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Unformatted text preview: ECE 178 Digital Image Processing Discussion Session #3 Anindya Sarkar & Mehmet Emre Sargin anindya,[email protected] January 26, 2007 1D Linear Convolution Example: Let us find the result of convolving a signal x[n] with itself, with the resultant output being y [ n ]. y [ n ] = x [ n ] * x [ n ] where x [ n ] = h a b c d e i , and * indicates linear discrete convolution. The boxed value represents the origin. Applying 1D convolution formula, the output y [ n ] obtained on passing a signal x [ n ] through a system with impulse response h [ n ] is given by: y [ n ] = X k x [ k ] h [ n k ]; here h [ n ] = x [ n ] (1) Superimpose x [ n ] on x [ n ] and sum up overlapping elements to find y [0] a b c d e e d c b a Output y [0] = ac + b 2 + ac Superimpose x [ n + 1] on x [ n ] and sum up overlapping elements to find y [1] a b c d e e d c b a Output y [1] = ad + bc + cb + da Superimpose x [ n + 2] on x [ n ] and sum up overlapping elements to find y [2] a b c d e e d c b a Output y [2] = ae + bd + c 2 + db + ae Superimpose x [ n + 3] on x [ n ] and sum up overlapping elements to find y [3] a b c d e e d c b a Output y [3] = be + cd + dc + eb 1 DS#3 ECE 178 Anindya Sarkar & Mehmet Emre Sargin anindya,[email protected] Superimpose x [ n + 4] on x [ n ] and sum up overlapping elements to find y [4] a b c d e e d c b a Output y [4] = ce + d 2 + ce Superimpose x [ n + 5] on x [ n ] and sum up overlapping elements to find y [5] a b c d e e d c b a Output y [5] = de + ed Superimpose x [ n + 6] on x [ n ] and sum up overlapping elements to find y [6] a b c d e e d c b a Output y [6] = e 2 In a similar manner, you can determine y [ n ] for n < 0. This time, you will shift0....
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This note was uploaded on 06/12/2009 for the course ECE 178 taught by Professor Manjunath during the Winter '08 term at UCSB.
 Winter '08
 MANJUNATH
 Image processing

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