On the Application of a Fast Polynomial Transform and the Chinese Remainder Theorem to Compute a Two-Dimensional Convolution
نویسندگان
چکیده
In this article, a fast algorithm is developed to compute two-dimensional convolutions of an array of d 1· d 2 complex number points, where d 2 = 2 and d 1 = 2m -r+ 1 for some I ,.; r ,.; m. This new algorithm requires fewer multiplications and about the same number of additions as the conventional FFT method for computing the two-dimensional convolution. It also has the advantage that the operation of transposing the matrix of data can be avoided.
منابع مشابه
DFT and FFT: An Algebraic View
In infinite, or non-periodic, discrete-time signal processing, there is a strong connection between the z-transform, Laurent series, convolution, and the discrete-time Fourier transform (DTFT) [10]. As one may expect, a similar connection exists for the DFT but bears surprises. Namely, it turns out that the proper framework for the DFT requires modulo operations of polynomials, which means work...
متن کاملDFT and FFT : An Algebraic View ∗ Markus Pueschel
by Markus Pueschel, Carnegie Mellon University In in nite, or non-periodic, discrete-time signal processing, there is a strong connection between the z-transform, Laurent series, convolution, and the discrete-time Fourier transform (DTFT) [10]. As one may expect, a similar connection exists for the DFT but bears surprises. Namely, it turns out that the proper framework for the DFT requires modu...
متن کاملApplication of Convolution of Daubechies Wavelet in Solving 3D Microscale DPL Problem
In this work, the triple convolution of Daubechies wavelet is used to solve the three dimensional (3D) microscale Dual Phase Lag (DPL) problem. Also, numerical solution of 3D time-dependent initial-boundary value problems of a microscopic heat equation is presented. To generate a 3D wavelet we used the triple convolution of a one dimensional wavelet. Using convolution we get a scaling function ...
متن کاملA Polynomial Approach to Fast Algorithms for Discrete Fourier-cosine and Fourier-sine Transforms
The discrete Fourier-cosine transform (cos-DFT), the discrete Fourier-sine transform (sin-DFT) and the discrete cosine transform (DCT) are closely related to the discrete Fourier transform (DFT) of real-valued sequences. This paper describes a general method for constructing fast algorithms for the cos-DFT, the sin-DFT and the DCT, which is based on polynomial arithmetic with Chebyshev polynomi...
متن کاملNumerical resolution of large deflections in cantilever beams by Bernstein spectral method and a convolution quadrature.
The mathematical modeling of the large deflections for the cantilever beams leads to a nonlinear differential equation with the mixed boundary conditions. Different numerical methods have been implemented by various authors for such problems. In this paper, two novel numerical techniques are investigated for the numerical simulation of the problem. The first is based on a spectral method utiliz...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010