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hw 6 sol

hw 6 sol - 1 EE102 Spring 2009-10 Systems and Signals Lee...

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1 EE102 Spring 2009-10 Lee Systems and Signals Homework #6 Solution Due: Tuesday May. 17 5PM 1. Single Sideband (SSB) Communication The double sideband (DSB) systems require a transmission bandwidth that is twice the sig- nal bandwidth. In this question we’ll look at a system where the transmission bandwidth and signal bandwidth are the same. The system is plotted below: × m ( t ) cos ( ω c t ) × cos ( ω c t ) m ( t ) Propagation Transmitter Receiver 2 Ideal Bandpass Ideal Lowpass x ( t ) y ( t ) z ( t ) (a) H ( j ω ) The signal m ( t ) is first modulated by cos( ω c t ) , and then passed through an ideal bandpass filter. The spectrum of the input M ( ) and the frequency response of the ideal bandpass filter H ( ) are - 2 π B 2 π B ω 2 π B ω c - ω c ω - ω c ω c 2 π B (b) (c) 1 M ( j ω ) H ( j ω ) The modulated signal is x ( t ) , and the output of the ideal bandpass is y ( t ) . This signal is transmitted, and processed by a synchronous receiver. Sketch the signal spectrum at (a) the output of the modulator X ( ) , (b) the output of the ideal bandpass Y ( ) , and

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2 (c) the output of the demodulator, Z ( ) . Label the bands in Y ( ) , and show where they end up in Z ( ) .
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