The problem of constructing an orthogonal set of eigenvectors for a DFT matrix is well studied. An elegant solution is mentioned by Matveev in [1]. In this paper, we present a distilled form of his solution including some steps unexplained in his paper, along with correction of typos and errors using more consistent notation. Then we compare the computational complexity of his method with the m...

a Nearly Tridiagonal Matrix Magdy Tawfik Hanna1 ABSTRACT A fully-fledged definition for the fractional discrete Fourier transform of type IV (FDFT-IV) is presented and shown to outperform the simple definition of the FDFT-IV which is proved to be just a linear combination of the signal, its DFT-IV and their flipped versions. This definition heavily depends on the availability of orthonormal eig...

This paper describes a novel feature-space VTLN method that models frequency warping as a linear interpolation of contiguous Mel filter-bank energies. The presented technique aims to reduce the distortion in the Mel filter-bank energy estimation due to the harmonic composition of voiced speech intervals and DFT sampling when the central frequency of band-pass filters is shifted. The presented i...

The error reduction of the non-parametric amplitude estimation of the periodic signals with the three-point interpolated discrete Fourier transform (DFT) using cosine windows is presented. The paper analyzes and compares the systematic bias errors and the noise error behavior of the amplitude estimation changing the order of Rife-Vincent windows class I (RV1), which are designed for maximizatio...

We propose and consolidate a definition of the discrete fractional Fourier transform that generalizes the discrete Fourier transform (DFT) in the same sense that the continuous fractional Fourier transform generalizes the continuous ordinary Fourier transform. This definition is based on a particular set of eigenvectors of the DFT matrix, which constitutes the discrete counterpart of the set of...

The increasing penetration of Distributed Energy Resources (DERs) at the low andmediumvoltage levels is determining major changes in the operational procedures of distribution networks (DNs) that are evolving from passive to active power grids. Such evolution is causing non-negligible problems to DN operators (DNOs) and calls for advanced monitoring infrastructures composed by distributed sensi...