fft bandpass filter in python

Question

What I try is to filter my data with fft. I have a noisy signal recorded with 500Hz as a 1d- array. My high-frequency should cut off with 20Hz and my low-frequency with 10Hz. What I have tried is:

fft=scipy.fft(signal) 
bp=fft[:]  
for i in range(len(bp)): 
    if not 10<i<20:
        bp[i]=0

ibp=scipy.ifft(bp)

What I get now are complex numbers. So something must be wrong. What? How can I correct my code?

Answer 1

There's a fundamental flaw in what you are trying to do here - you're applying a rectangular window in the frequency domain which will result in a time domain signal which has been convolved with a sinc function. In other words there will be a large amount of "ringing" in the time domain signal due to the step changes you have introduced in the frequency domain. The proper way to do this kind of frequency domain filtering is to apply a suitable window function in the frequency domain. Any good introductory DSP book should cover this.