Given a continuous time signal x(t). Sample the signal with a sampling rate of F=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 F=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)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Fourier Transform

In mathematics, the Fourier transformation is a mathematical transformation that rotates responsibilities by using region or time into tasks depending on the local or temporal frequency, such as the rendering of a musical track in step with existing volumes and frequencies. The term Fourier amendment refers to each illustration of the frequency range and the mathematical functionality related to the representation of the frequency domain and the function of space or time.

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Homework Help (7)

Given a continuous time signal x(t). Sample the signal with a sampling rate of F₁=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?
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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