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ECE405HW3Su2010

# ECE405HW3Su2010 - ECE 405 HOMEWORK#3 SUMMER 2010 DR JAMES S...

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ECE 405 HOMEWORK #3 SUMMER 2010 ©DR. JAMES S. KANG 1 Given ( ) 10, 3 3 10 0, 6 t t m t rect otherwise = = , (a) determine the Hilbert transform of ( ) m t . (b) If m(t) upper single-sideband modulates a carrier ( ) 100cos 2 1000 t π , what is the modulated waveform ( ) USSB m t ? 2 Determine the Hilbert transform of ( ) ( ) ( ) ( ) 4sin 12 cos 7 cos 3 m t t t t = . 3 Given ( ) 1, 10 0 10 1, 0 10 10 10 0, t t t t m t tri t otherwise + < = = + < , sketch the Hilbert transform by graphically performing the convolution ( ) ˆ m t ( ) 1 m t t π . 4 In the system shown below, assume that ( ) m t = +1 or –1. (a) Determine the output v o (t) when DSB–SC signal ( ) ( ) ( ) cos in c c v t A m t t ω = is applied at the input. (b) Determine the output when SSB–SC signal ( ) o v t ( ) ( ) ( ) ( ) ( ˆ cos cos in c c v t m t t m t t ) ω ω = + is applied at the input. (c) From the results of (a) and (b), state whether the system can be used to recover carrier from the modulated signals DSB–SC and SSB–SC.

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ECE405HW3Su2010 - ECE 405 HOMEWORK#3 SUMMER 2010 DR JAMES S...

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