(a) Let x[nj be a real periodic signal with period N and Fourier coefficients ak. (i) Show that if N is even, at least two of the Fourier coefficients within one period of ak are real. (ii) Show that if N is odd, at least one of the Fourier coefficients within one period of ak is real.
(a) Let x[nj be a real periodic signal with period N and Fourier coefficients ak. (i) Show that if N is even, at least two of the Fourier coefficients within one period of ak are real. (ii) Show that if N is odd, at least one of the Fourier coefficients within one period of ak is real.
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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Please answer the dotted red question. Thank you
![(a) Let x[nj be a real periodic signal with period N and Fourier coefficients ak.
(i) Show that if N is even, at least two of the Fourier coefficients within one
period of ak are real.
(ii) Show that if N is odd, at least one of the Fourier coefficients within one
period of ak is real.
(b) Find the closed-form expression of the convolution of the sequences
x(n) = (0.6)nu(n) and h(n) = (0.5)nu(n).
(c) ) A system with input x(t) and output y(t) is defined by the equation y(t) =
sin[x(t)].
Determine whether this system is invertible.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd72ada46-14c5-41d9-afcd-09396f15ae7b%2Fe52c23de-8013-47a0-8440-f80deaaeb971%2Fuk1wyto_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) Let x[nj be a real periodic signal with period N and Fourier coefficients ak.
(i) Show that if N is even, at least two of the Fourier coefficients within one
period of ak are real.
(ii) Show that if N is odd, at least one of the Fourier coefficients within one
period of ak is real.
(b) Find the closed-form expression of the convolution of the sequences
x(n) = (0.6)nu(n) and h(n) = (0.5)nu(n).
(c) ) A system with input x(t) and output y(t) is defined by the equation y(t) =
sin[x(t)].
Determine whether this system is invertible.
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