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QI) For the periodic signals x(f) and y() shown below: a) Find the exponential Fourier series for x(1) and y(1). b) Sketch the amplitude and phase spectra for signal x(f). c) Use Parseval's theorem to approximate the power of the periodic signal x(1) by calculating the power of the first N* harmonics, such that the strength of the N harmonic is 10% or more of the power of the DC component.

QI) For the periodic signals x(f) and y() shown below: a) Find the exponential Fourier series for x(1) and y(1). b) Sketch the amplitude and phase spectra for signal x(f). c) Use Parseval's theorem to approximate the power of the periodic signal x(1) by calculating the power of the first N* harmonics, such that the strength of the N harmonic is 10% or more of the power of the DC component.

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
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QI) For the periodic signals x(f) and y(f) shown below: х() y(t) -Sr -te e a) Find the exponential Fourier series for x(1) and y(1). b) Sketch the amplitude and phase spectra for signal x(f). c) Use Parseval's theorem to approximate the power of the periodie signal x(1) by calculating the power of the first N* harmonics, such that the strength of the Nh harmonic is 10% or more of the power of the DC component. Q2) The exponential Fourier series of a certain function is given as x() = (2+2)e" + j2e* + 3 - /2e" + (2 - /2)c* a) Sketch the exponential Fourier spectra. b) By inspection of the spectra in part (a), sketch the trigonometric Fourier spectra for x(t). Find the compact trigonometric Fourier series from these spectra. c) Show that the trigonometric series found in part (b) is equivalent to the exponential series for x(f). d) Find the signal bandwidth. Q3) Figure below shows the exponential Fourier spectra of a periodic signal x(r). a) By inspection of the Figure find the exponential Fourier series representing x(1). b) By inspection of the Figure, sketch the trigonometric Fourier spectra for x(1). c) By inspection of the trigonometric Fourier spectra found in part (b), find the trigonometric Fourier series for x(1). d) Show that the series found in parts (a) and (c) are equivalent. Q4)Find the response of an LTIC system with transfer function H(s) = x(1) = (2 +2)e*" + j2e* + 3 - j20" + (2 - j2)e* to the periodic input s+2s+3 Q5) Find the exponential Fourier scries for a periodic signal x(t) shown in Figure below The signal x(1) is applied at the input of an LTIC system shown above. Find the expression for the output y().
Transcribed Image Text:QI) For the periodic signals x(f) and y(f) shown below: х() y(t) -Sr -te e a) Find the exponential Fourier series for x(1) and y(1). b) Sketch the amplitude and phase spectra for signal x(f). c) Use Parseval's theorem to approximate the power of the periodie signal x(1) by calculating the power of the first N* harmonics, such that the strength of the Nh harmonic is 10% or more of the power of the DC component. Q2) The exponential Fourier series of a certain function is given as x() = (2+2)e" + j2e* + 3 - /2e" + (2 - /2)c* a) Sketch the exponential Fourier spectra. b) By inspection of the spectra in part (a), sketch the trigonometric Fourier spectra for x(t). Find the compact trigonometric Fourier series from these spectra. c) Show that the trigonometric series found in part (b) is equivalent to the exponential series for x(f). d) Find the signal bandwidth. Q3) Figure below shows the exponential Fourier spectra of a periodic signal x(r). a) By inspection of the Figure find the exponential Fourier series representing x(1). b) By inspection of the Figure, sketch the trigonometric Fourier spectra for x(1). c) By inspection of the trigonometric Fourier spectra found in part (b), find the trigonometric Fourier series for x(1). d) Show that the series found in parts (a) and (c) are equivalent. Q4)Find the response of an LTIC system with transfer function H(s) = x(1) = (2 +2)e*" + j2e* + 3 - j20" + (2 - j2)e* to the periodic input s+2s+3 Q5) Find the exponential Fourier scries for a periodic signal x(t) shown in Figure below The signal x(1) is applied at the input of an LTIC system shown above. Find the expression for the output y().
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