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Numerical Convolution

Numerical Convolution. EE 327. Numerical Convolution. Numerical evaluation of the convolution integral For difficult-to-solve convolution problems We will focus on the Matlab conv function. Discretizing the Time. Convolution Integral. Discretize the Time. n  sample value.

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Numerical Convolution

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  1. Numerical Convolution EE 327

  2. Numerical Convolution • Numerical evaluation of the convolution integral • For difficult-to-solve convolution problems • We will focus on the Matlab conv function

  3. Discretizing the Time Convolution Integral Discretize the Time n sample value T  sampling period

  4. Break the Integral into Pieces(T-second intervals)

  5. Let T be sufficiently small that is relatively constant over T Then

  6. In discrete-time notation

  7. Numerical Convolution in Matlab • Use conv function • yy = conv(T*hh,xx); • yy = conv(hh,T*xx);

  8. Keys to Numerical Convolution • Convert to discrete time • The smaller the sampling period, T, the more exact the solution • Tradeoff  computation time vs. exactness of solution • Remember to account for T in the convolution  ex. T*hh

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