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
icon
Related questions
Question
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: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.
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
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
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 1 images

Blurred answer
Knowledge Booster
Fourier Transformation
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,