tut2_problems_31_01_09

# tut2_problems_31_01_09 - Department of Electrical...

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Department of Electrical Engineering EE 308: Communication Systems (Spring 2009) Course Instructor: Prof. Abhay Karandikar Problem Set 2 1. An AM signal x c ( t ) = A c cos(2 πf c t ) m ( t ) is passed through a ﬁlter of impulse response h ( t ), resulting in an output v ( t ). Find the conditions on h ( t ) so that m ( t ) can be recovered from v ( t ) by synchronous detection. h ( t ) is called the “Sideband Shaping Filter”. For example, h ( t ) may be designed so as to pass one sideband of the AM signal completely, wheras retain only a trace or vestige of the other sideband. The resulting output v ( t ) is then called the Vestigial Sideband modulated signal. 2. Let x c ( t ) = cos ω c t + 0 . 2 cos ω m t sin ω c t . (a) Show that x c ( t ) is a combination AM-FM signal. (b) Sketch the phasor diagram at t = 0. 3. The envelope detector illustrated in Fig. 3 is to be used to demodulate the AM signal x c ( t ) = A c (1 + cos 2 πf m t ) cos 2 πf c t, f c >> f m . (a) Sketch the waveshape of the current through the diode.

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tut2_problems_31_01_09 - Department of Electrical...

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