.png){kind=icon}
.png){kind=icon}
Return
Method for finding optimal exponential decay coefficient in numerical Laplace transform for application to linear convolution
.png){kind=icon}
PRE
AI
DOI：10.1016/j.sigpro.2016.03.029.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
In this paper, a method based on the numerical Laplace transform is used for calculating the full linear convolution of real or complex signals. An algorithm for obtaining the last N values of the convolution is presented, along with a method for finding an optimal value for the decay coefficient of the transform. It is shown that the use of the numerical Laplace transform formulation allows the calculation of each half of the linear convolution independently, which has computational benefits. The numerical Laplace transform is expressed as the fast Fourier transform of signals that have been premultiplied by a decreasing exponential window characterized by decay coefficient c. The error of the resulting linear convolution depends on the value of the decay coefficient; undervalue results in the generation of wraparound error whereas overvalue causes amplification of Gibbs phenomenon. In this paper, a formula that optimizes the value of the decay coefficient is developed. A trade-off value for c is obtained and error analysis shows that it outperforms other coefficients proposed in the literature when applied to the calculation of linear convolution. The relative errors obtained are of the order of 10-(6)% and 10-(9)% for single and double precisions. (C) 2016 Elsevier B.V. All rights reserved.
Keywords:
Linear convolution
Weighted circular convolution
Generalized Fourier transform
Numerical Laplace transform
AI Summary
Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.