In order to improve the time-frequency resolutions of short-time fractional Fourier transform, adaptive short-time fractional Fourier transform (ASTFRFT) method is used in this paper. The optimal order of ASTFRFT is given by maximizing kurtosis of signals in fractional domain, where the window width of ASTFRFT is searched by the maximal Shannon entropy of timefrequency distribution. Short-time ...

where w(n) is an analysis window. At each time instant, the STFT is a discrete-time Fourier transform or discrete Fourier transform (DFT). Many DFT computing algorithms and architectures have been proposed. However, the direct use of the DFI' without considering the special sliding window effect of STFT is not an efficient approach. There are two major approaches for STFT. One is based on the f...

The Fourier descriptors (FDs) is a classical but still popular method for contour matching. The key idea is to apply the Fourier transform to a periodic representation of the contour, which results in a shape descriptor in the frequency domain. Fourier descriptors are most commonly used to compare object silhouettes and object contours; we instead use this well established machinery to describe...

Shape is an essential visual feature of an image and it is widely used to describe image content in image classification and retrieval. In this paper, two new Fourier-based approaches for contour-based shape description are presented. These approaches present Fourier descriptors in multiple scales, which improves the shape classification and retrieval accuracy. The proposed methods outperform o...

We present fast, spatially dispersionless and unconditionally stable high-order solvers for Partial Differential Equations (PDEs) with variable coefficients in general smooth domains. Our solvers, which are based on (i) A certain “Fourier continuation” (FC) method for the resolution of the Gibbs phenomenon, together with (ii) A new, preconditioned, FC-based solver for two-point boundary value p...

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-...

Nowadays, Radar systems have many applications and radar imaging is one of the most important of these applications. Inverse Synthetic Aperture Radar (ISAR) is used to form an image from moving targets. Conventional methods use Fourier transform to retrieve Doppler information. However, because of maneuvering of the target, the Doppler spectrum becomes time-varying and the image is blurred. Joi...

A framework for approximate signal processing is introduced which can be used to design novel classes of algorithms for performing DFT and STFT calculations. In particular , we focus on the derivation of multi-stage incremen-tal reenement algorithms that meet a variety of design criteria on the tradeoo achieved at each stage between solution quality and computational cost.

We study the windowed Fourier transform in the framework of Clifford analysis, which we call the Clifford windowed Fourier transform (CWFT). Based on the spectral representation of the Clifford Fourier transform (CFT), we derive several important properties such as shift, modulation, reconstruction formula, orthogonality relation, isometry, and reproducing kernel. We also present an example to ...