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Dr. Shoab Khan

Dr. Shoab Khan. Digital Signal Processing Lecture 3 LTI System. Applications. Convolution in the time domain:. y[n] = 2 –3 3 3 –6 0 1 0 0. Convolution. Useful Summation. Convolution. Stability. Causality. Causality & Stability- Example. Difference Equation.

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Dr. Shoab Khan

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  1. Dr. Shoab Khan Digital Signal Processing Lecture 3 LTI System

  2. Applications

  3. Convolution in the time domain: y[n] = 2 –3 3 3 –6 0 1 0 0

  4. Convolution

  5. Useful Summation

  6. Convolution

  7. Stability

  8. Causality

  9. Causality & Stability- Example

  10. Difference Equation • For all computationally realizable LTI systems, the input and output satisfy a difference equation of the form • This leads to the recurrence formula which can be used to compute the “present” output from the present and M past values of the input and N past values of the output

  11. Linear Constant-Coefficient Difference(LCCD) Equations

  12. Linear Constant-Coefficient Difference (LCCD) Equations…( Continued)

  13. Linear Constant-Coefficient Difference (LCCD) Equations….( Continued)

  14. First-Order Example • Consider the difference equation y[n] =ay[n−1] +x[n] We can represent this system by the following block diagram:

  15. Exponential Impulse Response • With initial rest conditions, the difference Equation has impulse response y[n] =ay[n−1] +x[n] h[n] =anu[n]

  16. Linear Constant-Coefficient Difference (LCCD) Equations….( Continued)

  17. Digital Filter Y = FILTER(B,A,X) filters the data in vector X with the filter described by vectors A and B to create the filtered data Y. The filter is a "Direct Form II Transposed" implementation of the standard difference equation: a(1)*y(n) = b(1)*x(n) + b(2)*x(n-1) + ... + b(nb+1)*x(n-nb) - a(2)*y(n-1) - ... - a(na+1)*y(n-na) [Y,Zf] = FILTER(B,A,X,Zi) gives access to initial and final conditions, Zi and Zf, of the delays.

  18. LTI summary

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