fourier.py
2d2cfe14a20dmaster

fourier.py
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			from numpy import *
			from numpy import fft


			####################################
			def tofrec(fmin,fmax,n,i):
			####################################
			nn = float(n)
			if i<=n/2+1:
			return (i/nn+0.5)*(fmax-fmin) + fmin
			else:
			return (i/nn-0.5)*(fmax-fmin) + fmin


			####################################
			def fourier(x,y):
			####################################
			'''

			Fct = Sum_(m=1,n) amp_m cos( 2.pi f_m phi + phi_m )
			= Sum_(m=1,n) amp_m cos( m phi + phi_m )

			m = 2.pi f_m

			'''

			dx = (x.max()-x.min())/(len(x)-1)
			fmin = -1./(2.*dx)
			fmax = -fmin

			#f = fromfunction(lambda ii:tofrec(fmin,fmax,len(x),ii) ,(len(x),))
			f = array([],float)
			for i in range(len(x)):
			f = concatenate((f,array([tofrec(fmin,fmax,len(x),i)])))


			## FFT ##
			ffft = fft.fft(y)

			amp = sqrt(ffft.real2 + ffft.imag2) # amplitude du signal d'entree
			phi = arctan2(ffft.imag,ffft.real) # phase a p/2 pres
			phi = fmod(phi+2pi,2.pi) # de 0 a 2*pi (ok avec phase positive)


			amp = 2.* amp / len(x) # doubler ok, /len(x) ???

			f = f[0:len(x)/2] # on sort que les frequences positives
			amp = amp[0:len(x)/2]
			phi = phi[0:len(x)/2]

			amp[0] = amp[0]/2.

			return f,amp, phi