How to correctly bandpass filter in frequency with MATLAB?

Question

i'm pretty new to matlab and signal processing, but I am working on a project and I am stuck. My goal is to do a band-pass fast Fourier transform (FFT) filter with cut-off frequencies of 0.5 Hz and 3 Hz from a real signal. My input signal is a signal sampled ad 405Hz and of around 35000 samples. My implementation looks like this:

%ZFiltered = My signal 
filtered = bandpass(fft(zFiltered), [0.5 3], sampling_frequency);
res = ifft(filtered);

subplot(2,1,1)
plot(zFiltered)

subplot(2,1,2)
plot(abs(res))

My questions are: Why do I get a signal which contains also imaginary part? Why does it look like this ?

Azim J Azim J · Accepted Answer · 2021-03-05T19:04:54

Your goal is unclear to me; here are three different approaches that your question hints at

filter your raw signal with a band-pass filter as your code attempts to do
use the fft and ifft functions to filter your raw signal
calculate the coefficients of a digital filter that would act as a band-pass filter when used with the filter function

Approach 1: filtering with bandpass function

Referring to the bandpass documentation, you would use your original signal and specify the filter band and sampling frequency as in:

filtered_signal = bandpass(zFiltered,[freq_low freq_high],sample_freq);
plot(zFiltered); hold on;
plot(filtered_signal);

where the inputs are the

zFiltered : original (unfiltered signal)
freq_low=0.5 : lowest frequency in Hz of the band pass range`
freq_high=3 : highest frequency in Hz of the band pass range
sample_freq=405 : the sampling frequency in Hz

Your approach using digital fast Fourier transform function fft produces complex results because you are looking at the actual components computed by the transform (which by definition are complex having both real and imaginary parts). You can compute the power of the signal with:

P = abs(res/n).^2;

which gives you the power of the signal for each frequency represented in the Fourier transform (see the fft function docs here for more information).

Approach 2: Filtering with fft ifft functions

Use the Fourier transform and inverse Fourier transform functions to filter the signal. The steps here are to use fft to get the signal into the frequency domain. Set the elements you want filtered to zero and then apply the inverse Fourier transform (ifft) to get the filtered signal. Each component represents a given discrete frequencies in the range between 0Hz and F_s/2 that contributes to the signal. Set components of the FFT you want to suppress to zoro and apply ifft to get back a filter signal. Please see the fft docs and ifft docs for information on these functions and some of the intricacies of working with signals in the frequency domain.

Approach 3: Filtering with the coefficeints of the standard difference equation

Computing the coefficients of a digital band pass filter. This approach calculates the coefficients (vectors A and B) of the standard difference equation (see filter docs for details). An example of a function that does this is butter which gives the coefficients that represent a Butterworth filter of a given frequency. You could also look at the designfilt function for more options.

How to correctly bandpass filter in frequency with MATLAB?

1 Answers