Discrete Fourier Transform

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Discrete Fourier Transform
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Multiply element-by-element
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Cumulative sum shows
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2 signals of same frequency and phase
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Multiply element-by-element
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Non-zero cumulative sum
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Same frequency but ?/2 phase difference
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Element-by element product with both sine and
cosine waves
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Cumulative sums
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Wave partly sine, partly cosine
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Element-by-element multiplication
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Cumulative sum
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dftsimp2demo(f, fs, timelen, amp) dftsimp2demo(200
, 1000, 0.02, 1)
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dftsimp2demo(f, fs, timelen, amp) dftsimp2demo(200
, 1000, 0.05, 1)
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dftsimp2demo(f, fs, timelen, amp) dftsimp2demo(200
, 10000, 0.05, 1)
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dftcomplex2demo(f1, f2, fs, timelen, a1,
a2) dftcomplex2demo(200, 400, 10000, 0.02, 5, 4)
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dftcomplex2demo(f1, f2, fs, timelen, a1,
a2) dftcomplex2demo(200, 400, 10000, 0.02, 5, 4)
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dftspeech2demo(wavfile, timelen) dftspeech2demo('a
test.wav', 0.04)
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dftspeech2demo(wavfile, timelen) dftspeech2demo('a
test.wav', 0.04)
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Use dB scale and frequencies to Fs /2
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dftspeech2demo(wavfile, timelen) dftspeech2demo(i
test.wav', 0.04)
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dftspeech2demo(wavfile, timelen) dftspeech2demo(i
test.wav', 0.04)
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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

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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

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Compact Formulae

• DFT

• IDFT