# I want to filter the x signal given using the following filters using the filter command.

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Deniz Bozdogan on 29 Nov 2021
Edited: Srijith Kasaragod on 2 Dec 2021
Hello, i have the following filters given to me:
FIR Filter:
y[n] = 0.4x[n]+0.3x[n1]+0.2x[n2]+0.1x[n3]
IIR Filter:
y[n] = 0.5y[n 1] 0.1y[n 2] + 0.3x[n] 0.2x[n 1] + 0.1x[n 2]
I want to filter the following signal using these two filters with filter command
x[n] = cos(0.1πn) + cos(0.5πn) + cos(0.9πn)
Can you help me on this problem, i could not understand the filter command. Thanks in advance

Srijith Kasaragod on 2 Dec 2021
Edited: Srijith Kasaragod on 2 Dec 2021
Hi Deniz,
Inorder to call "filter" function, you need to pass the denominator and numerator coefficents for the rational transfer function. To obtain the transfer function from the filter difference equation, you can apply Z-transform. For the FIR filter, the coefficients can be computed as:
Z-Transfrom gives,
rearranging,
From the transfer function, numerator and denominator coefficients are assigned to variables "b" and "a" respectively, and passed to "filter" function along with input signal.
n=-5:0.1:5;
x= cos(0.1*pi*n)+cos(0.5*pi*n)+cos(0.9*pi*n);
b=[0.4 0.3 0.2 0.1];
a=1;
y=filter(b,a,x);
plot(n,x);
hold on;
plot(n,y);
legend('signal','filteroutput');
hold off;
Similarly, you can filter "x" using IIR filter.
Hope this helps!

R2021b

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