matched filters

logistic_guy

Full Member
Joined
Apr 17, 2024
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423
here is the question

Find the matched filters \(\displaystyle g(T - t), 0 \leq t \leq T\), and find \(\displaystyle \int_{0}^{T}g(t)g(T- t)dt\) for the following waveforms.

(a) Rectangular pulse: \(\displaystyle g(t) = \sqrt{2/T}\).
(b) Sinc pulse: \(\displaystyle g(t) = sinc(t)\).
(c) Gaussian pulse: \(\displaystyle g(t) = (\sqrt{\pi/\alpha})e^{-\pi^2t^2/\alpha^2}\).


myattemb
i'll start with (b)
\(\displaystyle \int_{0}^{T}sinc(t)sinc(T- t)dt\)
the book have answer for \(\displaystyle T = 1\)
i'm very bad in integration and when i use wolframalfa website
\(\displaystyle \int_{0}^{1}sinc(t)sinc(1- t)dt = 0.893066\)
matched.png
it say wrong answer☹️

the book is wrong or the website is wrong?
 
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