Diagnostic of machine using the timefrequency representation of vibration is becoming widely used by many companies and experts. In recent years, the preventive maintenance is no more desirable and in fact it has evolved into the prediction maintenance. The current methods of machine diagnosis can not provide detailed diagnostics and condition prediction. This paper proposes the application of ...

The discrete Fourier transform (DFT) maps a nite number of discrete time-domain samples to the same number of discrete Fourier-domain samples. Being practical to compute, it is the primary transform applied to real-world sampled data in digital signal processing. The DFT has special relationships with the discrete-time Fourier transform and the continuous-time Fourier transform that let it be u...

During the last two decades, Maximum Likelihood estimation (ML) has been used to determine Direction Of Arrival (DOA) and signals propagated by the sources, using narrowband array signals. The algorithm fails in the case of wideband signals. As an attempt by the present study to overcome the problem, the array outputs are transformed into narrowband frequency bins, using short time Fourier tran...

We give a new characterization of the Gelfand triple of function spaces in (S0, L, S′ 0) by means of a family of time-frequency localization operators. The localization operators are defined by the short-time Fourier transform and determine the local time-frequency behavior, whereas the global timefrequency distribution is characterized by a sequence space norm. We also show that the alternativ...

We show that a stationary signal concept such as the Fourier transform (FT) can be linked to a time-varying (TV) concept such as linear TV filtering. In particular, we give a continuous-time and discrete-time linear TV filter interpretation to continuous-time FT and discrete Fourier transform (DFT), respectively. As a consequence, important variants such as warped DFT, DCT, DST also can be view...

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 ...

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...

The symmetry and periodicity properties of the discrete Fourier transform (DFT) allow a variety of useful and interesting decompositions. In particular, by clever grouping and reordering of the complex exponential multiplications it is possible to achieve substantial computational savings while still obtaining the exact DFT solution (no approximation required). Many “fast” algorithms have been ...

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...