A Class of Quadratic Time-frequency Representations Based on the Short-time Fourier Transform (original) (raw)
Related papers
Short-time fourier transform: two fundamental properties and an optimal implementation
IEEE Transactions on Signal Processing, 2003
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.
Uncertainty relations and time-frequency distributions for unsharp observables
1996
This paper deals with a new framework in analyzing the formal mathematical correspondence between quantum mechanics and time-frequency representations of a signal. It is also shown that joint time-frequency distributions have a close link with Heisenberg uncertainty relations if the observables are taken as fuzzy entities. This result contradicts the arguments of Cohen [IEEE Proc. 77(7):941 (1989)] regarding the time-frequency distributions and the uncertainty relation. It is postulated that these mechanisms will be of crucial importance in highly fragmented computation structures, such as neural networks, as they may exhibit a strong mutual interaction between data and operator.
Multiple window spectrogram and time-frequency distributions
Acoustics, Speech, and Signal …, 1994
We extend the spectrum estimation method of Thomson (1982, 1990) to non-stationary signals by formulating a multiple window spectrogram. The traditional spectrogram can be represented as a member of Cohen's class of time-frequency distributions (TFDs) where the smoothing kernel is the Wigner distribution of the signal temporal window. We show the unusual shape of the Cohen's class smoothing kernels corresponding to the Thomson method multiple windows. These are a class of smoothing ...
Kernel decomposition of time-frequency distributions
IEEE Transactions on Signal Processing, 1994
Bilinear time-frequency distributions (TFD's) offer improved tim+frequency resolution over linear representations, but suffer from difficult interpretation, higher implementation cost, and the lack of associated low-cost signal synthesis algorithms. In this paper, we introduce some new tools for the interpretation and quantitative comparison of high-resolution TFD's. These tools are used in related work to define lowcost high-resolution TFD's and to define linear, low-cost signal synthesis algorithms associated with high-resolution TFD's. First, each real-_valued TFD is associated with a self-adjoint linear operator $. The spectral representation of 4 expresses the TFD as a weighted sum of spectrograms (SP's). It is shown that the SP decomposition and Weyl correspondence do not yield useful interpretations for high-resolution TFD's due to the fact that 4) is not positive.
be in the form ITFT(w, t) = b(w-#'(t)). (3) If a window is used, we will consider IWT€T(w, t) = ITFT(w,t) * W(w) = W (w-$'(t)), where W (w) is the Fourier transfarrn (l T) of the window W (T). Absfract-This paper presents an analysis of the representation of instantaneous frequency using time-frequency distributions of energy density domain. Similarity to the "ideal" i i w t m t a m frequency presentation is chosen as a criterion for comparison of various distributions. Although all the commonly used distributions suffer from the artifacts along frequency axis, it is shown that the Wigner distribution is the best among them, with respect to this criterion. The generalization of Wigner distributiOn-LWI)-is intr'oduced to d e c ~ the artifacts. The properties of the LWD are analyzed. It is shown that, at the expense of an insignificant increase in computation time, much better results are obtained. The theory is illustrated by a numerical example with the frequency modulated signals.
Vector-valued time-frequency representations
IEEE Transactions on Signal Processing, 1996
Cohen's class of time-frequency distributions (TFD's), which includes the spectrogram (SP), Wigner distribution (WD), and reduced interference distributions (RID's) has become widely known as a useful signal analysis tool. Recently, it has been shown that every real-valued TFD can be written as a weighted sum of SP's. The "SP decomposition" has been used to construct fast approximations to desirable TFD's using the SP building block, for which there exist accessible and efficient hardware and software implementations.
A high-resolution quadratic time-frequency distribution for multicomponent signals analysis
IEEE Transactions on Signal Processing, 2001
Abstract The paper introduces a new kernel for the design of a high resolution time-frequency distribution (TFD). We show that this distribution can solve problems that the Wigner-Ville distribution (WVD) or the spectrogram cannot. In particular, the proposed distribution can resolve two close signals in the time-frequency domain that the two other distributions cannot. Moreover, we show that the proposed distribution is more accurate than the WVD and the spectrogram in the estimation of the instantaneous frequency of a ...