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# Quiz1 - x[n =(1/2)^n u[n a DTFT b DTFS c CTFS d CTFT...

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ECSE 304 Signals and Systems 2 Online Quiz #1 Solutions 1. What is the fundamental period of the following DT signal? x[n] = cos(pi*n/4) + sin(2*pi*n/6) a) 24 b) 6 c) 12 d) 48 Solution : The fundamental periods of cos(pi*n/4) and sin(2*pi*n/6) are N = 8 and N = 3, respectively. Thus, the fundamental period for their linear combination is N = 24. 2. Is the signal ( ) + = n j n x n 8 2 cos ] [ 2 π periodic? If so, determine the fundamental period. ( ) ,...} 1 , , 1 , , 1 { j j j n = is periodic with period N = 4. + = n n 4 2 cos 2 1 2 1 8 2 cos 2 π π is periodic with period N = 4 Thus, x [ n ] is periodic with fundamental period N = 4. 3. Identify the appropriate Fourier representation for the following signal:

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