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 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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Unformatted text preview: x[n] = (1/2)^n u[n] a) DTFT b) DTFS c) CTFS d) CTFT Solution : The signal is discrete and aperiodic so it must be analyzed with the DTFT. 4. Identify the appropriate Fourier representation for the following signal: x[n] = (j)^n where j^2 = -1 a) DTFT b) DTFS c) CTFS d) CTFT Solution: The signal is discrete and periodic (with N = 4) so it should be analyzed with the DTFS. 5. The DTFS and DTFT of a periodic DT signal have the same representation. Solution: True 6. The spectrum of a signal is measured and found to be continuous. The signal MUST be CT. Solution: False...
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Quiz1 - x[n =(1/2)^n u[n a DTFT b DTFS c CTFS d CTFT...

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