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A continuous time function, x(t), is sampled at a sampling period of At = 25 microseconds to form a discrete time signal, x[n], which is stored in a buffer that holds 256 samples. a.) If a discrete Fourier transform (DFT) is taken of the samples in the buffer to estimate the spectrum with the vector, X[k], what is the frequency in Hz repre- sented by the spacing between consecutive frequency samples? b.) If the X[k] = 320/j for k = 17 and X[k] = -320/j for k= 239. For all other values of k in the range 0 ≤ k ≤ N 1, X[k] = 0. What is x[n]? c) Assuming the original time signal, x(t), was oversampled to get x[n], what was x(t) before it was sampled?

A continuous time function, x(t), is sampled at a sampling period of At = 25 microseconds to form a discrete time signal, x[n], which is stored in a buffer that holds 256 samples. a.) If a discrete Fourier transform (DFT) is taken of the samples in the buffer to estimate the spectrum with the vector, X[k], what is the frequency in Hz repre- sented by the spacing between consecutive frequency samples? b.) If the X[k] = 320/j for k = 17 and X[k] = -320/j for k= 239. For all other values of k in the range 0 ≤ k ≤ N 1, X[k] = 0. What is x[n]? c) Assuming the original time signal, x(t), was oversampled to get x[n], what was x(t) before it was sampled?

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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A continuous time function, x(t), is sampled at a sampling period of At = 25 microseconds to form a discrete time signal, x[n], which is stored in a buffer that holds 256 samples. a.) If a discrete Fourier transform (DFT) is taken of the samples in the buffer to estimate the spectrum with the vector, X[k], what is the frequency in Hz repre- sented by the spacing between consecutive frequency samples? = b.) If the X[k] = 320/j for k= 17 and X[k] = values of k in the range 0 ≤ k ≤ N 1, X[k] = 0. What is x[n]? -320/j for k= 239. For all other c) Assuming the original time signal, r(t), was oversampled to get x[n], what was x(t) before it was sampled?
Transcribed Image Text:A continuous time function, x(t), is sampled at a sampling period of At = 25 microseconds to form a discrete time signal, x[n], which is stored in a buffer that holds 256 samples. a.) If a discrete Fourier transform (DFT) is taken of the samples in the buffer to estimate the spectrum with the vector, X[k], what is the frequency in Hz repre- sented by the spacing between consecutive frequency samples? = b.) If the X[k] = 320/j for k= 17 and X[k] = values of k in the range 0 ≤ k ≤ N 1, X[k] = 0. What is x[n]? -320/j for k= 239. For all other c) Assuming the original time signal, r(t), was oversampled to get x[n], what was x(t) before it was sampled?
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