(a) Derive the frequency-domain convolution of a spectrum M(w) =rect () and a spectrum G(w) = 8(w-10) + 8 (w + 10), where B > 0 and rect() is a rectangular spectrum with width B. Also, sketch the spectrum of the convolution output. (b) Derive the inverse Fourier transform of M(w) * G(w) in part Q3a, where the symbol * denotes the convolution in the frequency domain. Quote which transform pairs that you use.
(a) Derive the frequency-domain convolution of a spectrum M(w) =rect () and a spectrum G(w) = 8(w-10) + 8 (w + 10), where B > 0 and rect() is a rectangular spectrum with width B. Also, sketch the spectrum of the convolution output. (b) Derive the inverse Fourier transform of M(w) * G(w) in part Q3a, where the symbol * denotes the convolution in the frequency domain. Quote which transform pairs that you use.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(a)
-
Derive the frequency-domain convolution of a spectrum
M(w) = rect() and a spectrum G(w) = 8(w — 10) + 8(w + 10),
where B > 0 and rect() is a rectangular spectrum with width B.
Also, sketch the spectrum of the convolution output.
(b)
Derive the inverse Fourier transform of M(w) * G(w) in part Q3a,
where the symbol * denotes the convolution in the frequency
domain. Quote which transform pairs that you use.
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