Use the Fourier transform of cos(k2ot) to find the Fourier transform of a periodic signal x(t) with a Fourier series x(1) = 1+(0.5) cos(k2ot). k=1
Use the Fourier transform of cos(k2ot) to find the Fourier transform of a periodic signal x(t) with a Fourier series x(1) = 1+(0.5) cos(k2ot). k=1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please write in clear handwriting or via Word
![5.7 Use the properties of the Fourier transform in the following problems.
(a) Use the Fourier transform of cos(k2ot) to find the Fourier transform of a periodic signal
x (t) with a Fourier series
00
x(t) = 1+(0.5)* cos(k2ot).
k=1
(b) Find the Fourier transform of
1
x1(t)=
a > 0
12+ a²
by considering the properties of the transform. Hint: use the FT of e¬alrl for a > 0.
Answer: (b) X1(S2) = (1/a)e¬a\2].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F715ad422-c0c9-4bb1-9209-6734503c0d0c%2F93e60872-4589-4929-8e26-92af409a22b6%2F7505lfi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5.7 Use the properties of the Fourier transform in the following problems.
(a) Use the Fourier transform of cos(k2ot) to find the Fourier transform of a periodic signal
x (t) with a Fourier series
00
x(t) = 1+(0.5)* cos(k2ot).
k=1
(b) Find the Fourier transform of
1
x1(t)=
a > 0
12+ a²
by considering the properties of the transform. Hint: use the FT of e¬alrl for a > 0.
Answer: (b) X1(S2) = (1/a)e¬a\2].
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
