We address a particular set of extended Su-Schrieffer-Heeger models with $2n$ sites in the unit cell [SSH($2n$)], that we designate by Sine-Cosine [SC$(n)$], hopping terms defined as sequence $n$ sine-cosine pairs form $\{\sin(\theta_j),\cos(\theta_j)\}$, $j=1, \cdots,n$. These models, when squared, generate block-diagonal matrix representation one blocks corresponding to chain uniform local po...

In this paper, we propose a new M-channel wavelet bases called the cosine-modulated wavelets. We first generalize the theory of two-channel biorthogonal compactly supported wavelet bases to the M-channel case. A sufficient condition for the M-channel perfect reconstruction filter banks to construct M-channel compactly supported wavelet bases is given. By using this condition, a family of orthog...

An extremal problem for the coefficients of sine polynomials, which are nonnegativein [0, π], posed and discussed by Rogosinski and Szegő is under consideration. An analog of the Fejér-Riesz representation of nonnegativegeneral trigonometric and cosine polynomials is proved for nonnegativesine polynomials. Various extremal sine polynomials for the problem of Rogosinski and Szegő are obtained ex...

Some software libraries add special entry points to enable both the sine and cosine to be evaluated with one call for performance purposes. This paper proposes another method which does not involve new function names. By having the compiler front end recognize trigonometric function invocations, and replace them with a call to a common function which executes the code common to all the function...

Abstract. The modified discrete cosine transform (MDCT) and modified discrete sine transform (MDST) both for the evenly and oddly stacked systems are perfect reconstruction cosine/sine–modulated filter banks based on time domain aliasing cancellation (TDAC) employed in the current international audio coding standards and commercial audio compression products. Based on the matrix representation ...

Coarse-grained phase distributions are introduced that approximate to the Susskind–Glogower cosine and sine phase distributions. The integral relations between the phase distributions and the phase-parametrized fieldstrength distributions observable in balanced homodyning are derived and the integral kernels are analyzed. It is shown that the phase distributions can be directly sampled from the...

We present measurements of the electron ejection direction in the ionization of high (n=90) Rydberg states of rubidium subjected to few-cycle radio-frequency (RF) pulses. For weak pulses we find a strong asymmetry for even (cosine) pulses and no asymmetry for odd (sine) pulses. This asymmetry disappears for pulses longer than four RF cycles. For strong pulses, very large asymmetry is found for ...