Question on Match Filters

How do I create a MATLAB code for convolution to display the results below:

Consider a signal s1(t)=t^2, 0≤t≤1 so T=1. The signal is zero otherwise.

(a) Sketch the signal and the corresponding matched filter impulse response.

(b) What is the SNR at the output of the MF when sampled at t=T.

Assume noise PSD N0 to be 10^−12 Watt/Hz.

(c) Sketch the MF output signal versus time, showing the exact sample (from the signal) value to be obtained at the sampling instant. (Try plotting using computer, you can perform convolution)

[Steven Lord]

This sounds like a homework assignment. If it is, show us the code you've written to try to solve the problem and ask a specific question about where you're having difficulty and we may be able to provide some guidance.

If you aren't sure where to start because you're not familiar with how to write MATLAB code, I suggest you start with the free MATLAB Onramp tutorial to quickly learn the essentials of MATLAB.

If you aren't sure where to start because you're not familiar with the mathematics you'll need to solve the problem, I recommend asking your professor and/or teaching assistant for help.

[James Manns]

I believe I have worked out the solution in the attached. However, when I researched the conv in MATLAB, the examples seem to be with matrices. When dealing with the attached, I don't know how to set up the conv line. I also did not see a section on it in the Onramp tutorial.

[Image Analyst]

conv deals with vectors. conv2 deals with 2-D matrices.

Answer 1

[Abhishek]

Hi James,

I understand you want to perform the convolution of signal, defined in the interval,, with its matched filter impulse response.

To perform convolution of continuous time signals in MATLAB, here are some initial steps:

1. Define a time vector

step_size = 0.01

step_size = 0.0100

t = -2:step_size:2;

2. Define the signal

s_t = (t >= 0 & t <= 1) .* t.^2;
plot(t, s_t);

●

3. Get the matched filter impulse response

T = 1;
h_t = ((1-t) >= 0 & (1-t) <= 1) .* (1-t).^2;
plot(t, h_t);

With the variables ‘s_t’ and ‘h_t’ created, the next step is to perform convolution using the “conv” function, normalize the result (by multiplying the result with ‘step_size’) and plot it. The documentation for “conv” function can be found below:

https://www.mathworks.com/help/releases/r2024b/matlab/ref/conv.html

With the above mentioned steps, I hope you will be able to proceed successfully. For any clarifications, please feel free to reach out!