INTRODUCTION SUMMARY We present an exact and analytical expression for the Fourier transform of a function that has been sampled logarithmically. The procedure is significantly more efficient computationally than the fast Fourier transformation (FFT) for transforming functions or measured responses which decay slowly with increasing abscissa value. We illustrate the proposed method with an exam...

Tone mapping (TM) aims to display high dynamic range scenes on media with limited visual information reproduction. Logarithmic transformation is a widely used preprocessing method in TM algorithms. However, the conventional logarithmic does not take difference image properties into account, nor it consider tone algorithms, which are designed based luminance or gradient-domain features. There wi...

Logarithmic transformation of the data has been recommended by the literature in the case of highly skewed distributions such as those commonly found in information science. The purpose of the transformation is to make the data conform to the lognormal law of error for inferential purposes. How does this transformation affect the analysis? We factor analyze and visualize the citation environmen...

This article demonstrates how a three-parameter logarithmic transformation combined with an exponentially weighted moving average (EWMA) approach can be used to monitor the sample variance of a process. The computation of the parameters of the logarithmic transformation and the control limits are explained. An easy-to-use table is provided and an illustrative example is given. The performance o...

In this paper, an efficient algorithm of logarithmic transformation to Hirota bilinear form of the KdV-type bilinear equation is established. In the algorithm, some properties of Hirota operator and logarithmic transformation are successfully applied, which helps to prove that the linear terms of the nonlinear partial differential equation play a crucial role in finding the Hirota bilinear form...