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hw2_modulation_filtering

hw2_modulation_filtering - Massachusetts Institute of...

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Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.02 Intro to EECS II Spring 2008 Homework #2: Modulation and Filtering Distributed: February 15, 2008 Due: February 22, 2008 1. Given the system and signals shown in Figure 1, provide a labeled plot of W ( f ) and R ( f ) for the following cases of y ( t ) : a) ( ) ( ) ( ) sin 2 1.5 , y t kHz t π = b) ( ) ( ) ( ) 2cos 2 1.5 , y t kHz t π = c) ( ) ( ) ( ) cos 2 1 . y t kHz t π = Figure 1: Demodulating receiver and associated signals. 2. Given the filter frequency response shown in Figure 2, calculate y ( t ) for: x ( t ) = cos 2 π 900 kHz ( ) t ( ) + 3sin 2 π 2 MHz ( ) t ( ) + 5cos 2 π 3.1 MHz ( ) t ( ) Figure 2: Magnitude of frequency response H(f) of lowpass filter.
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3. You are given an input signal with a spectrum shown below. 1 a) Sketch the spectrum at points A, B, C, D of the system of modulators and filters shown below. b) If you place the signal at D into the block below D what frequency f x would you choose to recover the original input signal?
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