Adaptive fractional Fourier domain filtering
Signal Processing
Short-time fractional fourier transform and its applications
IEEE Transactions on Signal Processing
The discrete fractional Fourier transform based on the DFT matrix
Signal Processing
Windowed linear canonical transform and its applications
Signal Processing
Ballistic missile detection via micro-Doppler frequency estimation from radar return
Digital Signal Processing
Time-frequency analysis of signals using support adaptive Hermite-Gaussian expansions
Digital Signal Processing
Signal-adaptive discrete evolutionary transform as a sparse time-frequency representation
Digital Signal Processing
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Shift and rotation invariance properties of linear time-frequency representations are investigated. It is shown that among all linear time-frequency representations, only the short-time Fourier transform (STFT) family with the Hermite-Gaussian kernels satisfies both the shift invariance and rotation invariance properties that are satisfied by the Wigner distribution (WD). By extending the time-bandwidth product (TBP) concept to fractional Fourier domains, a generalized time-bandwidth product (GTBP) is defined. For mono-component signals, it is shown that GTBP provides a rotation independent measure of compactness. Similar to the TBP optimal STFT, the GTBP optimal STFT that causes the least amount of increase in the GTBP of the signal is obtained. Finally, a linear canonical decomposition of the obtained GTBP optimal STFT analysis is presented to identify its relation to the rotationally invariant STFT.