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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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