Thread Subject: Filter a sinusoidal signal

Hi All..

I'm currently trying to filter a FM signal... the code is below

clear all
close all
echo on
t0=.2; % signal duration
ts=0.001; % sampling interval
fc=250; % carrier frequency
fs=1/ts; % sampling frequency
t=[-t0/2:ts:t0/2]; % time vector
kf=100; % deviation constant
m=cos(2*pi*10*t); % the message signal
int_m(1)=0;
for i=1:length(t)-1 % integral of m
  int_m(i+1)=int_m(i)+m(i)*ts;
  echo off ;
end
echo on ;
u=cos(2*pi*fc*t+2*pi*kf*int_m); % modulated signal

%now lets filter the signal
[z,p] = butter(1,2*50/fs,'low');
filter_out = filter(50,[1 50],u); %this damn filter doesn't work!

subplot(2,1,1);
plot(t,u);
hold on;
plot(t,m,'r');

subplot(2,1,2);
plot(t,filter_out);
hold on;
plot(t,m,'r');


The plots are all there and stuff, all you need to do is to run the above code.
As you can see, the filter output gives me like a weird response, does anyone know why and what Im doing wrong?

I think im somehow implementing the butter function wrong..


Thanks in advance.

Regards,
Simon

Hi Simon, without going through your code line by line, one thing that stands out is
the following portion:

%now lets filter the signal
[z,p] = butter(1,2*50/fs,'low');
filter_out = filter(50,[1 50],u);

the outputs of your call to butter, (in your code, z and p), are the numerator and denominator coefficients of the filter respectively. You should use these coefficients in your call to filter. For example:

[z,p] = butter(1,2*50/fs,'low');
filter_out = filter(z,p,u);

 Also, you don't need the a0 term of one, notice that p(1)=1. The call to butter() has already included the zero-th order term. You can look at the response of your filter with

fvtool(z,p)

Hope that helps,
wayne


"Simon Luk" <simon.luk@student.uts.edu.au.REMOVETHIS> wrote in message <h08e7d$rls$1@fred.mathworks.com>...
> Hi All..
>
> I'm currently trying to filter a FM signal... the code is below
>
> clear all
> close all
> echo on
> t0=.2; % signal duration
> ts=0.001; % sampling interval
> fc=250; % carrier frequency
> fs=1/ts; % sampling frequency
> t=[-t0/2:ts:t0/2]; % time vector
> kf=100; % deviation constant
> m=cos(2*pi*10*t); % the message signal
> int_m(1)=0;
> for i=1:length(t)-1 % integral of m
> int_m(i+1)=int_m(i)+m(i)*ts;
> echo off ;
> end
> echo on ;
> u=cos(2*pi*fc*t+2*pi*kf*int_m); % modulated signal
>
> %now lets filter the signal
> [z,p] = butter(1,2*50/fs,'low');
> filter_out = filter(50,[1 50],u); %this damn filter doesn't work!
>
> subplot(2,1,1);
> plot(t,u);
> hold on;
> plot(t,m,'r');
>
> subplot(2,1,2);
> plot(t,filter_out);
> hold on;
> plot(t,m,'r');
>
>
> The plots are all there and stuff, all you need to do is to run the above code.
> As you can see, the filter output gives me like a weird response, does anyone know why and what Im doing wrong?
>
> I think im somehow implementing the butter function wrong..
>
>
> Thanks in advance.
>
> Regards,
> Simon

Hi Wayne,

Thanks for your help, I've made the changes you said. I think it's working..

[z,p] = butter(1,2*50/fs,'low');
filter_out = filter(z,p,u);

Is this sending the signal 'u' through a first order low pass filter with a cut off at 50Hz?

When I used fvtool(z,p), I have a normalized requency which I don't know how to interpret.

Can you/someone please confirm?


Thanks again.


Regards,
Simon