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- Jeffrey C. O'Neill, William J. Williams
- IEEE Trans. Signal Processing
- 1999

Many commonly used time–frequency distributions are members of the Cohen class. This class is defined for continuous signals, and since time–frequency distributions in the Cohen class are quadratic, the formulation for discrete signals is not straightforward. The Cohen class can be derived as the class of all quadratic time–frequency distributions that are… (More)

- Jeffrey C. O'Neill, Patrick Flandrin
- IEEE Trans. Signal Processing
- 2000

| We present results concerning three diierent types of quartic (fourth order) time-frequency distributions. First, we present new results on the recently introduced local ambiguity function, and show that it provides more reliable estimates of instantaneous chirp rate than the Wigner distribution. Second, we introduce the class of quartic, shift-covariant,… (More)

- Jeffrey C. O'Neill, William J. Williams
- ICASSP
- 1996

It has recently been claimed that many of the discrete time-frequency representations (TFRs), including the alias free generalize time-frequency distributions (AF-GDTFD), contain aliasing components. This paper shows that the class of AF-GDTFD does indeed displace both cross term and auto term energy in ways not characteristic of continuous TFRs, but this… (More)

- Jeffrey C. O'Neill, Patrick Flandrin, William J. Williams
- IEEE Signal Processing Letters
- 1999

Among the myriad of time-frequency distributions, the Wigner distribution stands alone in satisfying many desirable mathematical properties. Attempts to extend definitions of the Wigner distribution to discrete signals have not been completely successful. In this letter, we propose an alternative definition for the Wigner distribution, which has a clear… (More)

This paper presents a statistically based method for spotting target words in documents. The crux of the method is the representation of a word by a spatial (planar) point process evolving on a regular lattice of coordinate pairs. This is accomplished by extracting the coordinate pairs, i.e. pixel locations, where the binary bitmap values of the word are… (More)

Di erent signal realizations generated from a given source may not appear the same. Time shifts, frequency shifts, and scales are among the signal variations commonly encountered. Time-frequency distributions (TFDs) covariant to time and frequency shifts and scale changes re ect these variations in a predictable manner. Based on such TFDs, representations… (More)

- Jeffrey C. O'Neill, William J. Williams
- ICASSP
- 1995

In time-frequency analysis there are four bilinear domains commonly used: time-frequency, ambiguity, temporal auto-correlation, and spectral auto-correlation. This paper introduces four new domains that are quadralinear in the signal. These four domains are each a function of three of the four variables used in the bilinear domains. Properties of these… (More)

- Jeffrey C. O'Neill, Patrick Flandrin
- ICASSP
- 1999

In a previous paper [1] we presented a method for atomic decomposition with chirped, Gabor functions based on maximum likelihood estimation. In this paper we present the Cramér-Rao lower bounds for estimating the seven chirp parameters, and the results of a simulation showing that our sub-optimal, but computationally tractable, estimators perform well in… (More)

- Jeffrey C. O'Neill, William J. Williams
- ICASSP
- 1998

Cohen’s class of time-frequency distributions for continuous signals has recently been to extended to discrete signals using both an axiomatic approach and an operator theory approach. In this paper, we investigate the formulation of several classical timefrequency distributions (Wigner, Rihaczek, Margenau-Hill, Page, Levin, Born-Jordan, spectrogram) in the… (More)

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