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Numerical Analysis – Digital Signal Processing

Numerical Analysis – Digital Signal Processing. Hanyang University Jong-Il Park. Digital Signal Processing. Discrete Fourier Transform Fast Fourier Transform(FFT) Multi-dimensional FFT Convolution. Sampling and aliasing. Discrete Fourier Transform. Fourier Transform

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Numerical Analysis – Digital Signal Processing

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  1. Numerical Analysis – Digital Signal Processing Hanyang University Jong-Il Park

  2. Digital Signal Processing • Discrete Fourier Transform • Fast Fourier Transform(FFT) • Multi-dimensional FFT • Convolution

  3. Sampling and aliasing

  4. Discrete Fourier Transform • Fourier Transform • Discrete Fourier Transform DFT: IDFT:

  5. Fast Fourier Transform(FFT) [Danielson&Lanczos][Cooley&Tukey]

  6. Decimation-in-time FFT Cooley-Tukey Algorithm

  7. Sande-Tukey Algorithm

  8. Decimation-in-frequency FFT(I) Sande-Tukey Algorithm

  9. Decimation-in-frequency FFT (II)

  10. Why FFT? Further reading: http://en.wikipedia.org/wiki/Cooley-Tukey_FFT_algorithm

  11. Computation of FFT(I) input and output of four1() in NR in C

  12. Computation of FFT(II) • Eg. FFT

  13. 2D FFT(I)

  14. 2D FFT(II) * Generalization to L-dimension

  15. 2D FFT(III) • Eg. 2D FFT

  16. Convolution(I) • Def.

  17. Convolution(II) • Convolution theorem o direct convolution complex computation o FFT and multiplication less computation

  18. Convolution(III) • Convolution of discrete sampled function

  19. Convolution(IV) • Trouble in using DFT of finite duration End effects  Treated by zero padding • End effect

  20. Convolution(V) • Zero padding

  21. Convolution(VI) • Convolving very large data sets <Overlap-add method>

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