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

2. Division of Electrical and Computer Engineering, Hanyang University Digital Signal Processing Discrete Fourier Transform Fast Fourier Transform(FFT) Multi-dimensional FFT Convolution

3. Division of Electrical and Computer Engineering, Hanyang University Sampling and aliasing

4. Division of Electrical and Computer Engineering, Hanyang University Discrete Fourier Transform Fourier Transform Discrete Fourier Transform DFT: IDFT:

5. Division of Electrical and Computer Engineering, Hanyang University Fast Fourier Transform(FFT) [Danielson&Lanczos][Cooley&Tukey]

6. Division of Electrical and Computer Engineering, Hanyang University Decimation-in-time FFT Cooley-Tukey Algorithm

7. Division of Electrical and Computer Engineering, Hanyang University Sande-Tukey Algorithm

8. Division of Electrical and Computer Engineering, Hanyang University Decimation-in-frequency FFT(I) Sande-Tukey Algorithm

9. Division of Electrical and Computer Engineering, Hanyang University Decimation-in-frequency FFT (II)

10. Division of Electrical and Computer Engineering, Hanyang University Why FFT? Further reading: http://en.wikipedia.org/wiki/Cooley-Tukey_FFT_algorithm

11. Division of Electrical and Computer Engineering, Hanyang University Computation of FFT(I) input and output of four1() in NR in C

12. Division of Electrical and Computer Engineering, Hanyang University Computation of FFT(II) Eg. FFT

13. Division of Electrical and Computer Engineering, Hanyang University 2D FFT(I)

14. Division of Electrical and Computer Engineering, Hanyang University 2D FFT(II) * Generalization to L-dimension

15. Division of Electrical and Computer Engineering, Hanyang University 2D FFT(III) Eg. 2D FFT

16. Division of Electrical and Computer Engineering, Hanyang University Convolution(I) Def.

17. Division of Electrical and Computer Engineering, Hanyang University Convolution(II) Convolution theorem o direct convolution  complex computation o FFT and multiplication  less computation

18. Division of Electrical and Computer Engineering, Hanyang University Convolution(III) Convolution of discrete sampled function

19. Division of Electrical and Computer Engineering, Hanyang University Convolution(IV) Trouble in using DFT of finite duration  End effects  Treated by zero padding End effect

20. Division of Electrical and Computer Engineering, Hanyang University Convolution(V) Zero padding

21. Division of Electrical and Computer Engineering, Hanyang University Convolution(VI) Convolving very large data sets