How to apply a filter to a signal?

I have an input signal. I want to filter out the contents of that input at frequencies 60, 120, and 180Hz (there are unwanted interferences at those frequencies). To achieve this, I created zeros and poles at (what I understand to be) locations on the pole-zero plot that would filter the input signal. I am wondering if I have done that part correctly and how I can filter the input signal. Using the subplot command, I want to plot the original signal on the top panel, and the filtered signal on the bottom panel. The following is the code so far, but I either get errors or unexpected results depending on what I do to the number of poles on my transfer function.

k = 1;
z = [cos(pi/3)+sin(pi/3)*1i;
    cos(2*pi/3)+sin(2*pi/3)*1i;
    -1];
p = [1];%if I change this to "p = [1; -2; 1];", I would no longer get an error but an unexpected result instead
[b,a] = zp2tf(z,p,k);
[h,t1] = impz(b,a);
zplane(z,p);
pause
% create system
myFilter = tf(b,a);
% apply filter to time domain signal
[y_out, time] = lsim(myFilter,y,t);%y is the input signal
% plot for check
plot(time,[y; y_out']);

Answer 1

[Star Strider]

I do not understand the reason that the Control System Toolbox is being used for signal processing.

I would instead use the Signal Processing Toolbox bandstop function, with the 'ImpulseResponse','iir' name-value pair to design an efficient elliptical bandstop filter. It will be necessary to design three different filters, and run them in series.

Another option is to use a FIR filter to reject all of them at once. That would go something like this —

Fs = 1000;                                                              % Use Correct Sampling Frequency (Must Be Greater Than 370 Hz)
fcomb = [[55 59 61 64], [55 59 61 64]+60, [55 59 61 64]+120];
mags = [[1 0 1], [0 1], [0 1]];
dev = [[0.5 0.1 0.5], [0.1 0.5], [0.1 0.5]];
[n,Wn,beta,ftype] = kaiserord(fcomb,mags,dev,Fs);
hh = fir1(n,Wn,ftype,kaiser(n+1,beta),'noscale');

figure
freqz(hh, 1, 2^20, Fs)
set(subplot(2,1,1), 'XLim', [0 200])                                    % Zoom X-Axis
set(subplot(2,1,2), 'XLim', [0 200])                                    % Zoom X-Axis

This filter has a length of 281, so the signal length must be at least twice that for it to work. Use the filtfilt function to do the actual filtering.

.

[KibreabG]

Hi @Star Strider, thank you for your prompt and clear response!

I agree that I can use those two options you mentioned but I am trying to use my transfer function and the pole-zero plot in this process. The idea is that I more clearly understand how these things are related whilst obtaining the required filter.

[Star Strider]

O.K.

Experiment with that approach. If that is successful, post back.

One possibility to consider is to implement the transfer function as discrete rather than continuous, because all signals that can be represented in computers is actually discrete. The sampling periods of course must match.

.

[KibreabG]

RIght.

I am so far unsuccesful with my trials. I used the zeros and poles I specified in the initial post above in the filter and filtfilt functions and recieve unexpected results again. For both those functions, I used the follwing syntaxt:

yfilt = filter(b,a,y);
yfilt = filtfilt(b,a,y);%or

I think I am misuing these functions or my poles and zeros are not adequate. Are you still able to help @Star Strider?

[Star Strider]

I know. I ran the posted code and saw the errors.

There are textbook examples of filter design using transfer function and state-space representations, so perhaps consulting a hardcopy or online resource on filter design would be appropriate. Design the analog filter first, then use the bilinear transform (likely the most reliable) to transform it to a discrete system. Also, the usual approach is to design the lowpass prototype and then transform it to a highpass, bandpass or bandstop filter to get the desired final result. Analyse it before and after the transformation to be certain that the pole and zero placements and the result ing transfer function are still appropriate.

Filter design is not trivial and will take some time, however understanding it is definitely worth the effort.

.

[KibreabG]

Hi @Star Strider awesome, I finnaly figured it out. Thank you for your help!

[Star Strider]

As always, my pleasure!

.