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Figure P7.28(a) shows a system that converts a continuous-time signal to a discretetime
Chapter 7, Problem 7.28(choose chapter or problem)
Figure P7.28(a) shows a system that converts a continuous-time signal to a discretetime signal. The input x(t) is periodic with a period of 0.1 second. The Fourier series coefficients of x(t) are ( 1 Jkl ak = "2 , -oo < k < +oo. The lowpass filter H(jw) has the frequency response shown in Figure P7.28(b). The sampling period T = 5 x 10-3 second. (a) Show that x[n] is a periodic sequence, and determine its period. (b) Determine the Fourier series coefficients of x[n].
Questions & Answers
QUESTION:
Figure P7.28(a) shows a system that converts a continuous-time signal to a discretetime signal. The input x(t) is periodic with a period of 0.1 second. The Fourier series coefficients of x(t) are ( 1 Jkl ak = "2 , -oo < k < +oo. The lowpass filter H(jw) has the frequency response shown in Figure P7.28(b). The sampling period T = 5 x 10-3 second. (a) Show that x[n] is a periodic sequence, and determine its period. (b) Determine the Fourier series coefficients of x[n].
ANSWER:Step 1 of 3
Fourier series is an approximated process by which any non-standard signal is converted into a standard signal. The approximation of a given function by Fourier series gives a smooth function even when the function being approximated as discontinuities.