The short-time Fourier transform of a discrete-time signal, which is the Fourier transform of a “windowed” version of the signal, is interpreted as a sliding-window spectrum. This sliding-window spectrum is a function of two variables: a discrete time index, which represents the position of the window, and a continuous frequency variable. It is shown that the signal can be reconstructed from th...

The aim of this work is the application of the phase variation in vibration signal for fault detection on rotating machines. The vibration signal from the machine is modulated in amplitude and phase around a carrier frequency. The modulating signal in phase is determined after the Hilbert transform and is used, with the Fast Fourier Transform, to extract the harmonics spectrum in phase. This me...

The intrinsic spectrum that results from the coupling of spontaneous emission in a laser cavity can determine energy concentration and coherence lasers, which is crucial for optical high-precision measurements. To date, it has been difficult to analyze high-speed dynamics processes, especially under condition fast wavelength sweeping. In this work, new method proposed with decomposition into se...

In this paper, a new texture classification method is provided for dividing texture images into three classes: periodic, directional, and random. The method is based on the fact that for a directional texture image, the magnitudes of its Fourier spectrum will concentrate on a certain direction; for periodic, on several directions; and for random, spread out over all directions. To use this fact...

In this paper, we propose the Modulation Scale Spectrum as an extension of the Modulation Spectrum through the Scale domain. The Modulation Spectrum expresses the evolution over time of the amplitude content of various frequency bands by a second Fourier Transform. While its use has been proven for many applications, it is not scale-invariant. Because of this, we propose the use of the Scale Tr...