def cross_correlation(x, y):
"""
computes cross correlation between the two signals in the frequency domain. Returns a time series and frequency series
"""
N = len(x)
if N != len(y):
sys.exit("lengths don't agree in liapunov.cross_correlation")
cfx = fft.complex_forward_float([complex(r,-i) for r,i in x]) # fourier transform
cfy = fft.complex_forward_float([complex(r,i) for r,i in y])
fcc = cfy * cfx.conjugate()
tcc = fft.complex_inverse_float( fcc ) # multiply and take inverse fourier transform
return [[c.real, c.imag] for c in tcc], [[c.real, c.imag] for c in fcc] # return as a list of reals
def nmode_fft(t_P, q, verbose=False):
"""
defines my fft routine in one location
frequency spacing checked against the GSL documentation on 5/5/2013
"""
N_m = len(q)
freq = fft_freq(t_P) # frequency spacing to match GSL FFT
fq = []
for m in range(N_m):
if verbose:
print "computing FFT for mode " + str(m)
if verbose:
print "\tcasting time domain as complex"
cq = [complex(l[0], l[1]) for l in q[m]]
if verbose:
print "\tcomputing complex FFT"
cfq = list(fft.complex_forward_float(cq))
cfq = cfq[len(cfq) / 2 + 1 :] + cfq[: len(cfq) / 2 + 1]
if len(cfq) != len(freq):
print len(cfq)
print len(freq)
print len_t_P
sys.exit("Something's wrong in Nmode_utils.nmode_fft: len(cfq) != len(freq)")
if verbose:
print "\tappending complex FFT to fq in standard format (list of reals)"
fq.append([[L.real, L.imag] for L in cfq])
return freq, fq, N_m
def single_fft(t_P, A, verbose=False):
"""
performs the fft over the single value A and returns a list of lists of real numbers
"""
freq = fft_freq(t_P) # frequency spacing to match GSL FFT
if verbose: print "computing complex FFT"
cfA = list(fft.complex_forward_float(A))
cfA = cfA[len(cfA)/2+1:] + cfA[:len(cfA)/2+1]
if len(cfA) != len(freq):
print len(cfA)
print len(freq)
print len_t_P
sys.exit("Something's wrong in Nmode_utils.nmode_fft: len(cfq) != len(freq)")
if verbose: print "\tconverting complex FFT to standard format (list of reals)"
fA = [ [L.real, L.imag] for L in cfA ]
return freq, fA
