:
figure(figsize=(15,8))
PlotExampleSpectrum(ntf, M=1, osr=osr, f0=f0)

In [11]:
snr, amp = simulateSNR(ntf, osr, None, f0, nlev)

In [12]:
figure(figsize=(15,8))
if nlev == 2 and f0 == 0.:
snr_pred, amp_pred, k0, k1, se = predictSNR(ntf, osr)
plot(amp_pred, snr_pred, '-', label='predicted')
hold(True)
plot(amp, snr,'o-.g', label='simulated')
xlabel('Input Level (dBFS)')
ylabel('SQNR (dB)')
peak_snr, peak_amp = peakSNR(snr, amp)
msg = 'peak SQNR = %4.1fdB  \n@ amp = %4.1fdB  ' % (peak_snr, peak_amp)
text(peak_amp-10,peak_snr,msg, horizontalalignment='right', verticalalignment='center');
msg = 'OSR = %d ' % osr
text(-2, 5, msg, horizontalalignment='right');
hold(False)
figureMagic([-100, 0], 10, None, [0, 80], 10, None, [12, 6], 'Time-Domain Simulations')
legend(loc=2);

In [13]:
 # Dynamic range scaling
print 'Doing dynamic range scaling... ',
ABCD0 = ABCD.copy()
ABCD, umax, S = scaleABCD(ABCD0, nlev, f0)
#a, g, b, c = mapABCD(ABCD,form);
print 'Done.'
print "Maximum input magnitude: %.3f" % umax

Doing dynamic range scaling...  Done.
Maximum input magnitude: 0.867

In [14]:
print 'Verifying dynamic range scaling... ',
u = np.linspace(0, 0.95*umax, 30)
N = 1e4
N0 = 50
test_tone = np.cos(2*np.pi*f0*np.arange(N))
test_tone[:N0] = test_tone[:N0]*(0.5 - 0.5*np.cos(2*np.pi/N0*np.arange(N0)))
maxima = np.zeros((order, u.shape[0]))
for i in np.arange(u.shape[0]):
ui = u[i]
v, xn, xmax, y = simulateDSM(ui*test_tone, ABCD, nlev)
maxima[:, i] = xmax[:, 0]
if (xmax > 1e2).any():
print 'Warning, umax from scaleABCD was too high.'
umax = ui
u = u[:i]
maxima = maxima[:, :i]
break
print 'Done.'
print "Maximum DC input level: %.3f" % umax

Verifying dynamic range scaling...  Done.
Maximum DC input level: 0.867

In [15]:
colors = get_cmap('jet')(np.linspace(0, 1.0, order))
hold(True)
for i in range(order):
plot(u, maxima[i,:], 'o-', color=colors[i], label='State %d' % (i+1))
grid(True)
figureMagic([0, umax], None, None, [0, 1] , 0.1, 2, [12, 6], 'State Maxima')
xlabel('DC input')
ylabel('Maxima')
legend(loc='best');

In [16]:
a, g, b, c = mapABCD(ABCD, form)

In [17]:
adc = {
'order':order,
'osr':osr,
'nlev':nlev,
'f0':f0,
'ntf':ntf,
'ABCD':ABCD,
'umax':umax,
'peak_snr':peak_snr,
'form':form,
'coefficients':{
'a':a,
'g':g,
'b':b,
'c':c
}
}

In [18]:
print "Final ADC coefficients:"
print "  %s\n   %s" % ('a', adc['coefficients']['a'])
print "  %s\n   %s" % ('g', adc['coefficients']['g'])
print "  %s\n   %s" % ('b', adc['coefficients']['b'])
print "  %s\n   %s" % ('c', adc['coefficients']['c'])

Final ADC coefficients:
a
[ 0.085 -0.107 -0.066 -0.137 -0.256  0.1    0.008  0.186]
g
[ 0.71   0.733  0.928  0.847]
b
[ 0.085  0.     0.     0.     0.     0.     0.     0.     0.   ]
c
[ 0.744  0.159  0.8    0.3    0.631  0.342  0.762  2.99 ]


### System version information¶

In [19]:
#%install_ext http://raw.github.com/jrjohansson/version_information/master/version_information.py