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Given a continuous time signal x(t). Sample the signal with a sampling rate of Fs=100 samples/s. x(t) = cos(2π40t) ● What is the frequency of the cosine in Hz? What is the frequency of the cosine in rad/s? What is the frequency of the sampled cosine in normalized rad/s?

Given a continuous time signal x(t). Sample the signal with a sampling rate of Fs=100 samples/s. x(t) = cos(2π40t) ● What is the frequency of the cosine in Hz? What is the frequency of the cosine in rad/s? What is the frequency of the sampled cosine in normalized rad/s?

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Given a continuous time signal \( x(t) \). Sample the signal with a sampling rate of \( F_s = 100 \) samples/s. \[ x(t) = \cos(2\pi 40t) \] - What is the frequency of the cosine in Hz? - What is the frequency of the cosine in rad/s? - What is the frequency of the sampled cosine in normalized rad/s? - What is the frequency of the sampled cosine in normalized Hz? - Using \( N = 50 \), what is the DFT of the sampled signal? What are the indexes where the DFT is non-zero? - In MATLAB, generate the sampled signal and plot the magnitude of the DFT with index \( k \) on the x-axis. - In MATLAB, plot the magnitude of the DFT with Hz on the x-axis.
Transcribed Image Text:Given a continuous time signal \( x(t) \). Sample the signal with a sampling rate of \( F_s = 100 \) samples/s. \[ x(t) = \cos(2\pi 40t) \] - What is the frequency of the cosine in Hz? - What is the frequency of the cosine in rad/s? - What is the frequency of the sampled cosine in normalized rad/s? - What is the frequency of the sampled cosine in normalized Hz? - Using \( N = 50 \), what is the DFT of the sampled signal? What are the indexes where the DFT is non-zero? - In MATLAB, generate the sampled signal and plot the magnitude of the DFT with index \( k \) on the x-axis. - In MATLAB, plot the magnitude of the DFT with Hz on the x-axis.
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