Step response and Impulse response of IIR filter

Hi,

I am trying to plot the Step response and Impulse response of an IIR filter but I really do not know how as I am not using the designfilt to generate the filter based on frequency-response specifications I am using it as shown in the below code:

    [X,Fs] = audioread(filename); % reading the wav file 
    temp = Fs/2

    Wp = 170/temp; Ws = 220/temp;
    [n,Wn]= buttord(Wp, Ws, 4, 8);  % getting the order
    [z,p,k] = butter(n, Wn, 'low'); % IIR filter
    [sos,g] = zp2sos(z, p, k);
    
    y = filtfilt(sos, g, X); % signal after applying the filter

I applied the Step response and Impulse response in an FIR filter successfully as shown below:

    h = fir1(100, 170/temp, 'low'); % FIR filter
    % Impulse response of digital filter
    impz(h)
    % Step response of digital filter
    stepz(h)
    
    y = filter(h, 1, X);% signal after applying the filter

I can not do the same thing in the IIR filter. what should I do?

thanks in advance.

Answer 1

[Paul]

Hi Alex,

It would be helpful to know the value of temp. Absent that, it seem like

[hstep,tstep] = stepz(sos);
hstep = hstep*g;
[himp,timp] = impz(sos);
himp = himp*g;

should work.

[Alex sinWave]

I don't really understand what is the use of the hstep and himp as I just want the plots of the Impulse and Step response so would they be usfull in somethinf?

hstep = hstep*g;
himp = himp*g;

[Paul]

Once we have hstep and himp, just plot them.

Fs = 4000; % just making something up
temp = Fs/2;
Wp = 170/temp; Ws = 220/temp;
[n,Wn]  = buttord(Wp, Ws, 4, 8);  % getting the order
[z,p,k] = butter(n, Wn, 'low'); % IIR filter
[sos,g] = zp2sos(z, p, k);
[hstep,nstep] = stepz(sos);
hstep = hstep*g;
figure
stem(nstep,hstep);

figure
[himp,nimp] = impz(sos);
himp = himp*g;
stem(nimp,himp)