1 / 20

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.

brunsonc
Télécharger la présentation

Dr. Shoab Khan

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related