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Chapter 9 Computation of the Discrete Fourier Transform

Chapter 9 Computation of the Discrete Fourier Transform. 9.1 decimation-in-time FFT Algorithms 9.2 decimation-in-frequency FFT Algorithms 9.3 IFFT Algorithm 9.4 FFT Algorithm of real sequence 9.5 practical considerations （ software realization). Direct computation:.

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Chapter 9 Computation of the Discrete Fourier Transform

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  1. Chapter 9 Computation of the Discrete Fourier Transform 9.1 decimation-in-time FFT Algorithms 9.2 decimation-in-frequency FFT Algorithms 9.3 IFFT Algorithm 9.4 FFT Algorithm of real sequence 9.5 practical considerations（software realization)

  2. Direct computation: Complex multiplication: Complex addition: Real multiplication: Real addition:

  3. 9.1 decimation-in-time FFT Algorithms Figure 9.3

  4. Figure 9.9

  5. Figure 9.5

  6. Figure 9.10 strongpoint：in-place computations shortcoming：non-sequential access of data

  7. compare the operation quantity

  8. alternative forms： Figure 9.14 strongpoint：in-place computations shortcoming：non-sequential access of data

  9. Figure 9.15 shortcoming：not in-place computation non-sequential access of data

  10. Figure 9.16 shortcoming：not in-place computation strongpoint: sequential access of data

  11. Figure 9.17 9.2 decimation-in-frequency FFT Algorithms

  12. Figure 9.19

  13. Figure 9.18

  14. Figure 9.20

  15. the two kinds of butterfly computation are transpose of each other.

  16. alternative forms： Figure 9.22

  17. Figure 9.23

  18. Figure 9.24

  19. 1。 attention：the difference to transpose 9.3 IFFT Algorithm

  20. DIT-FFTDIF-IFFT

  21. DIF-FFTDIT-IFFT

  22. 2， step: （1）X*[k] （2）FFT{ } （3）（）*/N can transfer FFT subprogram directly 3。Method 3( exercise 9.1)

  23. 9.4 FFT Algorithm of real sequence

  24. in-place computation Figure 9.11 9.5 practical considerations

  25. must padding 0 to cause of bit-reversed order binary coding for position： 000 001 010 011 100 101 110 111 Figure 9.13

  26. Coefficient: WNr r=0,1,…N/2-1

  27. summary: 9.1 decimation-in-time FFT Algorithms 9.2 decimation-in-frequency FFT Algorithms 9.3 IFFT Algorithm 9.4 FFT Algorithm of real sequence 9.5 practical considerations（software realization)

  28. requirements： 1. derivation of decimation-in-time and decimation-in-frequency FFT algorithms, and draw the graphs ; 2. draw flow graph of IFFT; 3. special arithmetic of real-sequence FFT; 4. concepts of in-place computation and bit-reversed order.

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