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Discrete Fourier Transform

Discrete Fourier Transform. Multiply element-by-element. Cumulative sum shows:. 2 signals of same frequency and phase. Multiply element-by-element. Non-zero cumulative sum. Same frequency but  /2 phase difference. Element-by element product with both sine and cosine waves.

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Discrete Fourier Transform

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  1. Discrete Fourier Transform

  2. Multiply element-by-element

  3. Cumulative sum shows:

  4. 2 signals of same frequency and phase

  5. Multiply element-by-element

  6. Non-zero cumulative sum

  7. Same frequency but /2 phase difference

  8. Element-by element product with both sine and cosine waves

  9. Cumulative sums

  10. Wave: partly sine, partly cosine

  11. Element-by-element multiplication

  12. Cumulative sum

  13. dftsimp2demo(f, fs, timelen, amp) dftsimp2demo(200, 1000, 0.02, 1)

  14. dftsimp2demo(f, fs, timelen, amp) dftsimp2demo(200, 1000, 0.05, 1)

  15. dftsimp2demo(f, fs, timelen, amp) dftsimp2demo(200, 10000, 0.05, 1)

  16. dftcomplex2demo(f1, f2, fs, timelen, a1, a2) dftcomplex2demo(200, 400, 10000, 0.02, 5, 4)

  17. dftcomplex2demo(f1, f2, fs, timelen, a1, a2) dftcomplex2demo(200, 400, 10000, 0.02, 5, 4)

  18. dftspeech2demo(wavfile, timelen) dftspeech2demo('atest.wav', 0.04)

  19. dftspeech2demo(wavfile, timelen) dftspeech2demo('atest.wav', 0.04)

  20. Use dB scale and frequencies to Fs /2

  21. dftspeech2demo(wavfile, timelen) dftspeech2demo(‘itest.wav', 0.04)

  22. dftspeech2demo(wavfile, timelen) dftspeech2demo(‘itest.wav', 0.04)

  23. DFT Procedure • Given the window (frame) length, decide the base frequency • Multiply by sine wave at each multiple of base frequency • Multiply by cosine wave at each multiple of base frequency • Calculate magnitude and phase spectra using

  24. Complex Exponential • Given the window (frame) length, decide the base frequency • Multiply by sine wave at each multiple of base frequency • Multiply by cosine wave at each multiple of base frequency • Calculate magnitude and phase spectra using

  25. Compact Formulae • DFT • IDFT

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