Consider that there is a function, f(t), whose Fourier transform, F(omega) is 7 rect(omega/800). F (w) = 7rect () 800 a) Find f(t). b) Sketch f(t), including specifying the peak value and the x-axis crossing values.
Consider that there is a function, f(t), whose Fourier transform, F(omega) is 7 rect(omega/800). F (w) = 7rect () 800 a) Find f(t). b) Sketch f(t), including specifying the peak value and the x-axis crossing values.
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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Transcribed Image Text:Consider that there is a function, f(t), whose Fourier transform, F(omega)
is 7 rect(omega/800).
F (w)
Trect () .
800
a) Find f(t).
b) Sketch f(t), including specifying the peak value and the x-axis crossing
values.

Transcribed Image Text:Table 4.2
Fourier Transform Operations
Operation
f(t)
F (w)
Addition
fi(t) + f2(t)
F1 (w) + F2(w)
Scalar multiplication
kf (t)
kF(w)
Symmetry
F(t)
27 f(-w)
Scaling (a real)
f(at)
Time shift
f(t – to)
F (w)e-jwto
Frequency shift (wo real)
f(t)ejwot
F(w - wo)
Time convolution
fi(t) * f2(t)
F1 (w) F2(w)
Frequency convolution
fi(t)f2(t)
1
-Fi(w) * F2(w)
d" f
Time differentiation
(ju)"F(w)
dtn
| {(2) dz
F(w)
+ TF(0)6(w)
jw
Time integration
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