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Unformatted text preview: Carleton University SYSC 5504 Department of Systems and Computer Engineering ELG 6154 Principles of Digital Communications Fall 2009/10 Assignment #1 Due on Wednesday, October 14, 2007 1. Sketch the spectrum x ( f ) = T sin( [ f f c ] T ) [ f f c ] T 2 with f c = 1 GHz and T = 10- 7 seconds, then find the (a) null-to-null bandwidth, (b) the 3 dB bandwidth, and (c) the 99% power bandwidth (use numerical integration). 2. Suppose x ( t ) is a zero-mean stationary Gaussian random process with power spectral density x ( f ) is the input to a linear filter whose impulse response show below. A sample, Y , is taken of the output of the filter at time T .- 6 ? h ( t ) t 1 T T (a) Calculate the mean and variance of Y in terms of x ( f ) and T . (b) Upper bound the variance under the condition x ( f ) S for all f . 3. For the data signals s ( t ), s 1 ( t ), s 2 ( t ), and s 3 ( t ) shown below: (a) Find a set of orthonormal basis signals, and express the data signals as linear combinations of the basis signals.(a) Find a set of orthonormal basis signals, and express the data signals as linear combinations of the basis signals....
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- Fall '09