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EXERCISES: 1. Given the periodic signal x(t)=10cos²(2.5лt)+3cos(2πt)-8sin(3лt)cos(3лt)volts. (a) Determine manually the Fourier series of x(t) using trigonometric identities. Note: The Fourier series of x(t) is expressed as a sum of a constant, cosine terms, and sine terms. (b) Determine manually the period To of x(t) from its Fourier series as determined in (a). (c) Declare x(t) as a Scilab function and then plot it from -5

EXERCISES: 1. Given the periodic signal x(t)=10cos²(2.5лt)+3cos(2πt)-8sin(3лt)cos(3лt)volts. (a) Determine manually the Fourier series of x(t) using trigonometric identities. Note: The Fourier series of x(t) is expressed as a sum of a constant, cosine terms, and sine terms. (b) Determine manually the period To of x(t) from its Fourier series as determined in (a). (c) Declare x(t) as a Scilab function and then plot it from -5

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.4: Values Of The Trigonometric Functions
Problem 42E
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EXERCISES: 1. Given the periodic signal x(t)=10cos²(2.5лt)+3cos(2πt)-8sin(3лt)cos(3лt)volts. (a) Determine manually the Fourier series of x(t) using trigonometric identities. Note: The Fourier series of x(t) is expressed as a sum of a constant, cosine terms, and sine terms. (b) Determine manually the period To of x(t) from its Fourier series as determined in (a). (c) Declare x(t) as a Scilab function and then plot it from -5<t<5. From the plotted graph, determine the fundamental period To. Is the fundamental period as shown in the graph equal to the fundamental period determined in (b)? (d) Determine the Fourier series of x(t) using Scilab up to n=30. Note: When the constant or the coefficients of the sine and cosine terms is less than 0.001 as computed in Scilab, they are considered as numerically equal to zero. As such, the constant or the corresponding sine/cosine terms are not to be included in the Fourier series. Is the Fourier series of x(t) determined using Scilab similar to the Fourier series of x(t) as determined in (a)?
Transcribed Image Text:EXERCISES: 1. Given the periodic signal x(t)=10cos²(2.5лt)+3cos(2πt)-8sin(3лt)cos(3лt)volts. (a) Determine manually the Fourier series of x(t) using trigonometric identities. Note: The Fourier series of x(t) is expressed as a sum of a constant, cosine terms, and sine terms. (b) Determine manually the period To of x(t) from its Fourier series as determined in (a). (c) Declare x(t) as a Scilab function and then plot it from -5<t<5. From the plotted graph, determine the fundamental period To. Is the fundamental period as shown in the graph equal to the fundamental period determined in (b)? (d) Determine the Fourier series of x(t) using Scilab up to n=30. Note: When the constant or the coefficients of the sine and cosine terms is less than 0.001 as computed in Scilab, they are considered as numerically equal to zero. As such, the constant or the corresponding sine/cosine terms are not to be included in the Fourier series. Is the Fourier series of x(t) determined using Scilab similar to the Fourier series of x(t) as determined in (a)?
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