FFT w/ Hanning windowing (50% overlap of windows)

gistfile1.py

def fft_hann(t,pt,M):
    """
    Perform FFT with Hanning windowing,
    50% overlap of 2^M+1 windows.
    The resulting spectra are averaged.
    """

    # Amplitude correction of Hanning
    ampl_corr = 2. 
    # Signal length
    N = pt.shape[1]
    # Window length (amount of data pts/win)
    n = 2*N/(2**M+2)

    # Save spectra here
    spectra = {}

    # Loop over axes
    for itr in [0,1,2]:
        spectra[itr] = 0.
        # Loop over windows
        for jtr in range(0,2**M+1):
            begin = jtr*n/2
            end = begin+n
            spectra[itr] = (ampl_corr*np.abs(np.fft.fft(np.hanning(n)*pt[itr,begin:end])[0:n/2])/n*2.)**2+spectra[itr]
        # Do the averaging (avg of squares)
        spectra[itr] = np.sqrt(spectra[itr]/(2**M+1))

    # Frequencies
    freq = np.fft.fftfreq(n,t[1]-t[0])[0:n/2]

    return freq,spectra