Question on Match Filters

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James Manns
James Manns 2024-2-20
回答： Abhishek 2025-5-2
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)
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James Manns
James Manns 2024-2-20
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
Image Analyst 2024-2-20
conv deals with vectors. conv2 deals with 2-D matrices.

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回答（1 个）

Abhishek
Abhishek 2025-5-2
Ran in:
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!

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