Index altes From the narrow-band AF ambifunb Definition and properties ambifuwb From the narrow-band AF amgauss Example 2 anasing Analysis of local singularities atoms Time-frequency resolution | Pseudo-WVD doppler How to synthesize a | Definition fmlin Example 1 fmt From the Fourier transform friedman Friedman's instantaneous frequency density gdpower The localized bi-frequency kernel | The localized bi-frequency kernel | The localized bi-frequency kernel holder Analysis of local singularities htl The Hough transform for instfreq Instantaneous frequency locfreq Example 1 loctime Example 1 margtfr Marginals midpoint Interference structure momftfr Moments momttfr Moments movpwdph More on interferences: information movsc2wv The affine smoothed pseudo movsp2wv Separable smoothing noisecg Example 1 | How to synthesize a noisecu How to synthesize a plotsid Interference structure renyi Renyi information ridges Extraction of ridges and sgrpdlay Group delay sigmerge Example 1 tfrbert The localized bi-frequency kernel tfrbj Joint-smoothings of the WVD tfrcw Joint-smoothings of the WVD tfrdfla The localized bi-frequency kernel tfrgabor The Gabor Representation tfrideal The reassignment of the tfrmh The Rihaczek and Margenau-Hill tfrpage The Page distribution tfrpmh The Rihaczek and Margenau-Hill tfrppage The Page distribution tfrpwv Example 2 | Pseudo-WVD tfrri The Rihaczek and Margenau-Hill tfrrsp The reassignment of the | The reassignment of the tfrscalo The scalogram | The scalogram tfrsp Example 3 | The spectrogram tfrspaw Time-frequency smoothing interpretation tfrunter The localized bi-frequency kernel tfrwv Definition tfrzam Joint-smoothings of the WVD zak The Gabor Representation affine class General expressions affine group Properties | The affine group affine smoothed pseudo Wigner distribution The affine smoothed pseudo affine Wigner distributions The affine Wigner distributions analytic signal Instantaneous frequency | Sampling the WVD; the atom Definition atomic decomposition First class of solutions average frequency Localization and the Heisenberg-Gabor average time Localization and the Heisenberg-Gabor Balian-Low obstruction The discrete STFT Bertrand distribution The localized bi-frequency kernel | From the WVD to | Some examples bi-frequency kernel General expressions biorthonormal window The Gabor Representation bits of information Renyi information Born-Jordan distribution Joint-smoothings of the WVD Choi-Williams distribution Joint-smoothings of the WVD Cohen's class The spectrogram | The Cohen's class | The Cohen's class compatibility with filterings Properties compatibility with modulations Properties constant-Q analysis Definitions and interpretation continuous wavelet transform Definitions and interpretation D-Flandrin distribution The localized bi-frequency kernel | Some examples delay Definition and properties dilation covariance Properties discrete wavelet transform The discrete wavelet transform doppler Definition and properties Doppler effect Definition | Need of specific tools dyadic sampling The discrete wavelet transform energy Localization and the Heisenberg-Gabor energy conservation Properties | Properties exponent of regularity Analysis of local singularities fast Mellin transform From the Fourier transform Fourier transform Time representation and frequency frequency spreading Localization and the Heisenberg-Gabor Gabor coefficients The Gabor Representation Gabor logons The Gabor Representation Gabor representation The Gabor Representation group delay Group delay | Properties | Properties Heisenberg-Gabor inequality Example 1 Hilbert transform Instantaneous frequency Holder exponent Analysis of local singularities instantaneous amplitude Instantaneous frequency instantaneous frequency Instantaneous frequency | Properties instantaneous frequency density Friedman's instantaneous frequency density interference Interference structure interferences Interferences localized bi-frequency kernel distributions The localized bi-frequency kernel Margenau-Hill distribution The Rihaczek and Margenau-Hill | Some examples marginal properties Second class of solutions | Properties | Properties marginals Marginals Mellin transform From the Fourier transform Mellin's scale From the Fourier transform moments Moments narrow-band ambiguity function Definition and properties narrow-band limit Properties non-stationarity About stationarity Page distribution The Page distribution parameterization function Presentation perfect localization Properties product kernel distributions The product kernel distributions pseudo affine Wigner distributions The pseudo affine Wigner pseudo Wigner-Ville distribution Pseudo-WVD pseudo-Page distribution The Page distribution quadratic superposition principle The spectrogram | Interferences reassignment The reassignment method Reduced Interference Distributions Joint-smoothings of the WVD regularity Analysis of local singularities Renyi information Renyi information ridges Extraction of ridges and Rihaczek distribution The Rihaczek and Margenau-Hill scale Definitions and interpretation scalogram The scalogram | The scalogram short-time Fourier transform First class of solutions singularity Analysis of local singularities skeleton Extraction of ridges and smoothed pseudo affine Wigner distributions Time-frequency smoothing interpretation smoothed-pseudo Wigner-Ville distribution Separable smoothing spectrogram The spectrogram stationarity About stationarity support conservation Properties time localization Properties time spreading Localization and the Heisenberg-Gabor time-bandwidth product Localization and the Heisenberg-Gabor translation covariance Properties unitarity Properties | Properties Unterberger distributions The localized bi-frequency kernel | Some examples wavelets Definitions and interpretation Weyl-Heisenberg group Definition wide-band ambiguity function From the narrow-band AF Wigner-Hough transform The Wigner-Hough transform Wigner-Ville distribution Definition | Some examples Zak transform The Gabor Representation Zhao-Atlas-Marks distribution Joint-smoothings of the WVD
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