Python NumPy - FFT and Inverse FFT?

Question

So I've been working with FFT, and I'm currently trying to get a sound waveform from a file with FFT, (modify it eventually), but then output that modified waveform back to a file. I've gotten the FFT of the soundwave and then used an inverse FFT function on it, but the output file doesn't sound right at all. I haven't done any filtering on the waveform - I'm just testing out getting the frequency data and then putting it back into a file - it should sound the same, but it sounds wildly different. Any ideas?

-- EDIT --

I have since been working on this project a bit, but haven't yet gotten desired results. The outputted sound file is noisy (both more loud, as well as extra noise that wasn't present in the original file), and sound from one channel leaked into the other channel (which was previously silent). The input sound file is a stereo, 2-channel file with sound only coming from one channel. Here's my code:

 import scipy
 import wave
 import struct
 import numpy
 import pylab

 from scipy.io import wavfile

 rate, data = wavfile.read('./TriLeftChannel.wav')

 filtereddata = numpy.fft.rfft(data, axis=0)

 print (data)

 filteredwrite = numpy.fft.irfft(filtereddata, axis=0)

 print (filteredwrite)

 wavfile.write('TestFiltered.wav', rate, filteredwrite)

I don't quite see why this doesn't work...?

EDIT: I've zipped up the problem .py file and audio file, if that can help solve the issue here.

Answer 1

>>> import numpy as np
>>> a = np.vstack([np.ones(11), np.arange(11)])

# We have two channels along axis 0, the signals are along axis 1
>>> a
array([[  1.,   1.,   1.,   1.,   1.,   1.,   1.,   1.,   1.,   1.,   1.],
       [  0.,   1.,   2.,   3.,   4.,   5.,   6.,   7.,   8.,   9.,  10.]])
>>> np.fft.irfft(np.fft.rfft(a, axis=1), axis=1)
array([[  1.1       ,   1.1       ,   1.1       ,   1.1       ,
          1.1       ,   1.1       ,   1.1       ,   1.1       ,
          1.1       ,   1.1       ],
       [  0.55      ,   1.01836542,   2.51904294,   3.57565618,
          4.86463721,   6.05      ,   7.23536279,   8.52434382,
          9.58095706,  11.08163458]])
# irfft returns an even number along axis=1, even though a was (2, 11)

# When a is even along axis 1, we get a back after the irfft.
>>> a = np.vstack([np.ones(10), np.arange(10)])
>>> np.fft.irfft(np.fft.rfft(a, axis=1), axis=1)
array([[  1.00000000e+00,   1.00000000e+00,   1.00000000e+00,
          1.00000000e+00,   1.00000000e+00,   1.00000000e+00,
          1.00000000e+00,   1.00000000e+00,   1.00000000e+00,
          1.00000000e+00],
       [  7.10542736e-16,   1.00000000e+00,   2.00000000e+00,
          3.00000000e+00,   4.00000000e+00,   5.00000000e+00,
          6.00000000e+00,   7.00000000e+00,   8.00000000e+00,
          9.00000000e+00]])

# It seems like you signals are along axis 0, here is an example where the signals are on axis 0
>>> a = np.vstack([np.ones(10), np.arange(10)]).T
>>> a
array([[ 1.,  0.],
       [ 1.,  1.],
       [ 1.,  2.],
       [ 1.,  3.],
       [ 1.,  4.],
       [ 1.,  5.],
       [ 1.,  6.],
       [ 1.,  7.],
       [ 1.,  8.],
       [ 1.,  9.]])
>>> np.fft.irfft(np.fft.rfft(a, axis=0), axis=0)
array([[  1.00000000e+00,   7.10542736e-16],
       [  1.00000000e+00,   1.00000000e+00],
       [  1.00000000e+00,   2.00000000e+00],
       [  1.00000000e+00,   3.00000000e+00],
       [  1.00000000e+00,   4.00000000e+00],
       [  1.00000000e+00,   5.00000000e+00],
       [  1.00000000e+00,   6.00000000e+00],
       [  1.00000000e+00,   7.00000000e+00],
       [  1.00000000e+00,   8.00000000e+00],
       [  1.00000000e+00,   9.00000000e+00]])

Answer 2

1. You don't appear to be applying any filter here
2. You probably want to take the ifft of the fft (post-filtering), not of the input waveform.

Answer 3

Shouldn't it be more like this?

filtereddata = numpy.fft.fft(data)
# do fft stuff to filtereddata
filteredwrite = numpy.fft.ifft(filtereddata)
wavfile.write('TestFiltered.wav', rate, filteredwrite)

Answer 4

Two problems.

You are FFTing 2 channel data. You should only FFT 1 channel of mono data for the FFT results to make ordinary sense. If you want to process 2 channels of stereo data, you should IFFT(FFT()) each channel separately.

You are using a real fft, which throws away information, and thus makes the fft non-invertible.

If you want to invert, you will need to use an FFT which produces a complex result, and then IFFT this complex frequency domain vector back to the time domain. If you modify the frequency domain vector, make sure it stays conjugate symmetric if you want a strictly real result (minus numerical noise).