der the functions e-t, t> 0 g(t) = 0, f(t) cos(t); otherwise lace Transform of f and g separately, and use the Laplace Transf rem on L[f L[g] to show that tie Lapiacе raiisiorTI, по SIHOW CIle COIV au integral aS deined rC expression (10) results. 3.3. Now we switch to a Fourier Transform approach. Evaluate the Fourier Transforms of f and g separately, and use the Fourier Transform version of the convolution theorem on F(p) G(p) to show that (f*g)Fourier Sin(t) + cos(t) (11) 2 3.4. Evaluate directly the convolution integral as defined for the Fourier Transform. and show that
der the functions e-t, t> 0 g(t) = 0, f(t) cos(t); otherwise lace Transform of f and g separately, and use the Laplace Transf rem on L[f L[g] to show that tie Lapiacе raiisiorTI, по SIHOW CIle COIV au integral aS deined rC expression (10) results. 3.3. Now we switch to a Fourier Transform approach. Evaluate the Fourier Transforms of f and g separately, and use the Fourier Transform version of the convolution theorem on F(p) G(p) to show that (f*g)Fourier Sin(t) + cos(t) (11) 2 3.4. Evaluate directly the convolution integral as defined for the Fourier Transform. and show that
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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3.3 using the fourier transform, f and g are in the first picture and the question is in the second
![der the functions
e-t, t> 0
g(t) =
0,
f(t) cos(t);
otherwise
lace Transform of f and g separately, and use the Laplace Transf
rem on L[f L[g] to show that](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb2be41da-aca8-4ddf-b812-859c045817c4%2F7b42aaf2-a8e0-40e9-8e98-14faa1c16d36%2Fnfnsn47.jpeg&w=3840&q=75)
Transcribed Image Text:der the functions
e-t, t> 0
g(t) =
0,
f(t) cos(t);
otherwise
lace Transform of f and g separately, and use the Laplace Transf
rem on L[f L[g] to show that
Transcribed Image Text:tie Lapiacе
raiisiorTI,
по
SIHOW
CIle COIV
au
integral aS deined rC
expression (10) results.
3.3. Now we switch to a Fourier Transform approach. Evaluate the Fourier Transforms of f and
g separately, and use the Fourier Transform version of the convolution theorem on F(p) G(p) to show
that
(f*g)Fourier Sin(t) + cos(t)
(11)
2
3.4. Evaluate directly the convolution integral as defined for the Fourier Transform. and show that
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