(Difficulty: **) Pick the correct sentence(s) among the following ones regarding the DFT X of a signal x of length N, where N is odd. Remember the following definitions for an arbitrary signal (asterisk denotes conjugation): hermitian-symmetry: a [0] real and a[n] = x[N-n]* for n = 1, ..., N - 1. hermitian-antisymmetry: [0] = 0 and a[n] =-x[N-n]* for n = 1, ... , N - 1. If the signal x is hermitian-symmetric, then its DFT is real. If the signal x is hermitian-symmetric, then the DFT X is also hermitian-symmetric. If the signal x is hermitian antisymmetric, then its DFT X is purely imaginary. If the signal x is purely real, then the DFT X is purely imaginary.
(Difficulty: **) Pick the correct sentence(s) among the following ones regarding the DFT X of a signal x of length N, where N is odd. Remember the following definitions for an arbitrary signal (asterisk denotes conjugation): hermitian-symmetry: a [0] real and a[n] = x[N-n]* for n = 1, ..., N - 1. hermitian-antisymmetry: [0] = 0 and a[n] =-x[N-n]* for n = 1, ... , N - 1. If the signal x is hermitian-symmetric, then its DFT is real. If the signal x is hermitian-symmetric, then the DFT X is also hermitian-symmetric. If the signal x is hermitian antisymmetric, then its DFT X is purely imaginary. If the signal x is purely real, then the DFT X is purely imaginary.
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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![(Difficulty: **) Pick the correct sentence(s) among the following ones regarding the DFT X of a signal x of length N,
where N is odd.
Remember the following definitions for an arbitrary signal (asterisk denotes conjugation):
hermitian-symmetry: a[0] real and æ[n] = æ[N – n]* for n = 1,..., N – 1.
hermitian-antisymmetry: æ[0] = 0 and æ[n] = -x[N – n]* for n = 1, ..., N – 1.
If the signal x is hermitian-symmetric, then its DFT is real.
If the signal x is hermitian-symmetric, then the DFT X is also hermitian-symmetric.
If the signal x is hermitian antisymmetric, then its DFT X is purely imaginary.
If the signal x is purely real, then the DFT X is purely imaginary.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50334d75-c07e-4e43-8e73-685a1f000337%2Fc21a7a0e-025f-4c5e-8660-1ae6f123d9f8%2F995448f_processed.png&w=3840&q=75)
Transcribed Image Text:(Difficulty: **) Pick the correct sentence(s) among the following ones regarding the DFT X of a signal x of length N,
where N is odd.
Remember the following definitions for an arbitrary signal (asterisk denotes conjugation):
hermitian-symmetry: a[0] real and æ[n] = æ[N – n]* for n = 1,..., N – 1.
hermitian-antisymmetry: æ[0] = 0 and æ[n] = -x[N – n]* for n = 1, ..., N – 1.
If the signal x is hermitian-symmetric, then its DFT is real.
If the signal x is hermitian-symmetric, then the DFT X is also hermitian-symmetric.
If the signal x is hermitian antisymmetric, then its DFT X is purely imaginary.
If the signal x is purely real, then the DFT X is purely imaginary.
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