The Fourier transform of a function } (t) iš defihed by F(w) = f(t)e-jwtdt %3D a) Using the above definition, find the Fourier transform F(w) of the following function: f(t) = e=t + (t – 1)e-2t Ost<∞ b) Write down expressions for the modulus and the phase of F(@). c) Find the values for the modulus and phase of F(@) at w = 0, 1,5, co.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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The Fourier transform of a function f(t) is defined by
00
F(@) =
f(t)e-jutdt
-0-
a) Using the above definition, find the Fourier transform F(w) of the following function:
f(t) = e-t + (t – 1)e-2t
Ost<∞
b) Write down expressions for the modulus and the phase of F(@).
c) Find the values for the modulus and phase of F(@) at w = 0, 1,5, co.
Transcribed Image Text:The Fourier transform of a function f(t) is defined by 00 F(@) = f(t)e-jutdt -0- a) Using the above definition, find the Fourier transform F(w) of the following function: f(t) = e-t + (t – 1)e-2t Ost<∞ b) Write down expressions for the modulus and the phase of F(@). c) Find the values for the modulus and phase of F(@) at w = 0, 1,5, co.
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