Answered: 2. Given the periodic square function…

2. Given the periodic square function shown as x(t) -6 2 (a) Declare the function as a Scilab function and then plot it for -5

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section2.4: Average Rate Of Change Of A Function

Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.

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Question

2. Given the periodic square function shown as
x(t)
-6
2
(a) Declare the function as a Scilab function and then plot it for -5<t≤5.
(b) Determine the Fourier series of x(t) with 3 harmonic components.
(c) Determine the Fourier series of x(t) in magnitude-phase form with 3 harmonic components.
(d) Plot the graph of x(t) as reconstructed from its Fourier series with 3 harmonic components.
(e) Plot the graph of x(t) as reconstructed from its Fourier series with 10 harmonic components.
(f) Plot the graph of x(t) as reconstructed from its Fourier series with 20 harmonic components.
(g) Do the graphs exhibit Gibb's phenomenon?
Gibb's phenomenon is the presence of increasing fluctuations at the vicinity of the jump
discontinuity of a function.

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