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FFT and STFT

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Signal Representation by Harmonic Sinusoids

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  • Question
    • How to decompose it to harmonic sinusoids
    • How to find the coefficients of harmonic sinusoids
    • How to find the frequency components

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Fast Fourier Transform (FFT)

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FFT with Sampling Frequency

  • You can think this signal as a vibration signal from a rotating machinery with 60 Hz

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Implementing FFT Routine

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Single-sided FFT (or Positive FFT)

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STFT (Short-Time Fourier Transformation)

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Issue on FFT

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Issue on FFT

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Short-Time Fourier Transformation

  • Define analysis window
  • Define the amount of overlap between windows
    • e.g., 30%
  • Define a windowing function
    • e.g., Hann, Gaussian
  • Generate windowed segments
    • Multiply signal by windowing function
  • Apply the FFT to each windowed segment

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STFT in Python

  • Python function ‘spectrogram’ is useful for easily computing STFTs

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STFT: Time and Frequency

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STFT Resolution Trade-off

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