Matlab - Filter frequency response

Author

Filter frequency response

Udo Juerss

2006-12-27, 4:19 am

Hello,

how can I display the frequency response and phase shift of a
function? For a low pass filter, a running average like this:
"new_value = 0.95 * old_value + 0.05 * actual_value".

Thanks

Udo

Rune Allnor

2006-12-27, 8:17 am

Udo Juerss skrev:
> Hello,
>
> how can I display the frequency response and phase shift of a
> function? For a low pass filter, a running average like this:
> "new_value = 0.95 * old_value + 0.05 * actual_value".

There is a very specific terminology for filters, which you have
not used. With the proviso that I misunderstand your meaning,
what you have is a FIR filter. The recipe for plotting magniude
spectrum and phase response is scetched below (I assume
you do not have access to the signal processing toolbox).

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% First, collect the coefficients in a vector like this:

h = [0.95 0.05];

% Then compute the spectrum:

Nfft=1024;
H = fft(h,Nfft);

% Convert to polar representation:

[th,r]=cart2pol(real(H),imag(H));

% Construct a frequency vector:

fs = 1; % You did not specify the sampling frequency
fv = [0:Nfft-1]/Nfft*fs;

% Plot the spectrum:

fidx = find(fv<fs/2);

subplot(2,1,1)
plot(fv(fidx),r(fidx))

% Plot the phase response:

subplot(2,1,2)
plot(fv(fidx),th(fidx))

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

And that's it.

Rune

dbd

2006-12-28, 4:12 am

Rune Allnor wrote:
> Udo Juerss skrev:
>
> There is a very specific terminology for filters, which you have
> not used. With the proviso that I misunderstand your meaning,
> what you have is a FIR filter. The recipe for plotting magniude
> spectrum and phase response is scetched below (I assume
> you do not have access to the signal processing toolbox).

The running average is sometimes expressed as

Output(n) = (1-alpha) * Output(n-1) + alpha * Input(n)

This is an IIR filter. Try calculating a vector of outputs by this
formula for a unit impulse signal. That is, the first input is 1.0 and
the rest are 0's. For the first, nonexistant, previous output, use 0.0
and alpha = 0.05.

Then try Rune's plot with this output vector for H.

Dale B. Dalrymple
http://dbdimages.com

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