Pitch shifting in speech is presented based on the use of the phase vocoder in combination with spectral whitening and envelope reconstruction, applied respectively before and after the transformation. A band preservation technique is introduced to contain quality degradation when downscaling the pitch. The transposition ratio is fixed in advance by selecting analysis and synthesis window sizes...

Speaking in a very broad sense, the Fourier transform (FT) can be treated as a systematic way to decompose arbitrary function into a superposition of harmonic (“symmetrical”) functions. It is a fundamental tool for studying of various processes and for this reason it is present in basically every scientific discipline. In last decades, the Fourier transformation was used in distinctive fields s...

We study the transformation of the statistical mechanics of N particles to the statistical mechanics of fields, that are the collective coordinates, describing the system. We give an explicit expression for the functional Fourier transform of the Jacobian of the transformation from particle to collective coordinate and derive the Fokker-Planck equation in terms of the collective coordinates. Si...

Using the quadratic transformation and the generating function method we 3 4 R R → perform the Fourier transformation of the wave function of coordinates of hydrogen atom and we find the analytic expression of the wave function in momentum space. We derive the matrix elements between the basis to 4-dimensions and integral representation of the generating functions of Gegenbauer polynomials. We ...

Earlier comprehensive mathematical methods were developed for the study of periodicity of continuous and discrete numerical sequences, using Fourier transformation and allowing the definition of the spectral density of a numerical sequence. However, such an application of a Fourier transform demands presentation of a symbolic sequence as a numerical sequence in which the properties of any symbo...

In a recent paper, Bourchard et al. [1] proposed the block sum transformation, a method intended as an alternative to the discrete Fourier transform (DFT), with application to the analysis of excited vibrations of linear systems. In this note, we mention the existence of a number of alternative algorithms for the computation of the DFT, and show that the block sum transformation is equivalent t...

In this paper we propose two mathematical methods for more thoroughly analysis of the electrical activity recordings of some human organs: electrocardiograms, electroencephalograms, electromyograms. The spectrograms obtained through short time Fourier transformation and wavelet transformation may be used to evaluate the degree of similarity and difference between two recordings of a healthy and...

Utilizing the near- to far-field transformation based on the 3-D finite difference time domain (FDTD) method and Fourier transformation, the far-field profile of a photonic crystal organic light emitting diode is studied to understand the viewing angle dependence. The measured far-field profiles agree well with those of the simulation. The enhancement of the extraction efficiency in excess of 6...

We give geometric explanations and proofs of various mirror symmetry conjectures for T-invariant Calabi-Yau manifolds when instanton corrections are absent. This uses fiberwise Fourier transformation together with base Legendre transformation. We discuss mirror transformations of (i) moduli spaces of complex structures and complexified symplectic structures, Hp,q’s, Yukawa couplings; (ii) sl (2...

A Bäcklund transformation(BT) and a recurrence formula are derived by the homogeneous balance(HB) method. A initial problem of Burgers equations is reduced to a initial problem of heat equation by the BT, the initial problem of heat equation is resolved by the Fourier transformation method, substituting various solutions of the initial problem of the heat equation will yield solutions of the in...