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</math> | </math> | ||
===Answer 2=== | ===Answer 2=== | ||
| − | + | Claim that <math>CSFT{e^{j \pi (ax +by)}</math>? | |
| + | |||
===Answer 3=== | ===Answer 3=== | ||
Write it here. | Write it here. | ||
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[[2011_Fall_ECE_438_Boutin|Back to ECE438 Fall 2011 Prof. Boutin]] | [[2011_Fall_ECE_438_Boutin|Back to ECE438 Fall 2011 Prof. Boutin]] | ||
Revision as of 17:55, 12 November 2011
Contents
Continuous-space Fourier transform of a complex exponential (Practice Problem)
What is the Continuous-space Fourier transform (CSFT) of $ f(x,y)= e^{j \pi (ax +by) } $?
Justify your answer.
You will receive feedback from your instructor and TA directly on this page. Other students are welcome to comment/discuss/point out mistakes/ask questions too!
Answer 1
$ x[n] = \int_{-\infty}^{\infty}\int_{-\infty}^{\infty} e^{j \pi (ax +by) }e^{-2j \pi (ux +vy) }dxdy $
$ = \int_{-\infty}^{\infty}\int_{-\infty}^{\infty} e^{j \pi x(a-2u) }e^{j \pi y(b - 2v) }dxdy $ $ = \frac{1}{j\pi(a-2u)}\frac{1}{j\pi(b-2v)}[e^{j \pi x(a-2u)}e^{j \pi y(b - 2v) }]{-\infty}^{\infty} $ $ = {\infty} $
Answer 2
Claim that $ CSFT{e^{j \pi (ax +by)} $?
Answer 3
Write it here.
