Lecture5H - Lecture 5 DSP Convolution and correlation 5.1...

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Unformatted text preview: Lecture 5 DSP Convolution and correlation 5.1 Convolution: Convolution is a method which described the relation between the input to a linear time invariant system x(n), and the output y(n) . The convolution formula used to determine the output of an LTI system to any given arbitrary input signal ∑ ∑ ∞ −∞ = ∞ −∞ = − = − = k k k n x k h n y or k n h k x n y ) ( ) ( ) ( ) ( ) ( ) ( In most practical cases there are many more finite sample values in x(n) and probably also more in h(n) then superpose many more individual responses to find the output signal. The convolution method may also be performed graphically as described by the following example Example 5-1 : The impulse response of a linear time invariant system is h(n)=[1,2,1,-1] . Determine the response of the system to input signal x(n)= [1,2,3,1] Solution: Note that, the arrow show the sample value at n=0 -1 1 2 3 4 0.5 1 1.5 2 2.5 3 x(n) n-2-1 1 2 3-1-0.5 0.5 1 1.5 2 h(n) n ) 3 ( ) 3 ( ) 2 ( ) 2 ( ) 1 ( ) 1 ( ) ( ) ( ) ( ) ( ). ( ) ( 4 − + − + − + = − = ∑ = n h x n h x n h x n h x n y k n h k x n y k-2-1 1 2 3-1-0.5 0.5 1 1.5 2 n x(0)h(n)-1 1 2 3 4-2-1 1 2 3 4 x(1)h(n-1) n-1 1 2 3 4 5-4-2 2 4 6 x(2)h(n-2) n 1 2 3 4 5 6-1-0.5 0.5 1 1.5 2 x(3)h(n-3) n +-4-2 2 4 6-2 2 4 6 8 y(n) n 5.2 Convolution Properties • Commutative Property...
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This note was uploaded on 02/04/2012 for the course COMPUTER 101 taught by Professor Ahmed during the Spring '11 term at alamo.edu.

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Lecture5H - Lecture 5 DSP Convolution and correlation 5.1...

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