We present a theor of linear and quadratic time-frequency representations (&FRs) that are covariant to time-frequency displacement operators. The theory unifies important T F R classes (short-time Fourier transform, wavelet transform; Cohen’s, affine, hyperbolic, and power classes), and it allows the systematic construction of new TFRs that are covariant to a given operator.

variation of frequency and voltage by load changes in a microgrid is a challenge in droop control method. centralized restoration frequency or voltage in a microgrid requires communication link and therefore affects the advantage of decentralized droop control such as reliability, simplicity and inexpensiveness. this paper proposes a decentralized method that restores the frequency of a microgr...

Energy concentration of the S-transform in the time-frequency domain has been addressed in this paper by optimizing the width of the window function used. A new scheme is developed and referred to as a window width optimized S-transform. Two optimization schemes have been proposed, one for a constant window width, the other for time-varying window width. The former is intended for signals with ...

The most popular time-frequency analysis tool, the Short-Time Fourier Transform, suffers from blurry harmonic representation when voiced speech undergoes changes in pitch. These relatively fast variations lead to inconsistent bins in frequency domain and cannot be accurately described by the Fourier analysis with high resolution both in time and frequency. In this paper a new analysis tool, cal...

In audio processing applications, phase retrieval (PR) is often performed from the magnitude of short-time Fourier transform (STFT) coefficients. Although PR performance has been observed to depend on considered STFT parameters and data, extent this dependence not systematically evaluated yet. To address this, we studied three algorithms for various types content such as redundancy, time-freque...

The relationship between finite discrete Zak transform and finite Gabor expansion are well discussed in this paper. In this paper, we present two DFT-based algorithms for computing Gabor coefficients. One is based upon the time-split Zak transform, the other is frequencysplit Zak transform. These two methods are time and frequency dual pairs. Furthermore, we extend the relationship between fini...