EE3TP4-T3-ConvolutionInMatlab_v2_Lecture 12

EE3TP4-T3-ConvolutionInMatlab_v2_Lecture 12 - y n = h x n =...

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EE 3TP4 Convolution in MATLAB G. Badawy and T. Todd McMaster University 2010
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Convolution We define a mathematical operation on discrete-time signals called convolution , represented by: Given two discrete-time signals x 1 , x 2 We can also define convolutions for continuous-time signals. Given two continuous-time signals x 1 , x 2 x 1 x 2  n = k =−∞ x 1 k x 2 n k x 1 x 2  t = τ =−∞ x 1 τ x 2 t τ
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Convolution with impulse response For both continuous and discrete-time LTI systems, we define the impulse response as the special output that occurs when the input is an impulse function (Dirac delta for continuous-time systems, Kronecker Delta for discrete-time systems). This impulse response, called h, gives us the output for any input via convolution: Recall that the roles of h and x in the above may be reversed.
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Unformatted text preview: y n = h x n = k = h k x n k y t = h x t = h x t d Convolution in MATLAB The convolution in matlab is accomplished by using conv command. If u is a vector with length n and v is a vector with length m, then their convolution will be of length n+m-1 Convolution is a commutative operation. Convolution in time domain corresponds to multiplication in frequency domain. Example System Output The impulse response and input to the system is used to calculate the system output, an example follows Output...
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This note was uploaded on 02/01/2011 for the course ECE 3TP4 taught by Professor Drterrencetodd during the Fall '10 term at McMaster University.

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EE3TP4-T3-ConvolutionInMatlab_v2_Lecture 12 - y n = h x n =...

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