def calc_dft(sig_src_arr):
sig_dest_imx_arr = [None] * int((len(sig_src_arr) / 2))
sig_dest_rex_arr = [None] * int((len(sig_src_arr) / 2))
sig_dest_mag_arr = [None] * int((len(sig_src_arr) / 2))
for j in range(int(len(sig_src_arr) / 2)):
sig_dest_rex_arr[j] = 0
sig_dest_imx_arr[j] = 0
for k in range(int(len(sig_src_arr) / 2)):
for i in range(len(sig_src_arr)):
sig_dest_rex_arr[k] = sig_dest_rex_arr[k] + sig_src_arr[
i] * math.cos(2 * math.pi * k * i / len(sig_src_arr))
sig_dest_imx_arr[k] = sig_dest_imx_arr[k] - sig_src_arr[
i] * math.sin(2 * math.pi * k * i / len(sig_src_arr))
for x in range(int(len(sig_src_arr) / 2)):
sig_dest_mag_arr[x] = math.sqrt(
math.pow(sig_dest_rex_arr[x], 2) +
math.pow(sig_dest_imx_arr[x], 2))
style.use('ggplot')
f, plt_arr = plt.subplots(1, sharex=True)
f.suptitle("Discrete Fourier Transform (DFT)")
plt.xlim(0, 500)
plt.ylim(0, 20000)
plt.stem(sig_dest_mag_arr)
def matlab_fourier_anal(data, sample_rate = 1.0):
n = data.shape[0]
t = np.arange(n)
P.figure()
P.plot(t/sample_rate,data)
P.xlabel('Time Units')
P.ylabel('Data Magnitude')
Y = fftpack.fft(data);
freqs = np.arange(n/2.0) * sample_rate / n
power = np.abs(Y[:n/2.0])
P.figure()
markerline, stemlines, baseline = P.stem(freqs, power, '--')
P.setp(markerline, 'markerfacecolor', 'b')
# P.setp(baseline, 'color','r', 'linewidth', 2)
P.xlabel('Cycles/ Unit Time')
P.ylabel('Power')
P.title('Periodogram')
period = 1. / freqs
k = np.arange(50)
f = k / float(n)
power2 = power[k];
P.figure()
markerline, stemlines, baseline = P.stem(f, power2, '--')
P.setp(markerline, 'markerfacecolor', 'b')
P.setp(baseline, 'color','r', 'linewidth', 2)
P.xlabel('Unit Time / Cycle')
P.ylabel('Power')
P.title('Periodogram: First 50 periods')
def Skew_Tent_map_reseed(init, b, seed_funct, seed_step, steps):
xs = np.arange(steps)
ys = np.zeros((steps))
ss = np.zeros((steps))
zs = seed_funct(xs)
seedxs = []
seedys = []
sym = ""
ys[0] = init
for i in range(1, steps):
y = ys[i - 1]
if (i % seed_step == 0):
ys[i] = seed_funct(i)
seedxs.append([i])
seedys.append([ys[i]])
elif (y <= 1.0 and y >= 0.0):
ys[i] = np.exp(b) * y
sym += "A"
elif (y > 1.0 and y <= (1 + np.exp(-0.5 * b))):
ys[i] = -1 * np.exp(1.5 * b) * y + (np.exp(b) + np.exp(1.5 * b))
sym += "B"
elif (y > (1 + np.exp(-0.5 * b))):
ys[i] = np.exp(b) * y - (np.exp(0.5 * b) + np.exp(b))
sym += "C"
if (ys[i] >= 0.5):
ss[i] = 1.0
print(sym)
pl.plot(xs, ys)
#pl.plot(xs,zs)
pl.plot(xs, ss)
pl.stem(seedxs, seedys, linefmt='r')
pl.show()
def display_fit(xs, target, method, color=None, acronym=None, xmax=None, linewidth=2):
if not hasattr(method, "__iter__"):
method = (method,)
if not color is None:
color = (color,)
if not acronym is None:
acronym = (acronym,)
if not xs.shape[0] == 1:
raise ValueError("univariate data expected")
if xmax == None:
xmax = int(np.max(np.abs(xs.squeeze()))) + 1
x = np.linspace(-xmax, xmax, 2 * xmax / 0.01)
x = np.reshape(x, (1, x.size))
fits = [m.fit(x) for m in method]
if color is None:
for fit in fits:
plt.plot(x.squeeze(), fit, linewidth=linewidth)
else:
for fit, col in zip(fits, color):
plt.plot(x.squeeze(), fit, col, linewidth=linewidth)
if not acronym is None:
plt.legend(acronym)
target_xs = np.exp(target(xs.squeeze()))
target_x = np.exp(target(x.squeeze()))
plt.stem(xs.squeeze(), target_xs, linefmt="k-", markerfmt="ko", basefmt="k-")
plt.plot(x.squeeze(), target_x, "k")
x0, x1, y0, y1 = plt.axis()
plt.plot((x0, x1), (0, 0), "k")
plt.show()
def plot(self, marker='o', color='red', m=0, M=6000):
"""Plots the position / height of the peaks in the well
.. plot::
:include-source:
from fragment_analyser import Line, fa_data
l = Line(fa_data("alternate/peaktable.csv"))
well = l.wells[0]
well.plot()
"""
import pylab
if len(self.df) == 0:
print("Nothing to plot (no peaks)")
return
x = self.df['Size (bp)'].astype(float).values
y = self.df['RFU'].astype(float).values
pylab.stem(x, y, marker=marker, color=color)
pylab.semilogx()
pylab.xlim([1, M])
pylab.ylim([0, max(y)*1.2])
pylab.grid(True)
pylab.xlabel("size (bp)")
pylab.ylabel("RFU")
return x, y
def plot_weights(self):
import pylab
x,w = zip(*self.distribution)
pylab.stem(x,100*numpy.array(w))
pylab.title('Weight distribution')
pylab.xlabel(self.P.name)
pylab.ylabel('Percentage')
def plot_weights(self):
import pylab
x, w = zip(*self.distribution)
pylab.stem(x, 100*numpy.array(w))
pylab.title('Weight distribution')
pylab.xlabel(self.P.name)
pylab.ylabel('Percentage')
def plot(self, marker='o', color='red', m=0, M=6000):
"""Plots the position / height of the peaks in the well
.. plot::
:include-source:
from fragment_analyser import Line, fa_data
l = Line(fa_data("alternate/peaktable.csv"))
well = l.wells[0]
well.plot()
"""
import pylab
if len(self.df) == 0:
print("Nothing to plot (no peaks)")
return
x = self.df['Size (bp)'].astype(float).values
y = self.df['RFU'].astype(float).values
pylab.stem(x, y, marker=marker, color=color)
pylab.semilogx()
pylab.xlim([1, M])
pylab.ylim([0, max(y) * 1.2])
pylab.grid(True)
pylab.xlabel("size (bp)")
pylab.ylabel("RFU")
return x, y
def calc_dft(sig_src_arr):
sig_dest_imx_arr = [None]*int((len(sig_src_arr)/2))
sig_dest_rex_arr = [None]*int((len(sig_src_arr)/2))
sig_dest_mag_arr = [None]*int((len(sig_src_arr)/2))
for j in range(int(len(sig_src_arr)/2)):
sig_dest_rex_arr[j] =0
sig_dest_imx_arr[j] =0
for k in range(int(len(sig_src_arr)/2)):
for i in range(len(sig_src_arr)):
sig_dest_rex_arr[k] = sig_dest_rex_arr[k] + sig_src_arr[i]*math.cos(2*math.pi*k*i/len(sig_src_arr))
sig_dest_imx_arr[k] = sig_dest_imx_arr[k] - sig_src_arr[i]*math.sin(2*math.pi*k*i/len(sig_src_arr))
for x in range(int(len(sig_src_arr)/2)):
sig_dest_mag_arr[x] = math.sqrt(math.pow(sig_dest_rex_arr[x],2)+math.pow(sig_dest_imx_arr[x],2))
style.use('ggplot')
f,plt_arr = plt.subplots(1, sharex=True)
f.suptitle("Discrete Fourier Transform (DFT)")
#plt_arr[0].plot(sig_src_arr, color='red')
#plt_arr[0].set_title("Input Signal",color='red')
#plt_arr[1].plot(sig_dest_rex_arr, color='green')
#plt_arr[1].set_title("Frequency Domain(Real part)",color='green')
#plt_arr[2].plot(sig_dest_imx_arr, color='green')
#plt_arr[2].set_title("Frequency Domain(Imaginary part)",color='green')
#plt_arr[3].plot(sig_dest_mag_arr, color='magenta')
#plt_arr[3].set_title("Frequency Domain (Magnitude))",color='magenta')
plt.xlim(0,200)
#plt.ylim(0,1000)
plt.stem(sig_dest_mag_arr)
def decode_symbols(r, i, corr_index, r0, i0, Nbits, fs=48000, baud=300,
plot=False):
Ns = fs/baud
r = r[corr_index:]
i = i[corr_index:]
r0 = r0[corr_index:]
i0 = i0[corr_index:]
#print len(r)
#print len(r0)
#print len(i0)
r = r/np.max(r)*2.2 #change this 2 depending on the input amplitude
i = i/np.max(i)*2.2 #change this 2 depending on the input amplitude
if plot:
fig = plt.figure(figsize = (16,4))
plt.plot(2*r0)
plt.plot(r)
plt.title('Real part, raw input and normalized')
fig = plt.figure(figsize = (16,4))
plt.plot(2*i0)
plt.plot(i)
plt.title('Imaginary part, raw input and normalized')
####Decode
idx = np.r_[Ns/2:len(r):Ns]
#r = np.around(r)
#i = np.around(i)
r_dec = np.around(r[idx])
i_dec = np.around(i[idx])
if plot:
fig = plt.figure(figsize = (16,4))
plt.plot(2*r0)
plt.plot(r)
plt.plot(np.around(r))
plt.stem(idx, r_dec)
plt.title('Real part, decoded by sampling values as indicated')
fig = plt.figure(figsize = (16,4))
plt.plot(2*i0)
plt.plot(i)
plt.plot(np.around(i))
plt.stem(idx, i_dec)
plt.title('Imaginary part, decoded by sampling values as indicated')
fig = plt.figure(figsize = (8,8))
plt.scatter(r0*2, i0*2, c='r')
plt.scatter(r_dec, i_dec, c='g')
plt.title('Constellation of input message vs decoded symbols')
return r_dec + 1j*i_dec
def plot_reflection(self):
from pylab import stem, title, xlabel, ylabel
if self.reflection is not None:
stem(list(range(0, len(self.reflection))), abs(self.reflection))
title('Reflection coefficient evolution')
xlabel('Order')
ylabel('Reflection Coefficient absolute values')
else:
logging.warning("Reflection coefficients not available or not yet computed.")
def print_spectrum(spectrum, filename):
x = spectrum.mz
y = spectrum.intensity
pylab.stem(x, y, markerfmt='b,')
pylab.xlabel('m/z')
pylab.ylabel('Transformed intensity')
pylab.grid()
pylab.xlim(0.95*min(x), 1.05*max(x))
pylab.savefig(filename)
def binom(self):
n = 10
k = np.arange(n + 1)
pcoin = stats.binom.pmf(k, n, 0.5)
pl.stem(k, pcoin, basefmt='k-')
pl.margins(0, 1)
pl.savefig('./task1.png')
pl.show()
def plot_reflection(self):
from pylab import stem, title, xlabel, ylabel
if self.reflection is not None:
stem(list(range(0, len(self.reflection))), abs(self.reflection))
title('Reflection coefficient evolution')
xlabel('Order')
ylabel('Reflection Coefficient absolute values')
else:
logging.warning(
"Reflection coefficients not available or not yet computed.")
def plot_reflection(self):
from pylab import stem, title, xlabel, ylabel
if self.reflection is not None:
stem(list(range(0, len(self.reflection))), abs(self.reflection))
title('Reflection coefficient evolution')
xlabel('Order')
ylabel('Reflection Coefficient absolute values')
else:
import warnings
warnings.warn("""Reflection coefficients not available with
the current method.""")
def plot_reflection(self):
from pylab import stem, title, xlabel, ylabel
if self.reflection is not None:
stem(list(range(0, len(self.reflection))), abs(self.reflection))
title('Reflection coefficient evolution')
xlabel('Order')
ylabel('Reflection Coefficient absolute values')
else:
import warnings
warnings.warn("""Reflection coefficients not available with
the current method.""")
def nzcols_hist(P,file=None):
if file==None: pylab.ion()
else: pylab.ioff()
nzcols = +P.nzcols
Nmax = max(nzcols)
y = matrix(0,(Nmax,1))
for n in nzcols:
y[n-1] += 1
y = sparse(y)
f = pylab.figure(); f.clf()
pylab.stem(y.I+1,y.V)#; pylab.xlim(-1,Nmax+2)
if file: pylab.savefig(P._pname + "_nzcols_hist.png")
def plot_spectra(self):
""" Plots the original spectrum and the sum of cisoids.
"""
import pylab as plt
plt.plot(self.psd[0], self.psd[1])
freqs = [el[0] for el in self.soc]
ampls = [el[1] for el in self.soc]
plt.stem(freqs, ampls)
plt.xlabel(r'$f$ in Hz')
plt.ylabel(r'$S(f)$')
plt.show()
def fourier_analysis(sig, time_step = 1.0, top_freqs = 5, zoomed_num = 15):
time_vec = np.arange(0, len(sig), time_step)
sample_freq = fftpack.fftfreq(sig.size, d=time_step)
sig_fft = fftpack.fft(sig)
# Only take first half of sampling frequency
pidxs = np.where(sample_freq > 0)
freqs, power = sample_freq[pidxs], np.abs(sig_fft)[pidxs]
# plot with zoomed in sub plot
P.figure()
P.plot(freqs, power)
P.ylabel('Power')
P.xlabel('Frequency [Hz]')
axes = P.axes([0.3, 0.3, 0.5, 0.5])
P.title('Peak frequency')
P.stem(freqs[:zoomed_num], power[:zoomed_num])
#P.setp(axes, yticks=[])
#P.savefig('source/fftpack-frequency.png')
# Find top x frequencies to use in reconstruction
full_sort_idx = power.argsort()
find_idx = full_sort_idx >= top_freqs
sorted_power = power[sort_idx][::-1] # Sort decending
component_freqs = freqs[sort_idx[:top_freqs]]
# copy fft
reduced_sig_fft = sig_fft.copy()
# set all values not in component freqs to 0
L = np.array(reduced_sig_fft, dtype = bool)
L[sort_idx[:top_freqs]] = False
reduced_sig_fft[L] = 0
# Reconstruct signal
reconstruct_sig = fftpack.ifft(reduced_sig_fft)
# Plot original and reconstructed signal
P.figure()
P.plot(time_vec, sig)
P.plot(time_vec, reconstruct_sig, linewidth=2)
P.ylabel('Amplitude')
P.xlabel('Time [s]')
return sig_fft, reduced_sig_fft, reconstruct_sig, freqs, power, component_freqs
def demo(text=None):
from nltk.corpus import brown
import pylab
tt = TextTilingTokenizer(demo_mode=True)
if text is None: text = brown.raw()[:10000]
s, ss, d, b = tt.tokenize(text)
pylab.xlabel("Sentence Gap index")
pylab.ylabel("Gap Scores")
pylab.plot(range(len(s)), s, label="Gap Scores")
pylab.plot(range(len(ss)), ss, label="Smoothed Gap scores")
pylab.plot(range(len(d)), d, label="Depth scores")
pylab.stem(range(len(b)), b)
pylab.legend()
pylab.show()
def demo(text=None):
from nltk.corpus import brown
import pylab
tt=TextTilingTokenizer(demo_mode=True)
if text is None: text=brown.raw()[:10000]
s,ss,d,b=tt.tokenize(text)
pylab.xlabel("Sentence Gap index")
pylab.ylabel("Gap Scores")
pylab.plot(range(len(s)), s, label="Gap Scores")
pylab.plot(range(len(ss)), ss, label="Smoothed Gap scores")
pylab.plot(range(len(d)), d, label="Depth scores")
pylab.stem(range(len(b)),b)
pylab.legend()
pylab.show()
def main_Show(self, LIST, name, Num):
fix = np.ones(Num)
y = []
x = []
T = []
for i in range(Num):
x.append(i + 1)
y.append(LIST[i])
markerline, stemlines, baseline = pylab.stem(x, y, bottom=0.5)
pylab.setp(markerline, 'markerfacecolor', 'b')
pylab.setp(baseline, 'color', 'g', 'linewidth', 2)
pylab.lines = pylab.plot(x, 0.6 * fix, x, 0.4 * fix)
pylab.setp(pylab.lines, 'color', 'r', 'linewidth', 2)
pylab.xlabel('Examination')
pylab.ylabel('Discrimination Level')
#xticks(range(len(x)), T, size='small')
pylab.savefig('chart/{:>}.png'.format(name))
pylab.show()
lines = []
pylab.clf()
def plot_inflections(x, y):
"""
Plot inflection points in a curve.
"""
m = (y[2:] - y[:-2]) / (x[2:] - x[:-2])
b = y[2:] - m * x[2:]
delta = y[1:-1] - (m * x[1:-1] + b)
t = linspace(x[0], x[-1], 400)
import pylab
ax1 = pylab.subplot(211)
pylab.plot(t, monospline(x, y, t), '-b', x, y, 'ob')
pylab.subplot(212, sharex=ax1)
delta_x = x[1:-1]
pylab.stem(delta_x, delta)
pylab.plot(delta_x[delta < 0], delta[delta < 0], 'og')
pylab.axis([x[0], x[-1], min(min(delta), 0), max(max(delta), 0)])
def hist_mtx(mtx, tstr=''):
"""
Given a piano-roll matrix, 128 MIDI piches x beats, plot the pitch class histogram
"""
i_min, i_max = np.where(mtx.mean(1))[0][[0,-1]]
P.figure(figsize=(14.5,8))
P.stem(np.arange(i_max+1-i_min),mtx[i_min:i_max+1,:].sum(1))
ttl = 'Note Frequency'
if tstr: ttl+=': '+tstr
P.title(ttl,fontsize=16)
t=P.xticks(np.arange(0,i_max+1-i_min,3),pc_labels[i_min:i_max+1:3],fontsize=14)
P.xlabel('Pitch Class', fontsize=14)
P.ylabel('Frequency', fontsize=14)
ax = P.axis()
P.axis(xmin=-0.5)
P.grid()
def plot_inflections(x,y):
"""
Plot inflection points in the spline curve.
"""
m = (y[2:]-y[:-2])/(x[2:]-x[:-2])
b = y[2:] - m*x[2:]
delta = y[1:-1] - (m*x[1:-1] + b)
t = linspace(x[0],x[-1],400)
import pylab
ax1=pylab.subplot(211)
pylab.plot(t,monospline(x,y,t),'-b',x,y,'ob')
pylab.subplot(212, sharex=ax1)
delta_x = x[1:-1]
pylab.stem(delta_x,delta)
pylab.plot(delta_x[delta<0],delta[delta<0],'og')
pylab.axis([x[0],x[-1],min(min(delta),0),max(max(delta),0)])
def redraw(self):
self.clearStems()
for i in range(0, 3):
axes = pylab.subplot('13' + str(1 + i))
if (self.mode == "phase"):
self.plots[i][0].set_ydata(
scipy.angle(self.fts[self.index + i]))
else:
mag = abs(self.fts[self.index + i])
self.plots[i][0].set_ydata(mag)
peak = max(mag)
peakInd = list(mag).index(peak)
stem_marker, stem_lines, stem_base = pylab.stem([peakInd],
[peak], 'r-',
'ro')
self.stemMarkers.append(stem_marker)
self.stemBase.append(stem_base)
self.stemLines.append(stem_lines)
xres = self.fov / self.xsize
pylab.xlabel(self.axis[i] + ':' +
'{0:.3}'.format(xres *
(peakInd - len(mag) / 2)) + ' mm')
pylab.draw()
def impz(b,a=1):
impulse = np.repeat(0.,50); impulse[0] =1.
x = np.arange(0,50)
response = signal.lfilter(b,a,impulse)
pl.subplot(211)
pl.stem(x, response)
pl.ylabel('Amplitude')
pl.xlabel(r'n (samples)')
pl.title(r'Impulse response')
pl.subplot(212)
step = np.cumsum(response)
pl.stem(x, step)
pl.ylabel('Amplitude')
pl.xlabel(r'n (samples)')
pl.title(r'Step response')
pl.subplots_adjust(hspace=0.5)
def hist_mtx(mtx, tstr=''):
"""
Given a piano-roll matrix, 128 MIDI piches x beats, plot the pitch class histogram
"""
i_min, i_max = np.where(mtx.mean(1))[0][[0,-1]]
P.figure(figsize=(14.5,8))
P.stem(np.arange(i_max+1-i_min),mtx[i_min:i_max+1,:].sum(1))
ttl = 'Note Frequency'
if tstr: ttl+=': '+tstr
P.title(ttl,fontsize=16)
t=P.xticks(np.arange(0,i_max+1-i_min,3),pc_labels[i_min:i_max+1:3],fontsize=14)
P.xlabel('Pitch Class', fontsize=14)
P.ylabel('Frequency', fontsize=14)
ax = P.axis()
P.axis(xmin=-0.5)
P.grid()
def impz(b,a=1):
l = len(b)
impulse = numpy.repeat(0.,l); impulse[0] =1.
x = numpy.arange(0,l)
response = scipy.signal.lfilter(b,a,impulse)
pylab.subplot(211)
pylab.stem(x, response)
pylab.ylabel('Amplitude')
pylab.xlabel(r'n (samples)')
pylab.title(r'Impulse response')
pylab.subplot(212)
step = numpy.cumsum(response)
pylab.stem(x, step)
pylab.ylabel('Amplitude')
pylab.xlabel(r'n (samples)')
pylab.title(r'Step response')
pylab.subplots_adjust(hspace=0.5)
def impz(b,a=1):
l = len(b)
impulse = numpy.repeat(0.,l); impulse[0] =1.
x = numpy.arange(0,l)
response = scipy.signal.lfilter(b,a,impulse)
pylab.subplot(211)
pylab.stem(x, response)
pylab.ylabel('Amplitude')
pylab.xlabel(r'n (samples)')
pylab.title(r'Impulse response')
pylab.subplot(212)
step = numpy.cumsum(response)
pylab.stem(x, step)
pylab.ylabel('Amplitude')
pylab.xlabel(r'n (samples)')
pylab.title(r'Step response')
pylab.subplots_adjust(hspace=0.5)
def plot_spectra(self):
""" Plots the original Spectrum and the sum of sinusoids.
"""
import matplotlib as mp
mp.rc('font', family='serif', size=22)
import pylab as plt
freqs = [f[0] for f in self.sos]
negfreqs = [-f[0] for f in self.sos]
# convert the amplitudes of the sinusoids to a psd
ampls = [(a[1] / 2) ** 2 for a in self.sos]
plt.stem(freqs, ampls)
plt.stem(negfreqs, ampls)
plt.xlim(1.5 * negfreqs[-1], 1.5 * freqs[-1])
plt.ylim(0, 1.5 * max(ampls))
plt.xlabel(r'$f$ in Hz')
plt.ylabel(r'$\| S(f) \|$')
plt.show()
def graficarConvolucion():
limiteSup = 5
limiteInf = -5
imp = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]
print type(imp)
try:
print "graficarConvolucion impulso"
X = np.linspace(limiteInf, limiteSup, 11, endpoint=True)
Y = np.array(imp)
pl.stem(X, imp)
#pl.step(X,imp)
#fig, ax = plt.subplots()
#ax.stem(X, Y)
#plt.show()
pl.show()
except Exception as ex:
print "Error inesperado en gaficarConvolucion(): ", type(ex)
def impz(b,a=1):
'''
#Plot step and impulse response
from http://mpastell.com/2010/01/18/fir-with-scipy/
'''
l = len(b)
impulse = pylab.repeat(0.,l); impulse[0] =1.
x = numpy.arange(0,l)
response = signal.lfilter(b,a,impulse)
pylab.subplot(211)
pylab.stem(x, response)
pylab.ylabel('Amplitude')
pylab.xlabel(r'n (samples)')
pylab.title(r'Impulse response')
pylab.subplot(212)
step = numpy.cumsum(response)
pylab.stem(x, step)
pylab.ylabel('Amplitude')
pylab.xlabel(r'n (samples)')
pylab.title(r'Step response')
pylab.subplots_adjust(hspace=0.5)
def test_volterra():
f = array([-1200., -1000., 1000., 1200.])
v = array([2., 2., 2., 2.])
w = Waveform(f, v)
v1, v2, v31, v32 = lna_volterra(w)
pylab.subplot(4, 1, 1)
pylab.stem(v1.get_x()[0], v1.get_y())
pylab.subplot(4, 1, 2)
pylab.stem(v2.get_x()[0], v2.get_y())
pylab.subplot(4, 1, 3)
pylab.stem(v31.get_x()[0], v31.get_y())
pylab.subplot(4, 1, 4)
pylab.stem(v32.get_x()[0], v32.get_y())
pylab.show()
def test_volterra():
f=array([-1200.,-1000.,1000.,1200.])
v=array([2.,2.,2.,2.])
w=Waveform(f,v)
v1,v2,v31,v32=lna_volterra(w)
pylab.subplot(4,1,1)
pylab.stem(v1.get_x()[0],v1.get_y())
pylab.subplot(4,1,2)
pylab.stem(v2.get_x()[0],v2.get_y())
pylab.subplot(4,1,3)
pylab.stem(v31.get_x()[0],v31.get_y())
pylab.subplot(4,1,4)
pylab.stem(v32.get_x()[0],v32.get_y())
pylab.show()
def _add_stems_to_plot(interval, stem_bed, samples, plot):
stems = _get_stems_by_callers(stem_bed.tabix_intervals(interval))
callers = sorted(stems.keys())
caller_colormap = _get_caller_colormap(callers)
caller_heights = _get_caller_heights(callers, plot)
for caller in callers:
stem_color = caller_colormap[caller]
caller_stems = stems[caller]
stem_heights = list(repeat(caller_heights[caller], len(caller_stems)))
markerline, _, baseline = stem(caller_stems, stem_heights, "-.", label=caller)
setp(markerline, "markerfacecolor", stem_color)
setp(baseline, "color", "r", "linewidth", 0)
plt.legend()
def view_filter(h, fp=None, fs=None):
'''view filter'''
w, H = signal.freqz(h, 1)
H_phase = pl.unwrap([pl.degrees(cmath.phase(H[i])) for i in range(len(H))],
180)
H = 20 * pl.log10(abs(H[:]))
x = range(0, len(h))
step = pl.cumsum(h)
pl.figure(figsize=(16, 6.6), dpi=80)
pl.subplot(221)
pl.stem(x, h)
pl.ylabel('Amplitude')
pl.xlabel(r'n (samples)')
pl.title(r'Impulse response')
pl.text(0.2, 0.7, 'N_taps = {0}'.format(len(h)))
pl.subplot(222)
pl.stem(x, step)
pl.ylabel('Amplitude')
pl.xlabel(r'n (samples)')
pl.title(r'Step response')
pl.subplot(223)
pl.plot(w / (2.0 * pl.pi), H)
pl.ylabel('Magnitude (db)')
pl.xlabel(r'Normalized Frequency (x$\pi$rad/sample)')
pl.title(r'Frequency response')
if fp != None:
pl.axvline(fp, linewidth=1, color='k', ls='-')
if fs != None:
pl.axvline(fs, linewidth=1, color='k', ls='-')
pl.subplot(224)
pl.plot(w / (2.0 * pl.pi), H_phase)
pl.ylabel('Phase (radians)')
pl.xlabel(r'Normalized Frequency (Hz)')
pl.title(r'Phase response')
def impz(b, a=1):
'''
#Plot step and impulse response
from http://mpastell.com/2010/01/18/fir-with-scipy/
'''
l = len(b)
impulse = pylab.repeat(0., l)
impulse[0] = 1.
x = numpy.arange(0, l)
response = signal.lfilter(b, a, impulse)
pylab.subplot(211)
pylab.stem(x, response)
pylab.ylabel('Amplitude')
pylab.xlabel(r'n (samples)')
pylab.title(r'Impulse response')
pylab.subplot(212)
step = numpy.cumsum(response)
pylab.stem(x, step)
pylab.ylabel('Amplitude')
pylab.xlabel(r'n (samples)')
pylab.title(r'Step response')
pylab.subplots_adjust(hspace=0.5)
def view_filter(h, fp=None, fs=None):
'''view filter'''
w, H = signal.freqz(h,1)
H_phase = pl.unwrap([pl.degrees(cmath.phase(H[i])) for i in range(len(H))], 180)
H = 20 * pl.log10 (abs(H[:]))
x = range(0,len(h))
step = pl.cumsum(h)
pl.figure(figsize=(16, 6.6), dpi=80)
pl.subplot(221)
pl.stem(x, h)
pl.ylabel('Amplitude')
pl.xlabel(r'n (samples)')
pl.title(r'Impulse response')
pl.text(0.2, 0.7, 'N_taps = {0}'.format(len(h)))
pl.subplot(222)
pl.stem(x, step)
pl.ylabel('Amplitude')
pl.xlabel(r'n (samples)')
pl.title(r'Step response')
pl.subplot(223)
pl.plot(w/(2.0*pl.pi), H)
pl.ylabel('Magnitude (db)')
pl.xlabel(r'Normalized Frequency (x$\pi$rad/sample)')
pl.title(r'Frequency response')
if fp != None:
pl.axvline(fp, linewidth=1, color='k', ls='-')
if fs != None:
pl.axvline(fs, linewidth=1, color='k', ls='-')
pl.subplot(224)
pl.plot(w/(2.0*pl.pi), H_phase)
pl.ylabel('Phase (radians)')
pl.xlabel(r'Normalized Frequency (Hz)')
pl.title(r'Phase response')
def _add_stems_to_plot(interval, stem_bed, samples, plot):
stems = _get_stems_by_callers(stem_bed.tabix_intervals(interval))
callers = sorted(stems.keys())
caller_colormap = _get_caller_colormap(callers)
caller_heights = _get_caller_heights(callers, plot)
for caller in callers:
stem_color = caller_colormap[caller]
caller_stems = stems[caller]
stem_heights = list(repeat(caller_heights[caller], len(caller_stems)))
markerline, _, baseline = stem(caller_stems, stem_heights, '-.',
label=caller)
setp(markerline, 'markerfacecolor', stem_color)
setp(baseline, 'color', 'r', 'linewidth', 0)
plt.legend()
def demo(text=None):
from nltk.corpus import brown
import pylab
tt = TextTilingTokenizer(demo_mode=True)
if text is None: text = brown.raw()[:10000]
s, ss, d, b = tt.tokenize(text)
pylab.xlabel("Sentence Gap index")
pylab.ylabel("Gap Scores")
pylab.plot(range(len(s)), s, label="Gap Scores")
pylab.plot(range(len(ss)), ss, label="Smoothed Gap scores")
pylab.plot(range(len(d)), d, label="Depth scores")
pylab.stem(range(len(b)), b)
pylab.legend()
pylab.show()
"""s = tt.tokenize(text)
FILE = open("tiled","w")
FILE.writelines(s)
FILE.close()"""
# if __name__ == '__main__':
# content = open('toTile', 'r').read()
# demo(content)
def main():
x = pylab.randn(100)
t0 = time.clock()
y1 = ks_loop(x, 0.9, 10)
t_loop = time.clock() - t0
t0 = time.clock()
y2 = ks(x, 0.9, 10)
t_matrix = time.clock() - t0
print("Loop method took %g seconds." % t_loop)
print("Matrix method took %g seconds." % t_matrix)
# Make sure y1 and y2 are same within very small numeric
# error.
assert(pylab.sum(pylab.absolute(y1 - y2)) < 1e-10)
# Plot x and y
pylab.figure()
pylab.subplot(211)
pylab.stem(x)
pylab.ylabel('x')
pylab.subplot(212)
pylab.stem(y2)
pylab.ylabel('y')
pylab.xlabel('samples')
print("Generating the opening chord of Hard day's night by The Beatles ...")
Fs, T, chord = generate_cord()
pylab.figure()
pylab.plot(pylab.arange(0.0, T, 1.0/Fs), chord)
pylab.xlabel('time (sec)')
pylab.title('First Chord of Hard Days Night')
print("Writing the chord to chord.wav ...")
C = max(pylab.absolute(chord))
scipy.io.wavfile.write("chord.wav", Fs,
pylab.int16((2**15 - 1) * chord / C))
print("Done.")
pylab.show()
def lollipop(x, y, color=None, lw=2, ybot=0):
"""Plot lollipops (o's and sticks)
**Parameters:**
x, y : ndarrays
The data to be plotted
color : any matplotlib color, optional
plotting color
lw : float, optional
line width value in points
ybot : float, optional
Dummy parameter available for compatibility
**Returns:**
None
**Example:**
.. plot::
import matplotlib.pyplot as plt
import numpy as np
from deltasigma import lollipop
t = np.arange(1, 20)*1e-3
f = 20.
a = np.sin(2*np.pi*f*t)
lollipop(t, a)
plt.gcf().set_size_inches((8, 4))
plt.grid(True)
plt.show()
"""
if ybot:
warn('lollipop() got a non-zero ybot, but only ybot=0 is ' + \
'supported. Setting ybot to 0.')
markerline, stemlines, baseline = plt.stem(x, y, '-')
if not color or color == 'None':
color = stemlines[0].get_color()
lolli_fmt = {'linewidth': lw, 'color': color}
pop_fmt = {'mec': color, 'markerfacecolor':'None', \
'markersize':10, 'markeredgewidth': lw*1.1}
plt.setp(markerline, **pop_fmt)
plt.setp(stemlines, **lolli_fmt)
plt.setp(baseline, 'color','k')
def plotSignalAndRecoveredSignal(t,
u,
v,
fig_title,
spikes=False,
denoised=None):
"""
Compare two signals and plot the difference between them.
Parameters
----------
t : ndarray of floats
Times (s) at which the signal is defined.
u, v : ndarrays of floats
Signal samples.
"""
p.figure(figsize=(15, 10))
p.clf()
p.gcf().canvas.set_window_title(fig_title)
# p.subplot(211)
p.plot(t, u, 'b', label='u(t)')
if (spikes):
p.stem(t, v, 'r', label='u_rec(t)', use_line_collection=True)
else:
p.plot(t, v, 'r', label='u_rec(t)')
if (denoised != None):
p.plot(t, denoised, 'o', label='denoised u(t)')
p.xlabel('t (s)')
p.ylabel('u(t)')
p.legend()
p.title(fig_title)
p.gca().set_xlim(min(t), max(t))
p.draw_if_interactive()
def clique_hist(P,file=None):
if not P.ischordal: raise TypeError, "Nonchordal"
if file==None: pylab.ion()
else: pylab.ioff()
V = +P.V
p = chompack.maxcardsearch(V)
#Vc,n = chompack.embed(V,p)
symb = chompack.symbolic(V,p)
#D = chompack.info(Vc); N = len(D)
N = symb.Nsn
#Ns = [len(v['S']) for v in D]; Nu = [len(v['U']) for v in D]
#Nw = [len(v['U']) + len(v['S']) for v in D]
Ns = [len(v) for v in symb.supernodes()]
Nu = [len(v) for v in symb.separators()]
Nw = [len(v) for v in symb.cliques()]
f = pylab.figure(); f.clf()
f.text(0.58,0.40,"Number of cliques: %i" % (len(Nw)))
f.text(0.61,0.40-1*0.07,"$\sum | W_i | = %i$" % (sum(Nw)))
f.text(0.61,0.40-2*0.07,"$\sum | V_i | = %i$" % (sum(Ns)))
f.text(0.61,0.40-3*0.07,"$\sum | U_i | = %i$" % (sum(Nu)))
f.text(0.61,0.40-4*0.07,"$\max_i\,| W_i | = %i$" % (max(Nw)))
pylab.subplot(221)
Nmax = max(Nw)
y = matrix(0,(Nmax,1))
for n in Nw :
y[n-1] += 1
y = sparse(y)
pylab.stem(y.I+1,y.V,'k'); pylab.xlim(0, Nmax+1)
pylab.title("Cliques")
Nmax = max(Nu)
y = matrix(0,(Nmax,1))
if Nmax > 0:
pylab.subplot(222)
for n in Nu :
y[n-1] += 1
y = sparse(y)
pylab.stem(y.I+1,y.V,'k'); pylab.xlim(0, Nmax+1)
pylab.title("Separators")
pylab.subplot(223)
Nmax = max(Ns)
y = matrix(0,(Nmax,1))
for n in Ns :
y[n-1] += 1
y = sparse(y)
pylab.stem(y.I+1,y.V,'k'); pylab.xlim(0, Nmax+1)
pylab.title("Residuals")
if file: pylab.savefig(file)
pi = pl.pi
t = pl.arange(0,end)
f = 100
amps = [1.,0,1./3,0,1./5,0,1./7,0,1./9.]
ph = -pi/2
s = pl.zeros(end)
pl.subplot(311)
pl.title("harmonics")
pl.xlim(0,end)
k = 1
for a in amps:
p = a*pl.cos(2*pi*f*k*t/sr + ph)
pl.plot(t, p)
s += p
k += 1
pl.subplot(312)
pl.title("square wave")
pl.xlim(0,end)
pl.plot(t, s)
pl.subplot(313)
pl.title("spectrum")
end = len(amps)+1
pl.xlim(0,end)
pl.ylim(0,1.1)
pl.stem(pl.arange(1,end),amps,markerfmt=" ")
pl.tight_layout()
pl.show()
def main():
"""Show simple use cases for functionality provided by this module. Each
example below attempts to mimic the examples provided by mathworks MATLAB
documentation, http://www.mathworks.com/help/toolbox/signal/
"""
import pylab
argv = sys.argv
if len(argv) != 1:
print >>sys.stderr, 'usage: python -m pim.sp.multirate'
sys.exit(2)
#Downsample
x = numpy.arange(1, 11)
print 'Down Sampling %s by 3' % x
print downsample(x, 3)
print 'Down Sampling %s by 3 with phase offset 2' % x
print downsample(x, 3, phase=2)
#Upsample
x = numpy.arange(1, 5)
print 'Up Sampling %s by 3' % x
print upsample(x, 3)
print 'Up Sampling %s by 3 with phase offset 2' % x
print upsample(x, 3, 2)
#Decimate
t = numpy.arange(0, 1, 0.00025)
x = numpy.sin(2*numpy.pi*30*t) + numpy.sin(2*numpy.pi*60*t)
y = decimate(x,4)
pylab.figure()
pylab.subplot(2, 1, 1)
pylab.title('Original Signal')
pylab.stem(numpy.arange(len(x[0:120])), x[0:120])
pylab.subplot(2, 1, 2)
pylab.title('Decimated Signal')
pylab.stem(numpy.arange(len(y[0:30])), y[0:30])
#Interp
t = numpy.arange(0, 1, 0.001)
x = numpy.sin(2*numpy.pi*30*t) + numpy.sin(2*numpy.pi*60*t)
y = interp(x,4)
pylab.figure()
pylab.subplot(2, 1, 1)
pylab.title('Original Signal')
pylab.stem(numpy.arange(len(x[0:30])), x[0:30])
pylab.subplot(2, 1, 2)
pylab.title('Interpolated Signal')
pylab.stem(numpy.arange(len(y[0:120])), y[0:120])
#upfirdn
L = 147.0
M = 160.0
N = 24.0*L
h = signal.firwin(N-1, 1/M, window=('kaiser', 7.8562))
h = L*h
Fs = 48000.0
n = numpy.arange(0, 10239)
x = numpy.sin(2*numpy.pi*1000/Fs*n)
y = upfirdn(x, h, L, M)
pylab.figure()
pylab.stem(n[1:49]/Fs, x[1:49])
pylab.stem(n[1:45]/(Fs*L/M), y[13:57], 'r', markerfmt='ro',)
pylab.xlabel('Time (sec)')
pylab.ylabel('Signal value')
#resample
fs1 = 10.0
t1 = numpy.arange(0, 1 + 1.0/fs1, 1.0/fs1)
x = t1
y = resample(x, 3, 2)
t2 = numpy.arange(0,(len(y)))*2.0/(3.0*fs1)
pylab.figure()
pylab.plot(t1, x, '*')
pylab.plot(t2, y, 'o')
pylab.plot(numpy.arange(-0.5,1.5, 0.01), numpy.arange(-0.5,1.5, 0.01), ':')
pylab.legend(('original','resampled'))
pylab.xlabel('Time')
x = numpy.hstack([numpy.arange(1,11), numpy.arange(9,0,-1)])
y = resample(x,3,2)
pylab.figure()
pylab.subplot(2, 1, 1)
pylab.title('Edge Effects Not Noticeable')
pylab.plot(numpy.arange(19)+1, x, '*')
pylab.plot(numpy.arange(29)*2/3.0 + 1, y, 'o')
pylab.legend(('original', 'resampled'))
x = numpy.hstack([numpy.arange(10, 0, -1), numpy.arange(2,11)])
y = resample(x,3,2)
pylab.subplot(2, 1, 2)
pylab.plot(numpy.arange(19)+1, x, '*')
pylab.plot(numpy.arange(29)*2/3.0 + 1, y, 'o')
pylab.title('Edge Effects Very Noticeable')
pylab.legend(('original', 'resampled'))
pylab.show()
return 0
while sample_points < len(sampled):
sampled[sample_points] = xa[sample_points]
sample_points = sample_points+ init
sampled1 = np.sin(2 * np.pi *f * t * 0)
print len(sampled1)
sample_points1 = ((1.0 * f)/fs2)*1000
init = sample_points1
while sample_points1< len(sampled1):
sampled1[sample_points1] = xa[sample_points1]
sample_points1 = sample_points1+ init
print sample_points1
# Putting in subplots
py.subplot(3, 1, 1)
py.plot(t, xa)
py.subplot(3, 1, 2)
py.stem(t, sampled,'-')
py.subplot(3, 1, 3)
py.stem(t, sampled1,'-')
py.ylabel('Amplitude(Normalized)',size='medium')
py.xlabel('Time(in ms)',size='medium')
py.savefig('ouputdifferent.png',dpi=(300))
py.close()
# Putting in a single graph
py.plot(t, xa,t, sampled,t,sampled1)
py.title('Sampled waveforms')
py.legend(['Waveform','3KHz Sampling','5KHz Sampling'])
py.xlabel("Time(ms)")
py.ylabel("Amplitude(normalized)")
py.savefig('outputcombined.png',dpi=(300))
py.close()
# Sampling in 15KHz
def main():
"""Show simple use cases for functionality provided by this module. Each
example below attempts to mimic the examples provided by mathworks MATLAB
documentation, http://www.mathworks.com/help/toolbox/signal/
"""
import pylab
argv = sys.argv
if len(argv) != 1:
print('usage: python -m pim.sp.multirate', file=sys.stderr)
sys.exit(2)
#Downsample
x = numpy.arange(1, 11)
print('Down Sampling %s by 3' % x)
print(downsample(x, 3))
print('Down Sampling %s by 3 with phase offset 2' % x)
print(downsample(x, 3, phase=2))
#Upsample
x = numpy.arange(1, 5)
print('Up Sampling %s by 3' % x)
print(upsample(x, 3))
print('Up Sampling %s by 3 with phase offset 2' % x)
print(upsample(x, 3, 2))
#Decimate
t = numpy.arange(0, 1, 0.00025)
x = numpy.sin(2 * numpy.pi * 30 * t) + numpy.sin(2 * numpy.pi * 60 * t)
y = decimate(x, 4)
pylab.figure()
pylab.subplot(2, 1, 1)
pylab.title('Original Signal')
pylab.stem(numpy.arange(len(x[0:120])), x[0:120])
pylab.subplot(2, 1, 2)
pylab.title('Decimated Signal')
pylab.stem(numpy.arange(len(y[0:30])), y[0:30])
#Interp
t = numpy.arange(0, 1, 0.001)
x = numpy.sin(2 * numpy.pi * 30 * t) + numpy.sin(2 * numpy.pi * 60 * t)
y = interp(x, 4)
pylab.figure()
pylab.subplot(2, 1, 1)
pylab.title('Original Signal')
pylab.stem(numpy.arange(len(x[0:30])), x[0:30])
pylab.subplot(2, 1, 2)
pylab.title('Interpolated Signal')
pylab.stem(numpy.arange(len(y[0:120])), y[0:120])
#upfirdn
L = 147.0
M = 160.0
N = 24.0 * L
h = signal.firwin(N - 1, 1 / M, window=('kaiser', 7.8562))
h = L * h
Fs = 48000.0
n = numpy.arange(0, 10239)
x = numpy.sin(2 * numpy.pi * 1000 / Fs * n)
y = upfirdn(x, h, L, M)
pylab.figure()
pylab.stem(n[1:49] / Fs, x[1:49])
pylab.stem(
n[1:45] / (Fs * L / M),
y[13:57],
'r',
markerfmt='ro',
)
pylab.xlabel('Time (sec)')
pylab.ylabel('Signal value')
#resample
fs1 = 10.0
t1 = numpy.arange(0, 1 + 1.0 / fs1, 1.0 / fs1)
x = t1
y = resample(x, 3, 2)
t2 = numpy.arange(0, (len(y))) * 2.0 / (3.0 * fs1)
pylab.figure()
pylab.plot(t1, x, '*')
pylab.plot(t2, y, 'o')
pylab.plot(numpy.arange(-0.5, 1.5, 0.01), numpy.arange(-0.5, 1.5, 0.01),
':')
pylab.legend(('original', 'resampled'))
pylab.xlabel('Time')
x = numpy.hstack([numpy.arange(1, 11), numpy.arange(9, 0, -1)])
y = resample(x, 3, 2)
pylab.figure()
pylab.subplot(2, 1, 1)
pylab.title('Edge Effects Not Noticeable')
pylab.plot(numpy.arange(19) + 1, x, '*')
pylab.plot(numpy.arange(29) * 2 / 3.0 + 1, y, 'o')
pylab.legend(('original', 'resampled'))
x = numpy.hstack([numpy.arange(10, 0, -1), numpy.arange(2, 11)])
y = resample(x, 3, 2)
pylab.subplot(2, 1, 2)
pylab.plot(numpy.arange(19) + 1, x, '*')
pylab.plot(numpy.arange(29) * 2 / 3.0 + 1, y, 'o')
pylab.title('Edge Effects Very Noticeable')
pylab.legend(('original', 'resampled'))
pylab.show()
return 0
wspec = whitening.process(spec)
pitch, saliency = pitchACF.process(wspec)
if interactivePlot:
pylab.subplot(211)
pylab.hold(False)
pylab.plot(wspec[0, :plotSize])
acorred = acorr.process(wspec)
pylab.subplot(212)
pylab.hold(False)
pylab.plot(acorred[0, :plotSize], label='Noise Suppressed Spectrum')
pylab.hold(True)
pylab.stem(pitch / sampleRate * fftSize, saliency)
specs.append(spec[0, :])
wspecs.append(wspec[0, :])
pitches.append(pitch)
saliencies.append(saliency)
if interactivePlot:
pylab.ioff()
specs = scipy.array(specs)
wspecs = scipy.array(wspecs)
pitches = scipy.array(pitches)[:, 0]
saliencies = scipy.array(saliencies)[:, 0]
frameCount = specs.shape[0] - 1
from pylab import hist, plot, show, stem, figure
# Sample two normal distributions
# and create a bi-modal distribution
rv1 = stats.norm()
rv2 = stats.norm(2.0, 0.8)
samples = hstack([rv1.rvs(size=100),
rv2.rvs(size=100)])
# Use a Gaussian kernel density to
# estimate the PDF for the samples.
approximate_pdf = gaussian_kde(samples)
x = linspace(-3, 6, 200)
# Compare the histogram of the samples to
# the PDF approximation.
figure(1)
hist(samples, bins=25, normed=True)
plot(x, approximate_pdf(x), 'r')
# Example 2: A bunch of points at 0, one at 1.
samples2 = [0.0]*10 + [1.0]
pdf2 = gaussian_kde(samples2)
x2 = linspace(-1.0, 2, 500)
figure(2)
plot(x2, pdf2(x2), 'r')
stem([0,1], [1, 0.1])
show()
'meraki_auto_dl'
]
fig = pylab.figure(figsize=(16,12))
lns = None
for log in logs:
wifi_log = "%s_wireless.log" % log
f = open(wifi_log,'r')
latencies = []
for line in f.readlines()[1:-1]:
vals = string.split(line,'|')
print vals[1]
try:
lat = float(vals[1])
except:
lat = -1.0
latencies.append(lat)
if lns:
lns += pylab.stem(range(0, len(latencies)), latencies,'-.', label=log)
else:
lns = pylab.stem(range(0, len(latencies)), latencies, '-.')
f.close()
#labels = [l.get_label() for l in lns]
pylab.xlabel('time (s)')
pylab.ylabel('Latency (ms)')
#pylab.legend(lns, labels)
pylab.grid()
pylab.title('WiFi Latency (%s)' % output)
pylab.savefig("%s.pdf" % output)
def main(N, M=1):
# Generate uniform noise (each column is a realization).
noise1 = uniform_noise(N, M, a=-1.7, b=1.7)
# Generate Gaussian noise (each column is a realization).
noise2 = gaussian_noise(N, M)
write_and_play(8192, noise1[:, 0], "noise1")
write_and_play(8192, noise2[:, 0], "noise2")
pl.figure()
pl.subplot(211)
pl.stem(noise1[:100, 0])
pl.ylabel("noise1")
pl.subplot(212)
pl.stem(noise2[:100, 0])
pl.ylabel("noise2")
pl.xlabel("samples")
Noise1 = numpy.fft.fft(noise1, n=2**nextpow2(N), axis=0)
Noise2 = numpy.fft.fft(noise2, n=2**nextpow2(N), axis=0)
psdNoise1 = numpy.mean(numpy.abs(Noise1)**2, 1) / N
psdNoise2 = numpy.mean(numpy.abs(Noise2)**2, 1) / N
pl.figure()
pl.subplot(211)
pl.plot(numpy.arange(len(psdNoise1))/len(psdNoise1), psdNoise1)
pl.ylim(0, 1.5)
pl.ylabel("psdNoise1")
pl.subplot(212)
pl.plot(numpy.arange(len(psdNoise2))/len(psdNoise2), psdNoise2)
pl.ylim(0, 1.5)
pl.ylabel("psdNoise2")
pl.xlabel("normalized frequencies")
pl.figure()
pl.subplot(211)
pl.hist(noise1[:, 0], bins=50)
pl.ylabel("noise1 recurrences")
pl.subplot(212)
pl.hist(noise2[:, 0], bins=50)
pl.ylabel("noise2 recurrences")
pl.xlabel("values")
# Leaky integrator (filter).
h = leaky_integrator()
H = numpy.fft.fft(h, 2**nextpow2(N))
absH2 = numpy.abs(H)**2
# Filter noise.
N2 = N -len(h) + 1
yy2 = numpy.zeros((N2, M))
for i in range(M):
yy2[:, i] = numpy.convolve(noise2[:, i], h, mode="valid")
write_and_play(8192, yy2[:, 0], "filtered_noise2")
psdY2 = numpy.mean(numpy.abs(numpy.fft.fft(
yy2, n=2**nextpow2(N2), axis=0))**2, 1) / N2
pl.figure()
pl.subplot(311)
pl.plot(numpy.arange(len(psdNoise2))/len(psdNoise2), psdNoise2)
pl.ylim(0, 1.5)
pl.ylabel("psdNoise2")
pl.subplot(312)
pl.plot(numpy.arange(len(absH2))/len(absH2), absH2)
pl.ylim(0, 1.5)
pl.ylabel("squareMagH")
pl.subplot(313)
pl.plot(numpy.arange(len(psdY2))/len(psdY2), psdY2)
pl.ylim(0, 1.5)
pl.ylabel("psdY2")
pl.xlabel("normalized frequencies")
pl.show()
X=np.asarray(all_data[0])
X=np.r_[X,X+3]
color_iter = itertools.cycle(['r', 'g', 'b', 'c', 'm'])
vbgmm=mixture.VBGMM(n_components=30, alpha=1.00,covariance_type='full')
vbgmm.fit(X)
Y_=vbgmm.predict(X)
pl.subplot(4,1,1)
pl.plot(X)
pl.ylabel('value')
pl.subplot(4,1,2)
pl.plot(vbgmm.weights_,'-s')
pl.ylabel('mixing prob')
pl.subplot(4,1,3)
pl.stem(vbgmm.means_, '-.')
pl.ylabel('means')
pl.xlabel('components')
pl.subplot(4,1,4)
for i, (mean, color) in enumerate(zip(vbgmm.means_, color_iter)):
if not np.any(Y_==i):
continue
(X_idx,)=(Y_==i).nonzero()
pl.plot(X_idx,X[Y_==i], color=color)
pl.ylabel('centroid')