convolution_extra

# 1 0 1 n 1 additional notes on convolution

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Unformatted text preview: −1 n + 1, y ( n ) = 2 N − 1 − n, N − 1 ≤ n ≤ 2 N − 2 0, otherwise N y(n) ... ... ... ... -1 0 1 N-1 Additional Notes on Convolution Sum Computation 2N-1 n ECE 5650/4650 Modern DSP Notes 4 Example: Two finite duration sequences in sequence explicit representation: h(n) = {1, 2, 1, − 1}, ↑ x(n) = {1, 2, 3,1} ↑ – In the above notation the arrows indicate where n = 0 We need to evaluate the convolution sum for −1 ≤ n ≤ 5 – To evaluate construct the following table: – x(k) vs k h(n-k) 0 0 1 2 3 1 0 0 n = -1 -1 1 2 1 0 0 0 0 0 0 1 n=0 0 -1 1 2 1 0 0 0 0 0 4 n=1 0 0 -1 1 2 1 0 0 0 0 8 n=2 0 0 0 -1 1 2 1 0 0 0 8 n=2 0 0 0 0 -1 1 2 1 0 0 3 n=3 0 0 0 0 0 -1 1 2 1 0 -2 n=4 0 0 0 0 0 0 -1 1 2 1 -1 – y(n) The final output is thus y (n) = { 0,1, 4, 8, 8, 3, − 2, − 1, 0, 0 } ↑ –...
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## This document was uploaded on 02/25/2012.

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