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a) For a signal h(n)= {-1, 1, 2, 1, -1} ↑ Find the expression for the DTFT of the signal, i.e. derive H(w). What is the magnitude and what is the phase of H(w)? Hint: the expressions can be simplified quite a bit if you use symmetry (before deriving the magnitude/phase). b) Prove that the DTFT of an arbitrary even signal has a phase that is either 0 or rt (i.e. that the DTFT of such a signal is real). Hint: write DTFT as a sum of pairs of symmetric terms-then simplify

a) For a signal h(n)= {-1, 1, 2, 1, -1} ↑ Find the expression for the DTFT of the signal, i.e. derive H(w). What is the magnitude and what is the phase of H(w)? Hint: the expressions can be simplified quite a bit if you use symmetry (before deriving the magnitude/phase). b) Prove that the DTFT of an arbitrary even signal has a phase that is either 0 or rt (i.e. that the DTFT of such a signal is real). Hint: write DTFT as a sum of pairs of symmetric terms-then simplify

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Problem 3 a) For a signal h(n)= (-1, 1, 2, 1,-1) Find the expression for the DTFT of the signal, i.e. derive H(w). What is the magnitude and what is the phase of H(w)? Hint: the expressions can be simplified quite a bit if you use symmetry (before deriving the magnitude/phase). b) Prove that the DTFT of an arbitrary even signal has a phase that is either 0 or rt (i.e. that the DTFT of such a signal is real). Hint: write DTFT as a sum of pairs of symmetric terms-then simplify
Transcribed Image Text:Problem 3 a) For a signal h(n)= (-1, 1, 2, 1,-1) Find the expression for the DTFT of the signal, i.e. derive H(w). What is the magnitude and what is the phase of H(w)? Hint: the expressions can be simplified quite a bit if you use symmetry (before deriving the magnitude/phase). b) Prove that the DTFT of an arbitrary even signal has a phase that is either 0 or rt (i.e. that the DTFT of such a signal is real). Hint: write DTFT as a sum of pairs of symmetric terms-then simplify
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