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Discrete-time Fourier Transform

Discrete-time Fourier Transform. Prof. Siripong Potisuk. Derivation of the Discrete-time Fourier Transform. Recall DTFS pair. where. Thus,. Periodic in w with period 2 p. The limit of integration is over any interval of 2 p in w. DTFT Pair. Conditions for Convergence . Examples. IDTFT.

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Discrete-time Fourier Transform

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  1. Discrete-time Fourier Transform Prof. Siripong Potisuk

  2. Derivation of the Discrete-time Fourier Transform

  3. Recall DTFS pair where

  4. Thus, Periodic inw with period 2p The limit of integration is over any interval of2p inw

  5. DTFT Pair

  6. Conditions for Convergence

  7. Examples

  8. IDTFT

  9. 6) Complex Exponentials

  10. DTFT of Periodic Signals Recall the following DTFT pair: Represent periodic signal x[n]in terms of DTFS:

  11. Example: A discrete-time Sine Function

  12. Example: A discrete-time Periodic Impulse Train The DTFS coefficients for this signal are: ck

  13. Properties of DTFT

  14. Properties of DTFT

  15. Convolution Property

  16. Multiplication Property

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