A Fast Analysis-Based Discrete Hankel Transform Using Asymptotic Expansions

A Fast Analysis-Based Discrete Hankel Transform Using Asymptotic Expansions

A fast and numerically stable algorithm is described for computing the discrete Hankel transform of order 0 as well as evaluating Schlömilch and Fourier–Bessel expansions in O(N(logN)2/ loglogN) operations. The algorithm is based on an asymptotic expansion for Bessel functions of large arguments, the fast Fourier transform, and the Neumann addition formula. All the algorithmic parameters are se...

A fast FFT-based discrete Legendre transform

An O(N(logN)2/ loglogN) algorithm for computing the discrete Legendre transform and its inverse is described. The algorithm combines a recently developed fast transform for converting between Legendre and Chebyshev coefficients with a Taylor series expansion for Chebyshev polynomials about equallyspaced points in the frequency domain. Both components are based on the FFT, and as an intermediate...

Matlab code for the Discrete Hankel Transform

Very fast discrete Fourier transform, using number theoretic transform

It is shown that number theoretic transforms (NTT) can be used to compute discrete Fourier transform (DFT) very efficiently. By noting some simple properties of number theory and the DFT, the total number of real multiplications for a length-P DFT is reduced to (P — 1). This requires less than one real multiplication per point. For a proper choice of transform length and NTT, the number of shif...

Digital image Watermarking using Two Dimensional Discrete Wavelet Transform, Discrete Cosine Transform and Fast Fourier Transform

Abstract—In digital watermarking, a watermark is embedded into a cover text in such a way that the resulting watermarked signal is robust to certain distortion caused by either standard data processing in a friendly environment or malicious attacks in an unfriendly environment. This paper presents a digital image watermarking based on two dimensional discrete cosines transform (DCT2), two dimen...