WCHW7_Sol - CS5241 Wireless CommunicationsHW7 Solution 2010...

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CS5241 Wireless Communications–HW7 Solution 2010 Fall Name: Student ID: 1) This problem is concerned with the sampling of continuous-time signals. Under considera- tion are two signals x ( t ) and y ( t ) , which are bandlimited to 20 k HZ and 32 k Hz, respectively. a) Find the Nyquist sampling rate for x (2 t ) + y ( t ) b) Find the Nyquist sampling rate for x ( t ) y ( t ) Sol: a) Since W x ( t ) = 20 kHz , and x (2 t ) 1 2 X ( f 2 ) , thus W x (2 t ) = 2 × 20 kHz = 40 kHz . And W y ( t ) = 32 kHz , so the bandwidth of signal x (2 t )+ y ( t ) is W max = max(40 kHz, 32 kHz ) = 40 kHz . Therefore, f s = 2 × W max = 80 kHz . b) Since x ( t ) y ( t ) X ( f ) * Y ( f ) , so the bandwidth of signal W max = 20 kHz + 32 kHz = 52 kHz . Therefore, f s = 2 × W max = 104 kHz . 2) We consider that a signal is given by x ( t ) = 6cos(10 πt ) . Let x ( t ) be sampled at f s = 14 Hz to produce a sampled signal x s ( t ) . Find the expression for the spectrum X s ( f ) of x ( t ) and plot X s ( f ) . Sol:
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This note was uploaded on 02/08/2012 for the course ITT 650 taught by Professor Dewey during the Spring '11 term at UNC Asheville.

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WCHW7_Sol - CS5241 Wireless CommunicationsHW7 Solution 2010...

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