Signal Processing in the Time-Frequency Domain

Signal Processing in the Time-Frequency Domain

• Time-Frequency Linear Transformation. Advantage: similar to classical spectral methods in concept and strategy.
  • Short-Time-Fourier Transform (STFT)
    • Advantage: Allow easy comparison along the TFR (time-frequency representation).
    • Disadvantage: The width of the window is fixed during the whole analysis.
  • CWT: Continuous Wavelet Transform
    • Advantage: Minimize the redundancy and omitted information.
    • Disadvantage: Non-adaptive nature. High dependent of wavelet selection.
  • DWT: Discrete Wavelet Transform
  • UDWT: Undecimated Discrete Wavelet Transform
• Bilinear (or Quadratic) Transformation: Advantage: It can be analyzed the energy distribution of the considered signal.
  • WVD: Wigner Ville Distribution
    • Advantage: Basic time-frequency distribution.
    • Disadvantage: High cross-terms affectation.
  • PWVD: Pseudo Wigner-Ville
    • Advantage: Allows smooth cross-terms in frequency axes.
    • Disadvantage: Cross-terms affectation.
  • SPWVD: Smoothing Pseudo Wigner-Ville
    • Advantage: Allows smooth cross-terms in frequency axes.
    • Disadvantage: Reduce the cross-terms effects instead removing the original causes.
  • CWD: Choi-Williams Distribution
    • Advantage: Good trade-off between resolution and cross-term suppression.
    • It is necessary a configuration/analysis stage to obtain good results.
  • BJD: Bon-Jordan Distribution
    • Advantage: Marginal properties imposition in time and frequency.
    • Disadvantage: High cross-terms affectation.
  • ZAMD: Zao-Athlas Mark Distribution
    • Advantage: Smooth variant in frequency of BJD. High-resolution.
    • Disadvantage: Cross-terms affectation.
• Signal Decomposition. Advantage: Time-frequency information obtained from a different point of view.
  • HHT: Hilbert–Huang Transform
    • HHT
      • Advantage: It is a self-adaptive to he signal processing method.
      • Disadvantage: The number of IMFs cannot be controlled and this flexibility is lost.
    • EMD
    • EEMD
  • WPT: Wavelet Packet Transform
    • WPT
      • Advantage: IMF may have variable frequency contents depending of local signal properties.
      • Disadvantage: Performance of WPT depends on choice of wavelet, its similarity to analyzed signal.

Advantage

• Algorithms able to represent how the frequency contents vary with time.
• Non-stationary conditions can be analyzed.

Disadvantage

• In general, algorithms not so much validated industrially.
• High computational costs.