DSP in Matlab...digital filter

[nicolejess]

digital resonator matlab

Hi,

I am dealing with a digital resonator filter in Matlab.
The transfer function is K (z^2 / (z-p1)(z-p1*) ) where K is the gain.
It is simplified to K / (1 - 2 r cos 2pi f0 z^-1 + r^2 z^-2)

Given that samplig rate = 128kHz, resonant peak at f0 = 48kHz and 3dB bandwidth is 4kHz with unity gain at its resonant peak. I was asked to plot the magnitude and phase of the freq respone of this filter. This is the part that I need help.

I have found out that the filter coefficients are, K is 0.1322 and 2 r cos 2pi f0 = -1.2754 and -r^2 = -0.8133
What command should I use to plot the freq response ?
I have tried to look at freqz in Matlab but it says [h,w] = freqz(b,a,p)
where b, and a are the coefficients vector and p is the no. of points.
This confuses me because i don have any vector values for my coefficients. This filter is a digital resonator with 2 pole bandpass filter with a pair of complex poles near unit circle and resonates at f0.
I am basically just following my textbook to get the transfer function H(z) and the coefficients and gain K. Not so sure how to plot this freq response in Matlab.

Any help would be appreciated.
Thankyou.

Regards,
Nicole

 

[dora]

resonator filter matlab

As far as I got you need transfer function of the folowing filter


H(z)=0.1322/(1 +1.2754*z^-1+0.8133*z^-2)

check the help of freqz and use the fact z=exp(j*w*T)

so vectors of numrator and denumerator a and b should be created

b=[0.1322];
a=[1 1.2754 0.8133];

The function freq returns the sampled version of the continious frequency responce from DC (0 rad/sample) up to Nyquist frequency (pi rad/sample)

then if you don't use return arguments the freqz plots the result directly ... use

freqz(b,a,100);

freqz in this case plots the 100 samples (from the continious complex frequency responce)

Best Regards
dora

 

[flor39]

matlab digital filter design

Hi,

I have just started doing that filter too!
I know how to plot it but I am having trouble getting the coefficients.
Could you please tell me how you got the coefficients of the filter?

Thanks

Marat

 

[nj_jack]

digital resonator filter

digital fiter design is very easy to use the matlab.
it supplies many function and module for implementing digital fiter design and analysis.
you can refer to related matlab books.

 

[abhigopal]

matlab plot filtering

for digital filter design, refer "DSP using Matlab" by John G Proakis and Vinay Ingle. Its the best i have seen

 

[xwcwc1234]

matlab plot digital filter transfer function

Hi abhigopal,
Do you have the book "DSP using Matlab"? Can upload to the forum ?

 

[abhigopal]

magnitude and phase plots digital filter

hi, i have the book in the paper form, unfortunately not as an ebook. Will try and see if some of my friends have, if yes, will definitely upload..
Abhi