def test5():
N = 1024
H = genfhilbert(N)
hc = fourier.ifft(H)
h0 = [samp.real for samp in hc]
#NOTE: h0 has the impulse response centered about sample 0
#Negative time is the second half!
h = h0[N//2:] + h0[0:N//2] + [h0[0]] # Number of samples becomes odd!
stemplot(h)
def measure_methods(self, stopwatch, fil_data, freqs, DM, scale):
"""
Run and time all methods/modules
"""
# clipping
time_clipping = timer()
_, _ = clipping.clipping(freqs, fil_data)
stopwatch['time_clipping'] = timer() - time_clipping
# dedisperse
time_dedisp = timer()
fil_data = dedisperse.dedisperse(fil_data, disperion_measure=DM)
stopwatch['time_dedisp'] = timer() - time_dedisp
# timeseries
time_t_series = timer()
time_series = timeseries.Timeseries(fil_data)
stopwatch['time_t_series'] = timer() - time_t_series
# downsample
time_downsamp = timer()
time_series = time_series.downsample(scale)
stopwatch['time_downsample'] = timer() - time_downsamp
# fft vect
time_fft_vect = timer()
fourier.fft_vectorized(time_series)
stopwatch['time_fft_vect'] = timer() - time_fft_vect
# dft
time_dft = timer()
fourier.dft_slow(time_series)
stopwatch['time_dft'] = timer() - time_dft
# ifft
time_ifft = timer()
fourier.ifft(time_series)
stopwatch['time_ifft'] = timer() - time_ifft
# fft freq
time_fft_freq = timer()
fourier.fft_freq(10)
stopwatch['time_fft_freq'] = timer() - time_fft_freq
return stopwatch
def fft_repack(avg_len, std_len, child_len, pow, c1, c2, a1, a2):
# Zero-pad c1 and c2 if necessary
c1.extend([0 for i in range(nextpow2(len(c1)) - len(c1))])
c2.extend([0 for i in range(nextpow2(len(c2)) - len(c2))])
# Invert fft
c1 = ifft(c1)
c2 = ifft(c2)
#print "Truncated"
c1 = c1[:child_len]
c2 = c2[:child_len]
# TODO -- try interpolating back down to a smaller (child_len) size?
#print "fft crossover from:", \
# len(org1['org'][0]), len(org2['org'][0]), \
# "to", len(c1), len(c2)
# Get rid of imaginary components...
c1 = [ele.real for ele in c1]
c2 = [ele.real for ele in c2]
c1, c2 = repack(c1, c2, a1, a2)
return c1, c2
def test6():
N = 1024
f = 10
signal = [math.sin(2*f*math.pi*x/N) for x in xrange(N)]
Fsignal = fourier.fft(signal)
H = genfhilbert(N)
HFsignal = [Fsignal[i]*H[i] for i in xrange(len(Fsignal))]
hsignalc = fourier.ifft(HFsignal)
hsignal = [samp.real for samp in hsignalc]
mag = [math.sqrt(signal[x]*signal[x] + hsignal[x]*hsignal[x]) for x in xrange(len(hsignal))]
fig, ax = pyplot.subplots(1)
ax.plot(hsignal,'-r')
ax.plot(signal,'-b')
ax.plot(mag,'-k')
pyplot.show()
def kernel(F, G, t=None):
assert len(F) == len(G), "Input arrays must have equal length"
if len(t) == 0: t = np.arange(len(F))
# Calculate the fourier transforms of F and G
FF, f = fft(F, t)
FG, _ = fft(G, t)
# Calculate the inverse fourier transform of the quotient
k, tt = ifft(FG / FF, f)
k = np.real(k)
# Sort results by time value
sort = np.argsort(tt)
k = k[sort]
tt = tt[sort]
return k, tt
def test9():
N = 128
H = genf2hilbert(N)
hc = fourier.ifft(H)
h0 = [samp.imag for samp in hc]
h = h0[N//2:] + h0[0:N//2] + [h0[0]]
print len(h)
stemplot(h)
#Signal
Nsig = 1024
f = 50
signal = [math.sin(2*f*math.pi*x/Nsig) for x in xrange(Nsig)]
hilbsign, origsign = convolution.convolveorig(h, N//2, signal)
mag = [math.sqrt(origsign[x]*origsign[x] + hilbsign[x]*hilbsign[x]) for x in xrange(len(hilbsign))]
fig, ax = pyplot.subplots(1)
ax.plot(hilbsign,'-r')
ax.plot(origsign,'-b')
ax.plot(mag,'-k')
pyplot.show()
def test10():
N = 1024
f = 25
dd = N/2
nn = N/10
signal = [math.exp(-((dd-x)/nn)**2/2)*math.sin(2*f*math.pi*x/N) for x in xrange(N)]
###
Fsignal = fourier.fft(signal)
H = genf2hilbert(N)
HFsignal = [Fsignal[i]*H[i] for i in xrange(len(Fsignal))]
hsignalc = fourier.ifft(HFsignal)
hsignal = [samp.imag for samp in hsignalc]
rsignal = [samp.real for samp in hsignalc]
mag = [abs(hsignalc[x]) for x in xrange(len(hsignalc))]
###
fig, ax = pyplot.subplots(1)
ax.plot(signal,'-b')
ax.plot(hsignal,'-r')
ax.plot(mag,'-k')
pyplot.show()
def test11():
N = 1024
f = 25
dd = N/2
nn = N/10
signal = [math.exp(-((dd-x)/nn)**2/2)*math.sin(2*f*math.pi*x/N) for x in xrange(N)]
###
Nhilb = 256
H = genf2hilbert(Nhilb)
hc = fourier.ifft(H)
h0 = [samp.imag for samp in hc]
h = h0[Nhilb//2:] + h0[0:Nhilb//2] + [h0[0]]
###
hsignal, origsig = convolution.convolveorig(h, Nhilb//2, signal)
mag = [math.sqrt(origsig[x]*origsig[x] + hsignal[x]*hsignal[x]) for x in xrange(len(hsignal))]
###
fig, ax = pyplot.subplots(1)
ax.plot(origsig,'-b')
ax.plot(hsignal,'-r')
ax.plot(mag,'-k')
pyplot.show()
def test7():
N = 1024
f = 20
signal = [math.sin(2*f*math.pi*x/N) for x in xrange(N)]
#signal = [0]*512 + [1] + [0]*511
t = [x/N for x in xrange(N)]
Nhilb = 128
H = genfhilbert(Nhilb)
hc = fourier.ifft(H)
h0 = [samp.real for samp in hc]
hilb = h0[Nhilb//2:] + h0[0:Nhilb//2] + [h0[0]]
print len(hilb)
hilbsign, origsign = convolution.convolveorig(hilb, 64, signal)
print len(origsign)
print len(hilbsign)
#fig, ax = pyplot.subplots(1)
#ax.plot(t, signal,'-')
#pyplot.show()
mag = [math.sqrt(origsign[x]*origsign[x] + hilbsign[x]*hilbsign[x]) for x in xrange(len(hilbsign))]
fig, ax = pyplot.subplots(1)
ax.plot(hilbsign,'-r')
ax.plot(origsign,'-b')
ax.plot(mag,'-k')
pyplot.show()
