soln7 - EECS 216 2. #4.27: SOLUTIONS TO PROBLEM SET #7...

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EECS 216 SOLUTIONS TO PROBLEM SET #7 Winter 2008 1. #4.25: 10 sketches of spectra. See next page. 2. #4.27: 2a. The filter clips off the lower half of the modulated M ( ω ), leaving a right triangle. This is called single sideband (SSB), since only half the spectrum is transmitted. BUT: Note that all the information in the signal is still present (negative freqs). ADVANTAGES: Half the bandwidth, half the power, half the noise. The problem is: 2b. h ( t ) = sin( ω 0 + ω f ) t πt - sin( ω 0 t ) πt is noncausal impulse response, so it is non-realizable. In fact, this filter must be very sharp, since ω 0 >> ω f . How many dB/decade needed? So is SSB only of theoretical interest? No–there’s more than one way to do this: 3. #4.21: See lecture notes or #4.28 to see how to use Hilbert transforms for SSB. 3a. H ( ω ) = R e - jωt πt dt = R cos( ωt ) πt dt - j R sin( ωt ) πt dt (Fourier cosine and sine transforms). 1
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soln7 - EECS 216 2. #4.27: SOLUTIONS TO PROBLEM SET #7...

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