HW6.pdf - ECE 301 Homework 6 Continuous-time Fourier Series Question 1(a Find the exponential Fourier series and sketch the spectra for the periodic

HW6.pdf - ECE 301 Homework 6 Continuous-time Fourier Series...

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ECE 301 Homework 6 Continuous-time Fourier Series Question 1: (a) Find the exponential Fourier series and sketch the spectra for the periodic signal y(t) depicted in Fig.1. Fig.1 (b) Show that, in general, time-compression of a periodic signal by a factor expands the Fourier spectra along the axis by the same factor . Similarly show that the time expansion of a periodic signal by a factor compresses its Fourier spectra along the axis by the factor .
Question 2: (b) In class you learn the exponential fourier series and derived the expression for the Fourier coefficient using the concept of projections, orthogonal basis signals and energy in the basis signals. Use the same concepts to derive an expression for the trigonometric Fourier series. The trigonometric Fourier series is a special case of the exponential Fourier series which applies to real signals. The only difference is a simpler choice of basis signals which consists of “sine” and “cosine” functions.

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