Prove the convolution theorem below, Eqn. 19a.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Exercise 8 Prove the convolution theorem below, Eqn. 19a.
Property 9 The convolution theorem and the Fourier inverse.
and
If
91
92 are, respectively, the Fourier transforms of fi and f2, then the convolution theorem
states that
1
roo
F [fi (x) f2 (x)]
91 (k') g2 (k – k') dk'.
(19a)
Transcribed Image Text:Exercise 8 Prove the convolution theorem below, Eqn. 19a. Property 9 The convolution theorem and the Fourier inverse. and If 91 92 are, respectively, the Fourier transforms of fi and f2, then the convolution theorem states that 1 roo F [fi (x) f2 (x)] 91 (k') g2 (k – k') dk'. (19a)
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