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Challenge_11-1 - EEL 3135 Signals and Systems Dr Fred J...

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EEL 3135: Signals and Systems Dr. Fred J. Taylor, Professor Lesson Title: Convolution Lesson Number: 11 (Section 5-3) Challenge 11 Problem P5-6 in the text asks you to consider using an L=4 sample moving average filter to process a signal x[k]=(0.5) k u[k], where u[k] is a unit step function beginning at k=0. You are asked to determine the output y[k] for k [-5,10]. The textbook notes that the sum shown below, can be expressed in close form: a a a a N M N M k k - - = + = 1 ) 1 ( To illustrate, for M=0 and “a” arbitrary: a a a a a a a a a a a a a N k k N k k N k N k k k k k k k - - = - = - = + + + + = - = + = + = = + = = = 1 1 ... 1 1 1 ) 1 ( 0 1 0 0 1 0 0 3 2 --------------------- For a=0.5, the L=4 MA linear convolution yields:
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