Designing a higher order lowpass filter to avoid Gibbs phenomenon

Hello!

I'm designing a simple but higher order lowpass filter to get rid of the Gibbs Phenomenon. This is what I thought of. Am I correct? Is this a valid filter?

d = designfilt('lowpassiir', 'FilterOrder',20,... % Response type

'PassbandFrequency',400, ... % Frequency constraints

'MatchExactly','passband', ... % Design method options

'SampleRate',2000)

I want to keep it simple having only cutoff frequency and the order as variables. (I assumed 'Match exactly' should be 'passband' because I need the filter to depend on cutoff frequency. Is this not necessary?)

How should I compensate for the delay in this? Since it is an IIR filter, it's only a phase shift, am I right?

Thank you!!

Answer 1

[Star Strider]

I could not get that code to work.

Try this:

Fs = 2000;                                                  % Sampling Frequency (Hz)
Fn = Fs/2;                                                  % Nyquist Frequency (Hz)
Wp = 400/Fn;                                                % Normalised Passband (Passband = 5 Hz To 40 Hz)
Ws = 450/Fn;                                                % Normalised Stopband (Passband = 2 Hz To 45 Hz)
Rp =  1;                                                    % Passband Ripple/Attenuation
Rs = 60;                                                    % Stopband Ripple/Attenuation
[n,Wp] = ellipord(Wp, Ws, Rp, Rs);                          % Calculate Elliptic Filter Optimum Order
[z,p,k] = ellip(n, Rp, Rs, Wp,'low');                       % Elliptic Filter
[sos,g] = zp2sos(z,p,k);                                    % Second-Order-Section For Stability

figure
freqz(sos, 2^26, Fs)

To use it with filtfilt:

y_filtered = filtfilt(sos, g, y);

[Dhanushka Palipana]

Thanks for the code. I'll try it.

But, for this to use in my case, I should know passbands, stop bands, pass band ripple etc. I'd like a filter just having cutoff frequency and a very high order to avoid Gibbs phenomenon.

Stop band should be Nyquist frequency. But How do I decide the Rp and Rs?

freqz(sos, 2^26, Fs). What is 2^26 here?

[Star Strider]

My pleasure.

All that information is in my code. I even documented it with comments on every line. (Some of the comments were for a filter I designed for other purposes, however they remain essentially valid for this filter.)

The ‘Rp’ and ‘Rs’ valuess are parameters you specify, depending on what you want the filter to do. I usually use the ones I used in the example I posted.

‘Stop band should be Nyquist frequency.’

Not quite, actually. If specified, the band limits are not allowed to equal either 0 Hz (d-c) or the Nyquist frequency, only approach them. (A lowpass filter includes 0 Hz, and a highpass filter includes the Nyquist frequency. The frequency limits for a bandpass or bandstop filter must be between them.) In that event, the filter design is almost irrelevant. It will have a very gradual rolloff between 400 and 1000 Hz. (The elliptic filter design is characteristically efficient, however much depends on the result you want.)

[Dhanushka Palipana]

Thank you very much!

[Star Strider]

As always, my pleasure!