pcshw2 - THE STATE UNIVERSITY OF NEW JERSEY RUTGERS College...

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THE STATE UNIVERSITY OF NEW JERSEY RUTGERS College of Engineering Department of Electrical and Computer Engineering 332:322 Principles of Communications Systems Spring Problem Set 2 1. When Is a Carrier a Good Carrier?: Given an information signal m ( t ) you want to gen- erate r ( t ) = Am ( t ) cos(2 πf c t ) (1) However, life (your professor) is unkind and you’re only allowed to use cos 3 (2 πf c t ) as your carrier signal. That is, the first stage of your transmitter block diagram with m ( t ) as the input is going to be a multiplication by cos 3 (2 πf c t ) (instead of the usual sane cos(2 πf c t ) ). (a) Assume you can build any linear time invariant (LTI) filter you’d like. Can you fil- ter the output of the multiplier to obtain the desired signal? If so, what is the filter characteristic? (b) Suppose cos 2 (2 πf c t ) is the carrier. Repeat the previous part. (c) Suppose we generalize the carrier to be cos n (2 πf c t ) for n > 2 . When can you generate the desired r ( t ) using LTI filters. 2. Simple Envelope Detection: Consider the following AM signal s ( t ) = A c [1 + λ cos(2 πf m t )] cos (2 πf c t ) (2) The modulation factor is λ = 1 and f c f m . The AM signal is applied to an ideal envelope
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