def fft_based(input_signal, filter_coefficients, boundary=0):
"""applied fft if the signal is too short to be splitted in windows
Params :
input_signal : the audio signal
filter_coefficients : coefficients of the chirplet bank
boundary : manage the bounds of the signal
Returns :
audio signal with application of fast Fourier transform
"""
num_coeffs = filter_coefficients.size
half_size = num_coeffs//2
if boundary == 0:#ZERO PADDING
input_signal = np.lib.pad(input_signal, (half_size, half_size), 'constant', constant_values=0)
filter_coefficients = np.lib.pad(filter_coefficients, (0, input_signal.size-num_coeffs), 'constant', constant_values=0)
newx = ifft(fft(input_signal)*fft(filter_coefficients))
return newx[num_coeffs-1:-1]
elif boundary == 1:#symmetric
input_signal = concatenate([flipud(input_signal[:half_size]), input_signal, flipud(input_signal[half_size:])])
filter_coefficients = np.lib.pad(filter_coefficients, (0, input_signal.size-num_coeffs), 'constant', constant_values=0)
newx = ifft(fft(input_signal)*fft(filter_coefficients))
return newx[num_coeffs-1:-1]
else:#periodic
return roll(ifft(fft(input_signal)*fft(filter_coefficients, input_signal.size)), -half_size).real
def time_fft(data2, samplerate=100., inverse=False,hann=False):
'''
IF N_PARAMS() EQ 0 then begin
print, 'time_fft, data, samplerate=samplerate, inverse=inverse,hann=hann'
return, -1
ENDIF
'''
data=data2
if hann:
w1 = pl.hanning(len(data))
data = data*w1
#frequency axis:
freqs = pl.arange(1+len(data)/2)/float(len(data)/2.0)*samplerate/2. # wut.
if len(data) % 2 == 0 : freqs = pl.concatenate((freqs, -freqs[1:(len(freqs)-1)][::-1]))
if len(data) % 2 != 0 : freqs = pl.concatenate((freqs, -freqs[1:len(freqs)][::-1]))
response = pl.fft(data)
if inverse : response = pl.ifft(data)
out = {'freq': freqs, 'real': response.real, 'im': response.imag, 'abs': abs(response)}
return out
def decodefft(finf, data, dropheights=False):
#output: decoded data with the number of heights reduced
#two variables are added to the finfo class:
#deco_num_hei, deco_hrange
#data must be arranged:
# (channels,heights,times) (C-style, profs change faster)
#fft along the entire(n=None) acquired heights(axis=1), stores in data
num_chan = data.shape[0]
num_ipps = data.shape[2]
num_codes = finf.subcode.shape[0]
num_bauds = finf.subcode.shape[1]
NSA = finf.num_hei + num_bauds - 1
uppower = py.ceil(py.log2(NSA))
extra = int(2**uppower - finf.num_hei)
NSA = int(2**uppower)
fft_code = py.fft(finf.subcode, n=NSA, axis=1).conj()
data = py.fft(data, n=NSA,
axis=1) #n= None: no cropped data or padded zeros
for ch in range(num_chan):
for ipp in range(num_ipps):
code_i = ipp % num_codes
data[ch, :, ipp] = data[ch, :, ipp] * fft_code[code_i, :]
data = py.ifft(data, n=NSA, axis=1) #fft along the heightsm
if dropheights:
return data[:, :-extra - (num_bauds - 1), :]
else:
return data[:, :-extra, :]
def f( t, *args ):
for i,arg in enumerate(args): params[ free_params[i] ] = arg
tshift = params[-1]
ideal = fmodel( t, *args )
irf = cspline1d_eval( self.irf_generator, t-tshift, dx=self.irf_dt, x0=self.irf_t0 )
convoluted = pylab.real(pylab.ifft( pylab.fft(ideal)*pylab.fft(irf) )) # very small imaginary anyway
return convoluted
def decodefft(finf,data, dropheights = False):
#output: decoded data with the number of heights reduced
#two variables are added to the finfo class:
#deco_num_hei, deco_hrange
#data must be arranged:
# (channels,heights,times) (C-style, profs change faster)
#fft along the entire(n=None) acquired heights(axis=1), stores in data
num_chan = data.shape[0]
num_ipps = data.shape[2]
num_codes = finf.subcode.shape[0]
num_bauds = finf.subcode.shape[1]
NSA = finf.num_hei + num_bauds - 1
uppower = py.ceil(py.log2(NSA))
extra = int(2**uppower - finf.num_hei)
NSA = int(2**uppower)
fft_code = py.fft(finf.subcode,n = NSA,axis=1).conj()
data = py.fft(data,n=NSA,axis=1) #n= None: no cropped data or padded zeros
for ch in range(num_chan):
for ipp in range(num_ipps):
code_i = ipp % num_codes
data[ch,:,ipp] = data[ch,:,ipp] * fft_code[code_i,:]
data=py.ifft(data,n=NSA,axis=1) #fft along the heightsm
if dropheights:
return data[:,:-extra-(num_bauds-1),:]
else:
return data[:,:-extra,:]
def fft_smoothing(input_signal, sigma):
"""smooth the fast transform Fourier
Params :
input_signal : audio signal
sigma : relative to the length of the output signal
Returns :
a shorter and smoother signal
"""
size_signal = input_signal.size
#shorten the signal
new_size = int(floor(10.0 * size_signal * sigma))
half_new_size = new_size // 2
fftx = fft(input_signal)
short_fftx = []
for ele in fftx[:half_new_size]:
short_fftx.append(ele)
for ele in fftx[-half_new_size:]:
short_fftx.append(ele)
apodization_coefficients = generate_apodization_coeffs(
half_new_size, sigma, size_signal)
#apply the apodization coefficients
short_fftx[:half_new_size] *= apodization_coefficients
short_fftx[half_new_size:] *= flipud(apodization_coefficients)
realifftxw = ifft(short_fftx).real
return realifftxw
def my_transform(x,dir):
# my_transform - perform either FFT with energy conservation.
# Works on array of size (w,w,a,b) on the 2 first dimensions.
w = np.shape(x)[0]
if dir == 1 :
y = np.transpose(pyl.fft(np.transpose(x)))/np.sqrt(w)
else :
y = np.transpose(pyl.ifft(np.transpose(x)*np.sqrt(w)))
return y
def fast_fracdiff(x, d):
T = len(x)
np2 = int(2**np.ceil(np.log2(2 * T - 1)))
k = np.arange(1, T)
b = (1, ) + tuple(np.cumprod((k - d - 1) / k))
z = (0, ) * (np2 - T)
z1 = b + z
z2 = tuple(x) + z
dx = pl.ifft(pl.fft(z1) * pl.fft(z2))
return np.real(dx[0:T])
def FourierDerivative(f):
"""
this derivatie just works for periodic 2*pi multiple series
have to figure out how to make that work for any function
"""
N = np.size(f)
n = np.arange(0, N)
# df discrete differential operator
df = np.complex(0, 1) * py.fftshift(n - N / 2)
dfdt = py.ifft(df * py.fft(f))
return py.real(dfdt)
def FourierDerivative(f):
"""
this derivatie just works for periodic 2*pi multiple series
have to figure out how to make that work for any function
"""
N = np.size(f)
n = np.arange(0,N)
# df discrete differential operator
df = np.complex(0,1)*py.fftshift(n-N/2)
dfdt = py.ifft( df*py.fft(f) )
return py.real(dfdt)
def fast_fracdiff(x, cols, d):
for col in cols:
T = len(x[col])
np2 = int(2**np.ceil(np.log2(2 * T - 1)))
k = np.arange(1, T)
b = (1, ) + tuple(np.cumprod((k - d - 1) / k))
z = (0, ) * (np2 - T)
z1 = b + z
z2 = tuple(x[col]) + z
dx = pl.ifft(pl.fft(z1) * pl.fft(z2))
x[col + "_frac"] = np.real(dx[0:T])
return x
def _ConvFft(signal, FilterKernel):
"""
Convolution with fft much faster approach
works exactly as convolve(x,y)
"""
ss = numpy.size(signal);
fs = numpy.size(FilterKernel)
# padd zeros all until they have the size N+M-1
signal = numpy.append(signal, numpy.zeros(fs+ss-1-ss));
FilterKernel = numpy.append(FilterKernel, numpy.zeros(fs+ss-1-fs));
signal = pylab.real(pylab.ifft(pylab.fft(signal)*pylab.fft(FilterKernel)));
return signal[:fs+ss-1];
def _ConvFft(signal, filterkernel):
"""
Convolution with fft much faster approach
works exatcly as convolve(x,y)
"""
ss = numpy.size(signal)
fs = numpy.size(filterkernel)
# padd zeros all until they have the size N+M-1
signal = numpy.append(signal, numpy.zeros(fs + ss - 1 - ss))
filterkernel = numpy.append(filterkernel, numpy.zeros(fs + ss - 1 - fs))
signal = pylab.real(pylab.ifft(
pylab.fft(signal) * pylab.fft(filterkernel)))
return signal[:fs + ss - 1]
def __gauss(sacobj, Tn, alpha):
"""
Return envelope and gaussian filtered data
"""
import pylab as pl
data = pl.array(sacobj.data)
delta = sacobj.delta
Wn = 1 / float(Tn)
Nyq = 1 / (2 * delta)
old_size = data.size
pad_size = 2**(int(pl.log2(old_size)) + 1)
data.resize(pad_size)
spec = pl.fft(data)
spec.resize(pad_size)
W = pl.array(pl.linspace(0, Nyq, pad_size))
Hn = spec * pl.exp(-1 * alpha * ((W - Wn) / Wn)**2)
Qn = complex(0, 1) * Hn.real - Hn.imag
hn = pl.ifft(Hn).real
qn = pl.ifft(Qn).real
an = pl.sqrt(hn**2 + qn**2)
an.resize(old_size)
hn = hn[0:old_size]
return (an, hn)
def __gauss(sacobj, Tn, alpha):
"""
Return envelope and gaussian filtered data
"""
import pylab as pl
data = pl.array(sacobj.data)
delta = sacobj.delta
Wn = 1 / float(Tn)
Nyq = 1 / (2 * delta)
old_size = data.size
pad_size = 2**(int(pl.log2(old_size))+1)
data.resize(pad_size)
spec = pl.fft(data)
spec.resize(pad_size)
W = pl.array(pl.linspace(0, Nyq, pad_size))
Hn = spec * pl.exp(-1 * alpha * ((W-Wn)/Wn)**2)
Qn = complex(0,1) * Hn.real - Hn.imag
hn = pl.ifft(Hn).real
qn = pl.ifft(Qn).real
an = pl.sqrt(hn**2 + qn**2)
an.resize(old_size)
hn = hn[0:old_size]
return(an, hn)
def __init__(self,winSize,rate): self.twoPiJ=2.0*N.pi*complex(0,1) self.winSize=winSize self.chunkSize=winSize/2 self.hann=self._hanning() self.Hann=P.ifft(self.hann) self.rate=float(rate) self.freqT=rate/winSize self.nyquist=rate/2 self.binF = N.zeros(self.winSize,N.double) self.binF[0:self.winSize] = N.arange(0,rate,self.freqT) self.binFW = (self.binF+self.nyquist)%rate-self.nyquist
def InverseFT(shortft, Neven=False, fNyq=False, tOffset=0):
ftlist = [shortft.s1, shortft.s2, shortft.s3]
tslist = []
for ft in ftlist:
if ft.Offset1 == 0:
pftdata = ft.data
else:
pftdata = numpy.array([0] + list(ft.data))
if Neven == False:
nftdata = numpy.conj(numpy.flipud(pftdata))[:-1]
ftdata = numpy.concatenate((pftdata, nftdata))
elif (Neven, fNyq) == (True, True):
nftdata = numpy.conj(numpy.flipud(pftdata))[1:-1]
ftdata = numpy.concatenate((pftdata, nftdata))
elif (Neven, fNyq) == (True, False):
nftdata = numpy.conj(numpy.flipud(pftdata))[:-1]
ftdata = numpy.concatenate((pftdata, numpy.array([0]), nftdata))
N = ftdata.shape[0]
dt = 1. / (N * ft.Cadence1)
norm = numpy.sqrt(N / (2. * dt))
tsdata = pylab.ifft(norm * ftdata)
tsdata = numpy.real(tsdata)
tslist += [
Utilities3.Coarsable(data=tsdata, Offset1=tOffset, Cadence1=dt)
]
tsdict = {}
tsdict['s1'], tsdict['s2'], tsdict['s3'] = tslist[0], tslist[1], tslist[2]
return TimeSeries(**tsdict)
def detrend(data,detrend_Kernel_Length = 10,sampling_Frequency = 100000,channels = 8):
from pylab import fft, ifft, sin , cos,log,plot,show,conj,legend
import random
n=len(data[0])
detrend_fft_Length = (2**((log(detrend_Kernel_Length * sampling_Frequency)/log(2))))
ma = [1.0]*sampling_Frequency
ma.extend([0.0]*(detrend_fft_Length - sampling_Frequency))
mafft = fft(ma)
trend = [0.0]*n
for nch in range(channels):
count = 0
while count + detrend_fft_Length <= len(data[nch]):
temp = data[nch][count:count+int(detrend_fft_Length)]
y = fft(temp)
z = ifft( conj(mafft)*y)
for cc in xrange(count,count+(int(detrend_fft_Length)-sampling_Frequency)):
trend[cc] = z[cc-count].real / sampling_Frequency
count = count+(int(detrend_fft_Length)-sampling_Frequency)
for cc in xrange(len(trend)):
data[nch][cc] = data[nch][cc] - trend[cc]
def InverseFT( shortft , Neven=False , fNyq=False , tOffset=0 ):
ftlist = [ shortft.s1 , shortft.s2 , shortft.s3 ]
tslist = []
for ft in ftlist:
if ft.Offset1 == 0:
pftdata = ft.data
else:
pftdata = numpy.array( [0] + list( ft.data ) )
if Neven == False:
nftdata = numpy.conj( numpy.flipud( pftdata ) )[:-1]
ftdata = numpy.concatenate( ( pftdata , nftdata ) )
elif ( Neven , fNyq ) == ( True , True ):
nftdata = numpy.conj( numpy.flipud( pftdata ) )[1:-1]
ftdata = numpy.concatenate( ( pftdata , nftdata ) )
elif ( Neven , fNyq ) == ( True , False ):
nftdata = numpy.conj( numpy.flipud( pftdata ) )[:-1]
ftdata = numpy.concatenate( ( pftdata , numpy.array( [0] ) , nftdata ) )
N = ftdata.shape[0]
dt = 1. / ( N * ft.Cadence1 )
norm = numpy.sqrt( N / ( 2.*dt ) )
tsdata = pylab.ifft( norm * ftdata )
tsdata = numpy.real( tsdata )
tslist += [ Utilities3.Coarsable( data=tsdata , Offset1=tOffset , Cadence1=dt ) ]
tsdict = {}
tsdict['s1'] , tsdict['s2'] , tsdict['s3'] = tslist[0] , tslist[1] , tslist[2]
return TimeSeries( **tsdict )
def perform_convolution(x,h,bound="sym"):
"""
perform_convolution - compute convolution with centered filter.
y = perform_convolution(x,h,bound);
The filter 'h' is centred at 0 for odd
length of the filter, and at 1/2 otherwise.
This works either for 1D or 2D convolution.
For 2D the matrix have to be square.
'bound' is either 'per' (periodic extension)
or 'sym' (symmetric extension).
Copyright (c) 2004 Gabriel Peyre
"""
if bound not in ["sym", "per"]:
raise Exception('bound should be sym or per')
if np.ndim(x) == 3 and np.shape(x)[2] < 4:
#for color images
y = x;
for i in range(np.shape(x)[2]):
y[:,:,i] = perform_convolution(x[:,:,i],h, bound)
return y
if np.ndim(x) == 3 and np.shape(x)[2] >= 4:
raise Exception('Not yet implemented for 3D array, use smooth3 instead.')
n = np.shape(x)
p = np.shape(h)
nd = np.ndim(x)
if nd == 1:
n = len(x)
p = len(h)
if bound == 'sym':
#################################
# symmetric boundary conditions #
raise Exception('Not yet implemented')
else:
################################
# periodic boundary conditions #
if p > n:
raise Exception('h filter should be shorter than x.')
n = np.asarray(n)
p = np.asarray(p)
d = np.floor((p-1)/2.)
if nd == 1:
h = np.vstack((h[d:],np.vstack((np.zeros(n-p),h[:d]))))
y = np.real(pyl.ifft(pyl.fft(x)*pyl.fft(h)))
else:
h = np.vstack((h[d[0]:,:],np.vstack((np.zeros([n[0]-p[0],p[1]]),h[:(d[0]),:]))))
h = np.hstack((h[:,d[1]:],np.hstack((np.zeros([n[0],n[1]-p[1]]),h[:,:(d[1])]))))
y = np.real(pyl.ifft2(pyl.fft2(x)*pyl.fft2(h)))
return y
T=nFFT/rate f=1000.0 s=Spectral(nFFT,rate) nFrag=7 y=N.zeros(nFrag*fragSize,N.double) X1=s.freqVectH(f,0) D=s.deltaFF(f,T/2.0) for i in range(nFrag-1): chunk=N.real(P.ifft(X1)) y[i*fragSize:i*fragSize+nFFT] += chunk X1=X1*D*.8 # X2=s.Hann # X1 *= s.shiftVec(T/2) from matplotlib.pyplot import * plot(y) show()
def autoCorr(self, timeSeries): self.N = len(timeSeries) self.nfft = int(2 ** math.ceil(math.log(abs(self.N),2))) self.ACF = p.ifft(p.fft(timeSeries,self.nfft) * p.conjugate(p.fft(timeSeries,self.nfft))) self.ACF = list(p.real(self.ACF[:int(math.ceil((self.nfft+1)/2.0))])) self.plotAutoCorr()
def unweight2d(self, data, ov, bw):
print(" Applying UNWEIGHT with ov=[" + str(ov[0]) + "," + str(ov[1]) +
"] ... ")
n0 = data.shape[0]
n1 = data.shape[1]
# Percentage -> Pixels, secure having integers
#------------------------------------------------------------
bw0 = int(np.floor((bw[0] * n0 / 100.) / 2) * 2) # even integer
bw1 = int(np.floor((bw[1] * n1 / 100.) / 2) * 2) # even integer
ov0 = int(np.floor(ov[0]))
ov1 = int(np.floor(ov[1]))
#------------------------------------------------------------
spec0 = py.fft2(data)
spec0 = np.roll(spec0, data.shape[0] / 2, axis=0)
spec0 = np.roll(spec0, data.shape[1] / 2, axis=1)
# Hamming at processed bandwidth
#-----------------------------------------------
if 1:
t0 = np.arange(bw0) / float(bw0)
t1 = np.arange(bw1) / float(bw1)
hamming0 = 0.54 - 0.46 * np.cos(2 * np.pi * t0)
hamming1 = 0.54 - 0.46 * np.cos(2 * np.pi * t1)
unham0 = np.zeros(n0)
unham1 = np.zeros(n1)
unham0[n0 / 2 - bw0 / 2:n0 / 2 + bw0 / 2] = hamming0
unham1[n1 / 2 - bw1 / 2:n1 / 2 + bw1 / 2] = hamming1
#-----------------------------------------------
spec0_profile0 = np.abs(spec0).mean(axis=1)
maxv0 = 0.95 * np.max(np.abs(spec0_profile0))
spec0_profile1 = np.abs(spec0).mean(axis=0)
maxv1 = 0.95 * np.max(np.abs(spec0_profile1))
# Remove doppler shift and range spectrum shift
#------------------------------------------------------------------------------------------------------
corr0 = np.abs(
py.ifft(
py.fft(np.abs(spec0_profile0)) *
np.conj(py.fft(np.abs(unham0)))))
corr1 = np.abs(
py.ifft(
py.fft(np.abs(spec0_profile1)) *
np.conj(py.fft(np.abs(unham1)))))
peak0 = np.where(abs(corr0) == np.max(abs(corr0)))
off0 = n0 - peak0[0]
peak1 = np.where(abs(corr1) == np.max(abs(corr1)))
off1 = n1 - peak1[0]
spec0 = np.roll(spec0, off0, axis=0)
spec0 = np.roll(spec0, off1, axis=1)
spec0_profile0 = np.abs(spec0).mean(axis=1)
maxv0 = 0.95 * np.max(np.abs(spec0_profile0))
spec0_profile1 = np.abs(spec0).mean(axis=0)
maxv1 = 0.95 * np.max(np.abs(spec0_profile1))
#------------------------------------------------------------------------------------------------------
# Replace Unhamming filter by profile filter
#------------------------------------------------------------------------------
if 1:
unham0 = self.smooth(spec0_profile0 / maxv0, window_len=11)
unham1 = self.smooth(spec0_profile1 / maxv1, window_len=11)
#------------------------------------------------------------------------------
# Show profiles
#------------------------------------------------
show_plots = False
if show_plots:
plt.plot(spec0_profile0, 'k-', lw=1, color='blue')
plt.show()
plt.plot(spec0_profile1, 'k-', lw=1, color='red')
plt.show()
#------------------------------------------------
# Compare profiles to hamming filter
#----------------------------------------------------------------------------------------------------------------
if show_plots:
plt.plot(spec0_profile0, 'k-', lw=1, color='blue')
plt.plot(self.smooth(spec0_profile0, window_len=21),
'k-',
lw=1,
color='green')
plt.plot(maxv0 * unham0, 'k--', lw=1, color='red')
plt.show()
plt.plot(spec0_profile1, 'k-', lw=1, color='blue')
plt.plot(self.smooth(spec0_profile1, window_len=21),
'k-',
lw=1,
color='green')
plt.plot(maxv1 * unham1, 'k--', lw=1, color='red')
plt.show()
plt.plot(spec0_profile0[n0 / 2 - bw0 / 2:n0 / 2 + bw0 / 2],
'k-',
lw=1,
color='blue')
plt.plot(maxv0 * unham0[n0 / 2 - bw0 / 2:n0 / 2 + bw0 / 2],
'k-',
lw=1,
color='red')
plt.show()
plt.plot(spec0_profile1[n1 / 2 - bw1 / 2:n1 / 2 + bw1 / 2],
'k-',
lw=1,
color='blue')
plt.plot(maxv1 * unham1[n1 / 2 - bw1 / 2:n1 / 2 + bw1 / 2],
'k-',
lw=1,
color='red')
plt.show()
plt.plot(spec0_profile0[n0 / 2 - bw0 / 2:n0 / 2 + bw0 / 2] /
(maxv0 * unham0[n0 / 2 - bw0 / 2:n0 / 2 + bw0 / 2]),
'k-',
lw=1,
color='blue')
plt.show()
plt.plot(spec0_profile1[n1 / 2 - bw1 / 2:n1 / 2 + bw1 / 2] /
(maxv1 * unham1[n1 / 2 - bw1 / 2:n1 / 2 + bw1 / 2]),
'k-',
lw=1,
color='blue')
plt.show()
#----------------------------------------------------------------------------------------------------------------
# Unhamming
#------------------------------------------------------------------
#print " mean ..."+str(np.mean(abs(spec0)))
#print " Unhamming ..."
for k in range(0, n1):
spec0[n0 / 2 - bw0 / 2:n0 / 2 + bw0 / 2,
k] /= unham0[n0 / 2 - bw0 / 2:n0 / 2 + bw0 / 2] # range (y)
for k in range(0, n0):
spec0[k, n1 / 2 - bw1 / 2:n1 / 2 +
bw1 / 2] /= unham1[n1 / 2 - bw1 / 2:n1 / 2 +
bw1 / 2] # azimuth (x)
#print " Unhamming done."
#print " mean ..."+str(np.mean(abs(spec0)))
#------------------------------------------------------------------
# Show profiles
#------------------------------------------------
if show_plots:
abs_spec0 = np.abs(spec0)
spec0_profile0 = abs_spec0.sum(axis=1)
spec0_profile1 = abs_spec0.sum(axis=0)
plt.plot(spec0_profile0, 'k-', lw=1, color='blue')
plt.show()
plt.plot(spec0_profile1, 'k-', lw=1, color='red')
plt.show()
#------------------------------------------------
spec0 = np.roll(-spec0, data.shape[0] / 2, axis=0)
spec0 = np.roll(-spec0, data.shape[1] / 2, axis=1)
# Zero padding
#--------------------------------------------------------------------------------------
n0 = spec0.shape[0]
n1 = spec0.shape[1]
zeros0 = np.zeros((bw0 * (ov0 - 1), n1), float) + 1j * np.zeros(
(bw0 * (ov0 - 1), n1), float)
spec1 = np.concatenate(
(spec0[0:bw0 / 2, :], zeros0, spec0[-bw0 / 2:, :]), axis=0) * ov0
n0 = spec1.shape[0]
n1 = spec1.shape[1]
zeros1 = np.zeros((n0, bw1 * (ov1 - 1)), float) + 1j * np.zeros(
(n0, bw1 * (ov1 - 1)), float)
spec2 = np.concatenate(
(spec1[:, 0:bw1 / 2], zeros1, spec1[:, -bw1 / 2:]), axis=1) * ov1
#--------------------------------------------------------------------------------------
# Show zeros padding results
#--------------------------------------------------------------------------------
'''
plt.imshow(np.abs(spec0), origin='lower', interpolation='none', cmap=plt.cm.BuGn)
plt.show()
plt.imshow(np.abs(spec1), origin='lower', interpolation='none', cmap=plt.cm.BuGn)
plt.show()
plt.imshow(np.abs(spec2), origin='lower', interpolation='none', cmap=plt.cm.BuGn)
plt.show()
'''
#--------------------------------------------------------------------------------
data = py.ifft2(spec2)
print(" Applying UNWEIGHT with ov=[" + str(ov[0]) + "," + str(ov[1]) +
"] done. ")
return data
for i in range(winSize):
R[i]=N.exp(j*N.pi*i)
yChunk=s.tVect()
y=N.zeros(samples,N.float)
player= player.Player()
nChunks = int(samples/chunkSize)
w=s.hanning()
W=P.fft(w)
P.plot(abs(W))
P.show()
for i in range(nChunks-1):
i1=i*chunkSize
i2=i1+winSize
z=N.double(P.ifft(X1))
y[i1:i2] += z*w
X1 *= R
player.play(y)
import pylab from math import pi, sin from conv import conv, noise, plot N = 128 # number of taps ff = 20 # frequency of filter f1 = 10 # frequency of first sine f2 = 50 # frequency of second sine t = 8 # number of taps in filter # create FIR mask mask = [1.0]*ff + [0.0]*(N-ff) # create FIR template temp = abs(pylab.ifft(mask)) # truncate, mirror template filt = [temp[i] for i in range (8,0,-1)] filt += [temp[i] for i in range (0,9,+1)] # use it x = [(sin (2.0*pi*f1*i/N) + sin (2.0*pi*f2*i/N)) for i in range (N)] y = conv (x, filt)[:N] # plot FFT before & after F = abs(pylab.fft(x)) G = abs(pylab.fft(y)) # plot all pylab.close (5) pylab.figure (5)
def perform_convolution(x, h, bound="sym"):
"""
perform_convolution - compute convolution with centered filter.
y = perform_convolution(x,h,bound);
The filter 'h' is centred at 0 for odd
length of the filter, and at 1/2 otherwise.
This works either for 1D or 2D convolution.
For 2D the matrix have to be square.
'bound' is either 'per' (periodic extension)
or 'sym' (symmetric extension).
Copyright (c) 2004 Gabriel Peyre
"""
if bound not in ["sym", "per"]:
raise Exception('bound should be sym or per')
if np.ndim(x) == 3 and np.shape(x)[2] < 4:
#for color images
y = x
for i in range(np.shape(x)[2]):
y[:, :, i] = perform_convolution(x[:, :, i], h, bound)
return y
if np.ndim(x) == 3 and np.shape(x)[2] >= 4:
raise Exception(
'Not yet implemented for 3D array, use smooth3 instead.')
n = np.shape(x)
p = np.shape(h)
nd = np.ndim(x)
if nd == 1:
n = len(x)
p = len(h)
if bound == 'sym':
#################################
# symmetric boundary conditions #
d1 = np.asarray(p).astype(int) / 2 # padding before
d2 = p - d1 - 1 # padding after
if nd == 1:
################################# 1D #################################
nx = len(x)
xx = np.vstack((x[d1:-1:-1], x, x[nx - 1:nx - d2 - 1:-1]))
y = signal.convolve(xx, h)
y = y[p:nx - p - 1]
elif nd == 2:
################################# 2D #################################
#double symmetry
nx, ny = np.shape(x)
xx = x
xx = np.vstack(
(xx[d1[0]:-1:-1, :], xx, xx[nx - 1:nx - d2[0] - 1:-1, :]))
xx = np.hstack(
(xx[:, d1[1]:-1:-1], xx, xx[:, ny - 1:ny - d2[1] - 1:-1]))
y = signal.convolve2d(xx, h, mode="same")
y = y[(2 * d1[0]):(2 * d1[0] + n[0] + 1),
(2 * d1[1]):(2 * d1[1] + n[1] + 1)]
else:
################################
# periodic boundary conditions #
if p > n:
raise Exception('h filter should be shorter than x.')
n = np.asarray(n)
p = np.asarray(p)
d = np.floor((p - 1) / 2.)
if nd == 1:
h = np.vstack((h[d:], np.vstack((np.zeros(n - p), h[:d]))))
y = np.real(pyl.ifft(pyl.fft(x) * pyl.fft(h)))
else:
h = np.vstack((h[int(d[0]):, :],
np.vstack((np.zeros([n[0] - p[0],
p[1]]), h[:int(d[0]), :]))))
h = np.hstack(
(h[:, int(d[1]):],
np.hstack((np.zeros([n[0], n[1] - p[1]]), h[:, :int(d[1])]))))
y = np.real(pyl.ifft2(pyl.fft2(x) * pyl.fft2(h)))
return y
def unweight2d(self, data, ov, bw):
print(" Applying UNWEIGHT with ov=["+str(ov[0])+","+str(ov[1])+"] ... ")
n0 = data.shape[0]
n1 = data.shape[1]
# Percentage -> Pixels, secure having integers
#------------------------------------------------------------
bw0 = int(np.floor( (bw[0]*n0/100.) /2) * 2) # even integer
bw1 = int(np.floor( (bw[1]*n1/100.) /2) * 2) # even integer
ov0 = int(np.floor(ov[0]))
ov1 = int(np.floor(ov[1]))
#------------------------------------------------------------
spec0 = py.fft2(data)
spec0 = np.roll(spec0,data.shape[0]/2, axis=0)
spec0 = np.roll(spec0,data.shape[1]/2, axis=1)
# Hamming at processed bandwidth
#-----------------------------------------------
if 1:
t0 = np.arange(bw0)/float(bw0)
t1 = np.arange(bw1)/float(bw1)
hamming0 = 0.54-0.46*np.cos(2*np.pi*t0)
hamming1 = 0.54-0.46*np.cos(2*np.pi*t1)
unham0 = np.zeros(n0)
unham1 = np.zeros(n1)
unham0[n0/2-bw0/2:n0/2+bw0/2] = hamming0
unham1[n1/2-bw1/2:n1/2+bw1/2] = hamming1
#-----------------------------------------------
spec0_profile0 = np.abs(spec0).mean(axis=1); maxv0 = 0.95 * np.max(np.abs(spec0_profile0))
spec0_profile1 = np.abs(spec0).mean(axis=0); maxv1 = 0.95 * np.max(np.abs(spec0_profile1))
# Remove doppler shift and range spectrum shift
#------------------------------------------------------------------------------------------------------
corr0 = np.abs( py.ifft( py.fft(np.abs(spec0_profile0)) * np.conj(py.fft(np.abs(unham0))) ))
corr1 = np.abs( py.ifft( py.fft(np.abs(spec0_profile1)) * np.conj(py.fft(np.abs(unham1))) ))
peak0 = np.where(abs(corr0) == np.max(abs(corr0))); off0 = n0 - peak0[0]
peak1 = np.where(abs(corr1) == np.max(abs(corr1))); off1 = n1 - peak1[0]
spec0 = np.roll(spec0, off0, axis=0)
spec0 = np.roll(spec0, off1, axis=1)
spec0_profile0 = np.abs(spec0).mean(axis=1); maxv0 = 0.95 * np.max(np.abs(spec0_profile0))
spec0_profile1 = np.abs(spec0).mean(axis=0); maxv1 = 0.95 * np.max(np.abs(spec0_profile1))
#------------------------------------------------------------------------------------------------------
# Replace Unhamming filter by profile filter
#------------------------------------------------------------------------------
if 1:
unham0 = self.smooth(spec0_profile0 / maxv0, window_len=11)
unham1 = self.smooth(spec0_profile1 / maxv1, window_len=11)
#------------------------------------------------------------------------------
# Show profiles
#------------------------------------------------
show_plots = False
if show_plots:
plt.plot(spec0_profile0,'k-', lw=1, color='blue')
plt.show()
plt.plot(spec0_profile1,'k-', lw=1, color='red')
plt.show()
#------------------------------------------------
# Compare profiles to hamming filter
#----------------------------------------------------------------------------------------------------------------
if show_plots:
plt.plot(spec0_profile0,'k-', lw=1, color='blue')
plt.plot(self.smooth(spec0_profile0,window_len=21),'k-', lw=1, color='green')
plt.plot(maxv0 * unham0,'k--', lw=1, color='red')
plt.show()
plt.plot(spec0_profile1,'k-', lw=1, color='blue')
plt.plot(self.smooth(spec0_profile1,window_len=21),'k-', lw=1, color='green')
plt.plot(maxv1 * unham1,'k--', lw=1, color='red')
plt.show()
plt.plot(spec0_profile0[n0/2-bw0/2:n0/2+bw0/2],'k-', lw=1, color='blue')
plt.plot(maxv0 * unham0[n0/2-bw0/2:n0/2+bw0/2],'k-', lw=1, color='red')
plt.show()
plt.plot(spec0_profile1[n1/2-bw1/2:n1/2+bw1/2], 'k-', lw=1, color='blue')
plt.plot(maxv1 * unham1[n1/2-bw1/2:n1/2+bw1/2], 'k-', lw=1, color='red')
plt.show()
plt.plot(spec0_profile0[n0/2-bw0/2:n0/2+bw0/2] / (maxv0 * unham0[n0/2-bw0/2:n0/2+bw0/2]),'k-', lw=1, color='blue')
plt.show()
plt.plot(spec0_profile1[n1/2-bw1/2:n1/2+bw1/2] / (maxv1 * unham1[n1/2-bw1/2:n1/2+bw1/2]),'k-', lw=1, color='blue')
plt.show()
#----------------------------------------------------------------------------------------------------------------
# Unhamming
#------------------------------------------------------------------
#print " mean ..."+str(np.mean(abs(spec0)))
#print " Unhamming ..."
for k in range(0,n1):
spec0[n0/2-bw0/2:n0/2+bw0/2,k] /= unham0[n0/2-bw0/2:n0/2+bw0/2] # range (y)
for k in range(0,n0):
spec0[k,n1/2-bw1/2:n1/2+bw1/2] /= unham1[n1/2-bw1/2:n1/2+bw1/2] # azimuth (x)
#print " Unhamming done."
#print " mean ..."+str(np.mean(abs(spec0)))
#------------------------------------------------------------------
# Show profiles
#------------------------------------------------
if show_plots:
abs_spec0 = np.abs(spec0)
spec0_profile0 = abs_spec0.sum(axis=1)
spec0_profile1 = abs_spec0.sum(axis=0)
plt.plot(spec0_profile0,'k-', lw=1, color='blue')
plt.show()
plt.plot(spec0_profile1,'k-', lw=1, color='red')
plt.show()
#------------------------------------------------
spec0 = np.roll(-spec0,data.shape[0]/2, axis=0)
spec0 = np.roll(-spec0,data.shape[1]/2, axis=1)
# Zero padding
#--------------------------------------------------------------------------------------
n0 = spec0.shape[0]
n1 = spec0.shape[1]
zeros0 = np.zeros((bw0 * (ov0-1),n1),float) + 1j * np.zeros((bw0 * (ov0-1),n1),float)
spec1 = np.concatenate( (spec0[0:bw0/2,:], zeros0, spec0[-bw0/2:,:]), axis=0) * ov0
n0 = spec1.shape[0]
n1 = spec1.shape[1]
zeros1 = np.zeros((n0,bw1 * (ov1-1)),float) + 1j * np.zeros((n0,bw1 * (ov1-1)),float)
spec2 = np.concatenate( (spec1[:,0:bw1/2], zeros1, spec1[:,-bw1/2:]), axis=1) * ov1
#--------------------------------------------------------------------------------------
# Show zeros padding results
#--------------------------------------------------------------------------------
'''
plt.imshow(np.abs(spec0), origin='lower', interpolation='none', cmap=plt.cm.BuGn)
plt.show()
plt.imshow(np.abs(spec1), origin='lower', interpolation='none', cmap=plt.cm.BuGn)
plt.show()
plt.imshow(np.abs(spec2), origin='lower', interpolation='none', cmap=plt.cm.BuGn)
plt.show()
'''
#--------------------------------------------------------------------------------
data = py.ifft2(spec2)
print(" Applying UNWEIGHT with ov=["+str(ov[0])+","+str(ov[1])+"] done. ")
return data
def build_fft(input_signal,
filter_coefficients,
threshold_windows=6,
boundary=0):
"""generate fast transform fourier by windows
Params :
input_signal : the audio signal
filter_coefficients : coefficients of the chirplet bank
threshold_windows : calcul the size of the windows
boundary : manage the bounds of the signal
Returns :
fast Fourier transform applied by windows to the audio signal
"""
num_coeffs = filter_coefficients.size
#print(n,boundary,M)
half_size = num_coeffs // 2
signal_size = input_signal.size
#power of 2 to apply fast fourier transform
windows_size = 2**ceil(log2(num_coeffs * (threshold_windows + 1)))
number_of_windows = floor(signal_size // windows_size)
if number_of_windows == 0:
return fft_based(input_signal, filter_coefficients, boundary)
windowed_fft = empty_like(input_signal)
#pad with 0 to have a size in a power of 2
windows_size = int(windows_size)
zeropadding = np.lib.pad(filter_coefficients,
(0, windows_size - num_coeffs),
'constant',
constant_values=0)
h_fft = fft(zeropadding)
#to browse the whole signal
current_pos = 0
#apply fft to a part of the signal. This part has a size which is a power
#of 2
if boundary == 0: #ZERO PADDING
#window is half padded with since it's focused on the first half
window = input_signal[current_pos:current_pos + windows_size -
half_size]
zeropaddedwindow = np.lib.pad(window, (len(h_fft) - len(window), 0),
'constant',
constant_values=0)
x_fft = fft(zeropaddedwindow)
elif boundary == 1: #SYMMETRIC
window = concatenate([
flipud(input_signal[:half_size]),
input_signal[current_pos:current_pos + windows_size - half_size]
])
x_fft = fft(window)
else:
x_fft = fft(input_signal[:windows_size])
windowed_fft[:windows_size - num_coeffs] = (ifft(
x_fft * h_fft)[num_coeffs - 1:-1]).real
current_pos += windows_size - num_coeffs - half_size
#apply fast fourier transofm to each windows
while current_pos + windows_size - half_size <= signal_size:
x_fft = fft(input_signal[current_pos - half_size:current_pos +
windows_size - half_size])
#Suppress the warning, work on the real/imagina
windowed_fft[current_pos:current_pos + windows_size -
num_coeffs] = (ifft(x_fft * h_fft)[num_coeffs -
1:-1]).real
current_pos += windows_size - num_coeffs
# print(countloop)
#apply fast fourier transform to the rest of the signal
if windows_size - (signal_size - current_pos + half_size) < half_size:
window = input_signal[current_pos - half_size:]
zeropaddedwindow = np.lib.pad(
window,
(0, int(windows_size - (signal_size - current_pos + half_size))),
'constant',
constant_values=0)
x_fft = fft(zeropaddedwindow)
windowed_fft[current_pos:] = roll(ifft(
x_fft * h_fft), half_size)[half_size:half_size +
windowed_fft.size - current_pos].real
windowed_fft[-half_size:] = convolve(input_signal[-num_coeffs:],
filter_coefficients,
'same')[-half_size:]
else:
window = input_signal[current_pos - half_size:]
zeropaddedwindow = np.lib.pad(
window,
(0, int(windows_size - (signal_size - current_pos + half_size))),
'constant',
constant_values=0)
x_fft = fft(zeropaddedwindow)
windowed_fft[current_pos:] = ifft(
x_fft * h_fft)[num_coeffs - 1:num_coeffs + windowed_fft.size -
current_pos - 1].real
return windowed_fft
def create_interf(freq,resp,band=[], plt=False,sav=False, res=1.0, two=False):
'''
print, "create_interf, freq, resp, tc=tc, plt=plt,sav=sav, band=band, res=res, bw=bw, two=two"
print, "freq, resp - put in your own frequency and response data"
print, "/plt plots the band pass and interferrogram"
print, "/sav saves the interferrogram to a text file"
print, "band = band, res=res, /bw - use these to create freq/resp band with create_band"
print, "/two - put 2 interferrograms in a row"
return, 0
'''
# def where_closest(value,array):
# abs_diff = pl.array(abs(array-value))
# wh=pl.where(abs_diff == min(abs_diff))[0]
# wh_closest = abs_diff[wh]
# return wh_closest
if len(band) != 0:
r = create_band(band, res)
freq = r['Freq']
resp = r['resp']
if band[1] == band[0]:
resp = pl.zeros(len(freq))
k = where_closest(band[0], freq)
resp[k[0]] = 1.0
#if freq(0) != 0 then return with warning!
if freq[0] != 0:
print 'Must go down to zero frequency'
return -1
#Let's be careful with these n's
#From DFanning
#Let N=8, N/2 = 4, then F_ns for 0,1,2,3,4, -3,-2,-1 NOTE: no -4!
n = pl.arange(len(freq)/2.+1)
x = 30*n/(max(freq)-min(freq)) #30 to go from GHz to icm
intf = pl.ifft(resp)
x2 = pl.concatenate((x, -(x[1:len(x)-2])[::-1])) #Crap. should this be -2 or -1
if len(freq) % 2 == 1 : x2 = pl.concatenate((x, -(x[1:len(x)-1])[::-1]))
#plot, freq, resp
#oplot, freq, FFT(intf), color=1
if two:
x2 = pl.concatenate((x2, x2+2*max(x2)))
intf = pl.concatenate((intf, intf))
q = x2.argsort()
x2 = x2[q]
intf = (intf[q]).real
result ={'x': x2, 'intf':intf}
if plt:
if len(band) != 0 : rtemp = create_band(band, res, plt=True)
pl.plot(freq, resp)
pl.title('Band')
pl.figure()
pl.plot(x2, intf.real)
pl.xlabel('Optical Delay (cm)')
pl.ylabel('Response')
pl.title('Interferrogram')
#if sav:
# openw, 1, sav
# x0 = result.x(0:n_elements(x2)-1)
# outp = [[x0], [real_part(result.intf)], [imaginary(result.intf)]]
# printf, 1, transpose(outp)
# close, 1
return result