Python: Frequency Analysis of Sound Files

Question

I am generating some sound files that play tones at various frequencies with a certain number of harmonics.
Ultimately, these sounds will be played on a device with a small speaker.

I have the frequency response curve of the speaker and want to do the following in Python:

1. Plot the frequency spectrum of sound file. I need a take the FFT of the file and plot it with gnuplot
2. Apply a nonlinear transfer function based on the frequency response curve in the data sheet.
3. Plot the result after the function is applied.

Does anyone know :

• What the simplest way to do this would be?
• or of an Application (GNU/Linux based) that could do this for me?

Answer 1

you can use numpy and matPlotLib. Something like the code below:

spectrum = numpy.fft.fft(signal)
frequencies = numpy.fft.fftfreq(len(spectrum))
pylab.plot(frequencies,spectrum)
pylab.show()

That will show a graph of the fft spectrum.

Answer 2

I know you didn't mention Pylab/Matplotlib, but it works. Here is an example (assumes single-channel signal):

x, fs, nbits = audiolab.wavread('schubert.wav')
audiolab.play(x, fs)
N = 4*fs    # four seconds of audio
X = scipy.fft(x[:N])
Xdb = 20*scipy.log10(scipy.absolute(X))
f = scipy.linspace(0, fs, N, endpoint=False)
pylab.plot(f, Xdb)
pylab.xlim(0, 5000)   # view up to 5 kHz

Y = X*H
y = scipy.real(scipy.ifft(Y))

Answer 3

scipy has an FFT and hooks nicely into gnuplot. You should be able to use the signal module to do the math.