This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 discretetime crosscorrelators using the code words { c i } . 2. (CSE: 7.47) Consider a digital communication system that transmits information via QAM over a voiceband 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....
View Full
Document
 Spring '08
 Staff
 Recursion

Click to edit the document details