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7assignment - ECEN 455: Assignment 7 Problems: 1. (CSE:...

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Unformatted text preview: ECEN 455: Assignment 7 Problems: 1. (CSE: 7.31) A Hadamard matrix is defined as a matrix whose elements are 1 and its row vectors are pairwise orthogonal. In the case where n is a power of 2, and n n Hadamard matrix is constructed by means of the recursion H 2 = bracketleftbigg 1 1 1- 1 bracketrightbigg H 2 n = bracketleftbigg H n H n H n- H n bracketrightbigg Let c i denote the i th row of an n n Hadamard matrix as defined above. Show that the wave- forms constructed as s i ( t ) = n summationdisplay k =1 c ik p ( t- kT c ) , i = 1 , 2 ,...,n are orthogonal, where p ( t ) is an arbitrary pulse confined to the time interval t T c . Show that the matched filters (or crosscorrelators) for the n waveforms { s i ( t ) } can be realized by a single filter (or correlator) matched to the pulse p ( t ) followed by a set of n discrete-time crosscorrelators using the code words { c i } . 2. (CSE: 7.47) Consider a digital communication system that transmits information via QAM over a voice-band telephone channel at a rate 2400 symbols/second. The additive noise is assumed to be white and Gaussian. Determine the E b /N required to achieve an error probability of 10 5 at 4800 bps. Repeat (1) for a bit rate of 9600 bps. Repeat (1) for a bit rate of 19200 bps....
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7assignment - ECEN 455: Assignment 7 Problems: 1. (CSE:...

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