Plotting Frequency Spectrum using Matlab with hold function

Question

Suppose I have successfully generated a Single-sided Power spectrum as follows:

X_mags = abs(fft(signal));
bin_vals = [0 : N-1];
fax_Hz = bin_vals*fs/N;
N_2 = ceil(N/2);
plot(fax_Hz(1:N_2), 20*log10(X_mags(1:N_2)));`

now I want to plot a second graph on top of the first one:

hold on;

Lastly I perform an LPC analysis on the signal and calculate the frequency response. The frequency response should be plotted on top of the Power spectrum, so:

[a, g] = lpc(signal,N);
[h,f] = freqz(b,a,N,fs);
plot(?);

For the sake of simplicity, let's assume the parameters are all correctly given, how should I write the plot function for having a correct display of the frequency response? A simple plot(f) doesn't work.

Can someone explain why? Thanks

Answer 1

A simple plot(f) tries to plot frequency vector, isn' t it?

Check the code below:

X_mags   = abs(fft(signal));
bin_vals = [0 : N-1];
fax_Hz   = bin_vals*fs/N;
N_2      = ceil(N/2);

[a, g]   = lpc(signal,N);
[h, f]   = freqz(b, a, N, fs);

figure,

hold on,
plot(f, 20*log10(abs(h)), 'r');
plot(fax_Hz(1:N_2), 20*log10(X_mags(1:N_2)));
title('Frequency Spectrum');
xlabel('Frequency (Hz)'); 
ylabel('Amplitude (dB)');
legend('Frequency Response', 'Single-sided Power spectrum')

Btw, there is a MATLAB function db() for decibel calculation. That might be useful.

Answer 2

The response h is complex, so you'll want to get the magnitude of the response via multiplication by its complex conjugate.:

plot(f, 10*log10(h.*conj(h)));

Note the use of 10*log10 because the operation above squares the amplitude response held in h.

Or, if you're less interested in being pedantic about working with complex numbers, you could just take the absolute value of the complex values, being sure to 20*log10 because the abs does not square the values

plot(f, 20*log10(abs(h)));