Saturday, 9 May 2015

Filtering an ideal signal with FFT

Hi everyone! Remember that in the last article I wrote that you can use the FFT to clean a signal from background noise? Well here is an example of signal filtering.

We start by generating a signal and then add some random noise using the random number generator in numpy. Here is the noisy signal:


Now, our signal is made up of two main frequencies: 20 and 30 Hz while the rest is mainly background noise. You can check this in the FFT of the signal:

FFT of the signal

Suppose we’d like to isolate the 20 Hz bit, that means we’d have to set to 0 each value in the Spectrum which is greater or lower than 20 Hz. Let’s block out everything outside 18 and 22 Hz and then apply the inverse FTT. Here is the signal we found (blue) compared to the exact signal we wanted to find (red). At the bottom of the graph there is the error between the two signals, notice that it is not that high, (at worst we missed 0.08, however on average we missed less).


Here is the python code I used to make this.

Have fun!


  1. Isn't this is what is called FIR filter? Only, you avoid the FFT -- > IFFT, just do convolution.

    1. Hi, the idea was to have a look at the signal in the frequency domain using the fast fourier transform. As far as I know, a FIR system/filter is a different thing.