How to get from discrete time impulse response vector to plot of frequency spectrum
Hello, I'm very new to DSP concepts and signal processing in MATLAB so please go easy on me. I have the following code that I've begun working on which is the BZT of an RLC filter. I want to take the DFT of my impulse response y[n] and end up with a magnitude plot Y(f). I know that I can use the fft() and plot() functions for this. I've seen examples using linspace/logspace vectors which I'll need to define before being able to plot this thing, and some such things as NFFTs (to enable a faster fft?) but I'm not really sure how to put it all together here. Any help/insight would be really appreciated. CODE: R=0.1; % resistor L=0.0016; % inductor C=0.0016; % capacitor resF=1/sqrt(L*C); % resonant frequency sampRate=44100; % sampling rate (Hz) T=1/sampRate; % sample period prewarpF=(2/T)*tan(resF*T/2); % prewarp factor a=(2/T)*R*C; b=(2/(T*prewarpF))^2; e0=a/(a+b+1); e1=(2-2*b)/(a+b+1); e2=(1+b-a)/(a+b+1); N=2048; % number of taps x=zeros(1,N); % input vector x(5) = 1; % impulse at delta(n-5) y=zeros(1,N); % output vector for n = 5 : N y(n) = e0*x(n) - e0*x(n-2) - e1*y(n-1) - e2*y(n-2); end
Prashant Kumar answered .
2025-11-20
y(n) = e0*x(n) - e0*x(n-2) - e1*y(n-1) - e2*y(n-2);
You difference equation has the following form as a rational transfer function.
A = [1 e1 e2]; B = [e0 -e0];
So the frequency response is
[H,F] = freqz(B,A,[],44100);
plot(F,20*log10(abs(H)));
xlabel('Hz');
You can see from the above that the response is lowpass.