In this paper, we develop some methods to save the bandwidth required in the fractional domain. The fractional domain is the transformed domain of the fractional Fourier transform (FRFT). It is the intermediate of the time domain and the frequency domain. We find that, with the aid of the fractional Hilbert transform and other techniques, we can save 112 or 314 of the bandwidth in the fractiona...

The continuous fractional Fourier transform (FRFT) performs a spectrum rotation of signal in the time–frequency plane, and it becomes an important tool for time-varying signal analysis. A discrete fractional Fourier transform has been recently developed by Santhanam and McClellan, but its results do not match those of the corresponding continuous fractional Fourier transforms. In this paper, we...

The purpose of this presentation is to demonstrate the practical interest of an original improvement of the classic Fourier analysis. The n-th order short-time Fourier Transform (FT) extends the classic short-time Fourier transform by also considering the first n signal derivatives. This technique greatly improves Fourier analysis precision not only in frequency and amplitude but also in time, ...

A 3D windowed Fourier transform is proposed for fringe sequence analysis, which processes the joint spatial and temporal information of the fringe sequence simultaneously. The 2D windowed Fourier transform in the spatial domain and the 1D windowed Fourier transform in the temporal domain are two special cases of the proposed method. The principles of windowed Fourier filtering and windowed Four...

magnetotelluric (mt) method is an important passive surface geophysical method which uses the earth’s natural electromagnetic fields to investigate the electrical resistivity structure of the subsurface. the depth of investigation of mt is much higher than that of other electromagnetic (em) methods (vozoff, 1991). for a general conductivity distribution in the earth, the horizontal electric fie...

Aimed at solving the problems of Precision code’s complex acquisition procedures and its long acquisition time in satellite navigation, this paper makes an architecture analysis of the commonly used direct acquisition algorithms of Precision code, making an improvement of the common local pseudorandom code based glide Fast Fourier Transform acquisition architecture. Besides those, it also puts ...

By use of window functions, time-frequency analysis tools like Short Time Fourier Transform overcome a shortcoming of the Fourier Transform and enable us to study the timefrequency characteristics of signals which exhibit transient oscillatory behavior. Since the resulting representations depend on the choice of the window functions, it is important to know how they influence the analyses. One ...

The windowed Fourier transform (short time Fourier transform) and the S-transform are widely used signal processing tools for extracting frequency information from non-stationary signals. Previously, the windowed Fourier transform had been adopted for signals on graphs and has been shown to be very useful for extracting vertex-frequency information from graphs. However, high computational compl...

7 Trigonometric Identities, Complex Exponentials and Periodic Sequences 26 7.1 Basic Trigonometric Identities . . . . . . . . . . . . . . . . . . 26 7.2 Basic Trigonometric Integrals . . . . . . . . . . . . . . . . . . 28 7.3 Basic Properties of Complex Numbers . . . . . . . . . . . . . 29 7.4 Complex Numbers and Trigonometrical Identities . . . . . . . 31 7.5 The Exponential of a Complex Numbe...