A quantum compiler is a software program for decomposing (“compiling”) an arbitrary unitary matrix into a sequence of elementary operations (SEO). Coppersmith showed that the NB-bit Discrete Fourier Transform matrix UFT can be decomposed in a very efficient way, as a sequence of order(NB ) elementary operations. Can a quantum compiler that doesn’t know a priori about Coppersmith’s decomposition...

Today, many of the computations in signal processing and wireless communication applications are linked with complex analysis of several functions. These complex functions are combination of sine and cosine terms that generally spread in the channel. Most of these functions can be split into elementary functions. Today user’s desire every gadget must be smaller in size and simple to operate (“K...

The proposed contribution describes a method for the detection and classification of harmonic transients, as they occur in electrical networks. The method uses, as bases, a special class of wavelet-packets, i. e. smooth biorthogonal sine and cosine-packets in order to find the best ’’Shannon-basis“. The algorithm is based on the minimization of Shannon‘s function for the decomposed wanted signa...

The one-dimensional quantum sine-Gordon system with a linear spatial modulation is investigated in a special case, β2 =4π. The model is tranformed into a massive Thirring model and then is exactly diagonalized, the energy spetrum of the model is obtained. Our result clearly demonstrates that cancelling the cosine term without any considering is unadvisable. The one-dimensional (1D) quantum sine...

This article pushes the role of sine and cosine functions beyond traditional purpose determining sides a right triangle, into realm lengths any triangle with practically same ease. Extended are formulated dependent on two angles (instead one) — sin*(α,γ) cos*(α,γ)—that allow (via direct application) computation shorter scalene as resul...

This paper is concerned with the definitions of the discrete fractional cosine transform (DFRCT) and the discrete fractional sine transform (DFRST). The definitions of DFRCT and DFRST are based on the eigen decomposition of DCT and DST kernels. This is the same idea as that of the discrete fractional Fourier transform (DFRFT); the eigenvalue and eigenvector relationships between the DFRCT, DFRS...

In this paper, we provide a concise proof of Oppenheim’s double inequality relating to the cosine and sine functions. In passing, we survey this topic.

A new motion estimation scheme, Discrete-Cosine/SineTransform Based Motion Estimation (DXT-ME) utilizing the principle of orthogonality of cosine and sine functions to estimate, in the transform domain, displacements from the motion information contained in the pseudo-phases of the images of moving objects, is proposed. The computational complexity of this method is only O ( N 2 ) + O d c t for...

In this note, using the multisection series method, we establish the formulas for various power sums of sine or cosine functions.