How I applly a bandpass filter in a signal?

I would like to know how I applly a bandpass filter between 0 and 20 Hz in a signal that the it variable to be 'signal' in matlab.

[Star Strider]

Is this a homework assignment?

[Guilherme de Melo]

It is a seismic data of science research, but I never used matlab.

Answer 1

[Star Strider]

Since it is research, here is your filter:

Fs = 1000;                                                  % Sampling Frequency (Hz)
Fn = Fs/2;                                                  % Nyquist Frequency (Hz)
Wp = [1.0   20]/Fn;                                         % Passband Frequency (Normalised)
Ws = [0.5   21]/Fn;                                         % Stopband Frequency (Normalised)
Rp =   1;                                                   % Passband Ripple (dB)
Rs = 150;                                                   % Stopband Ripple (dB)
[n,Ws] = cheb2ord(Wp,Ws,Rp,Rs);                             % Filter Order
[z,p,k] = cheby2(n,Rs,Ws);                                  % Filter Design
[sosbp,gbp] = zp2sos(z,p,k);                                % Convert To Second-Order-Section For Stability

figure(3)
freqz(sosbp, 2^16, Fs)                                      % Filter Bode Plot

filtered_signal = filtfilt(sosbp, gbp, original_signal);    % Filter Signal

Insert the correct value for the sampling frequency ‘Fs’. It must be at least 45 Hz for this filter to work.

NOTE — This bandpass filter will eliminate d-c (constant) offset or a slowly varying baseline. A filter with a lower passband of 0 Hz is a lowpass filter, not a bandpass filter. A lowpass filter requires only changes in ‘Wp’ and ‘Ws’ to pass everything from 0 Hz to 20 Hz:

Wp = 20/Fn;                                                 % Passband Frequency (Normalised)
Ws = 21/Fn;                                                 % Stopband Frequency (Normalised)

The default design for discrete filters is a lowpass filter, so you do not specifically have to specify 'low' here. (All other designs require transformation from the lowpass design. The Signal Processing Toolbox does this if you ask it to.)

[Mikk Laanes]

Came to wonder how was that 45 Hz limit determined for the filter to work? And how can one determine it for one's own filter?

[Star Strider]

The upper passband in the original Question is 20 Hz, so the Nyquist frequency must be more than that, and the sampling frequency ‘Fs’ is 2 times the Nyquist frequency. I chose 45 Hz. It is always best to choose the highest sampling frequency that makes sense for a particular signal. This is termed ‘oversampling’ and means that the filters will work optimally. With respect to ADC design, it is necessary to use a hardware anti-aliasing (Bessel) lowpass filter with the stopband at the Nyquist frequency at the ADC input to prevent frequencies higher than the Nyquist frequency from being aliased in the sampled signal.

[Mikk Laanes]

Thanks a lot for the elaborate answer, Star Strider!

[Star Strider]

My pleasure!

[Chappi]

Hi, can I ask why dont you just use

bandpass(signal,[0 20],45)?

WHy do you have to go through so many steps Star Strider? I am a researcher as well but very new in signal processing. THank you very much

[Mikk Laanes]

@Chappi, by just using the 'bandpass' command, you allow Matlab to use a minimum-order filter with a stopband attenuation of 60 dB. If this is sufficient for your application, then go with that. Star Strider's method of designing allows one to make the filter requirements more strict, or relaxed. Because you can then easily control the stopband and passband ripple, as well as the transition width.

To provide an example of having the possibility to apply stricter attenuation in the stopband, I have attached a figure below. Hope that helps to explain.

By the way, another easy way of designing a filter (let's take the already suggested filter) is using the command (but I do not know how much stability is lost by not using the 'zp2sos' command?):

lpFilt = designfilt('bandpassiir', ...
                    'StopbandFrequency1',0.5,'PassbandFrequency1', 1, ...
                    'PassbandFrequency2',20,'StopbandFrequency2', 21, ...
                    'StopbandAttenuation1',150,'PassbandRipple', 1, ...
                    'StopbandAttenuation2',150, ...
                    'DesignMethod','cheby2','SampleRate',fs);
 figure
 freqz(lpFilt,2^16,fs)
 
 filtered_signal = filtfilt(lpFilt, original_signal);  

Maybe to bear in mind that allowing a passband ripple of 1dB, can cause an error of

in the magnitude of the signal.

Answer 2

[Chad Greene]

Hi Guilherme,

If you have the signal processing toolbox you can use my filter1 function. Syntax would be

yfilt = filter1('bp',y,'fc',[0 20],'fs',Fs);

where Fs is the sampling frequency.

[hssien rezk]

hi Chad Greene

thanks for your work , and i want to ask how i can apply this filter in matrix not vector .

Answer 3

[giannisk patra]

I would like to know how I applly a bandpass filter between 2 and 45 Hz in a signal that the it variable to be 'signal' in matlab. I have fs=160Hz. Can you please tell me the matlab code for this?