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Chapter 3
Joint Time-Frequency Analysis Algorithms
Quadratic JTFA Algorithms
The quadratic JTFA algorithms include the following:
•
STFT spectrogram
•
Wigner–Ville distribution (WVD)
•
Pseudo Wigner–Ville distribution (PWVD)
•
Cohen’s class
•
Choi–Williams distribution (CWD)
•
cone-shaped distribution
•
Gabor spectrogram
•
adaptive spectrogram
STFT Spectrogram
The STFT-based spectrogram is defined as the square of the STFT:
SP [ m∆M, n ] =
∑ s [ i ]γ [ i – m∆M ]e
– j 2πni ⁄ N 2
i=0
where N denotes the number of frequency bins, and ∆M denotes the time
sampling interval. The STFT-based spectrogram is simple and fast but
suffers from the window effect.
Figures 3-1 and 3-2 illustrate the window effect of the STFT spectrogram.
With a narrowband window (Figure 3-1), the time-dependent spectrum has
high frequency resolution but poor time resolution. With a wideband
window (Figure 3-2), the time-dependent spectrum has poor frequency
resolution but high time resolution.
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3-3
Signal Processing Toolset