This paper deals with the Catalan, Hankel, binomial transforms of generalized bivariate Fibonacci and Lucas polynomials. Also, some useful results such as generating functions, Binet formulas, summations defined by using recurrence relations these special polynomials are presented. Furthermore, certain important among deduced obtained new formulas. Finally, Catalan Cassini formulas for also der...

Abstract In this paper, we study the nonuniform fast Fourier transform with nonequispaced spatial and frequency data (NNFFT) sinc as its application. The computation of NNFFT is mainly based on nodes equispaced frequencies (NFFT). employs two compactly supported, continuous window functions. For fixed nonharmonic bandwidth, show that error $$\sinh$$ <mml:math xmlns:mml="http://www.w3.org/1998/M...

Light diffraction by volume Fresnel zone plates (VFZPs) is simulated by the Hankel transform beam propagation method (Hankel BPM). The method utilizes circularly symmetric geometry and small step propagation to calculate the diffracted wave fields by VFZP layers. It is shown that fast and accurate diffraction results can be obtained with the Hankel BPM. The results show an excellent agreement w...

This letter proposes a fast implementation of the regularity-constrained discrete sine transform (R-DST). The original DST \textit{leaks} lowest frequency (DC: direct current) components signals into high (AC: alternating subbands. property is not desired in many applications, particularly image processing, since most natural images concentrate DC subband. characteristic filter banks whereby th...

Discrete cosine and sine transforms closely approximate the Karhunen–Loeve transform for first-order Markov stationary signals with high low correlation coefficients, respectively. sinusoidal can be used in data compression, digital filtering, spectral analysis pattern recognition. Short-time based on discrete are suitable adaptive processing time–frequency of quasi-stationary data. The general...