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Digital Signal Processing: DTFT Properties & Filters, Ideal Delay, Lowpass Filters, Linear Phase Symmetry

Explore the practical applications of Digital Signal Processing with lecture insights on DTFT properties, ideal delay, lowpass filters, and linear phase symmetry. Understand frequency response, magnitude, angle plots, and DTFT characteristics for efficient signal processing.

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Digital Signal Processing: DTFT Properties & Filters, Ideal Delay, Lowpass Filters, Linear Phase Symmetry

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  1. Dr. Shoab Khan Digital Signal Processing Lecture 4 DTFT

  2. Complex Exp Input Signal

  3. The Frequency Response

  4. Delay and First Difference

  5. More on the Ideal Delay

  6. Discrete Time Fourier Transform

  7. Fourier with DTFT Mag-Phase

  8. Properties

  9. Properties…(cont)

  10. Symmetric Properties DTFT Properties:

  11. Consequences of Hermitian Symmetry If then And symmetry

  12. DTFT- Sinusoids

  13. DTFT of Unit Impulse

  14. Ideal Lowpass Filter

  15. Example

  16. Magnitude and Angle Form

  17. Magnitude and Angle Plot

  18. Example

  19. w w - w - w 2 j j j 2 j = + + + + e 2 e 3 2 e e = w + w + 2 cos( 2 ) 4 cos( ) 3 Real and Even ( Zero Phase) Consider an LTI system with an even unit sample response DTFT is

  20. Real & Even (Zero Phase) • Frequency response is real, so system has “zero” phase shift • This is to be expected since unit sample response is real and even.

  21. Linear Phase symmetryLP

  22. Useful DTFT Pairs

  23. Convolution Theorem

  24. Linear Phase… ( cont.)

  25. freqfilter

  26. Frequency Response of DE

  27. Matlab

  28. Example

  29. Ideal Filters

  30. Ideal Filters

  31. Ideal Lowpass Filter

  32. h[n] of ideal filter

  33. Approximations

  34. Freq Axis

  35. Inverse System

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