In this paper we prove analogous theorems like Leindler’s [3] using the so-called A-transform of the B-transform of the partial sums of Fourier series. In addition, more than two such transforms are introduced and for them analogous results are showed as well.

We develop the pruned continuous Haar transform and the fast continuous Fourier series, two fast and efficient algorithms for rectilinear polygons. Rectilinear polygons are used in VLSI processes to describe design and mask layouts of integrated circuits. The Fourier representation is at the heart of many of these processes and the Haar transform is expected to play a major role in techniques e...

The use of the Hilbert transform for time/frequency analysis of signals is briefly considered. While the Hilbert transform is based on arbitrary continuous signals, most practical signals are digitially sampled and time-limited. To avoid aliasing in the sampling process the signals must also be bandlimited. It is argued that it is reasonable to consider such sampled signals as periodic (this is...

This tutorial paper describes the methods for constructing fast algorithms for the computation of the discrete Fourier transform (DFT) of a real-valued series. The application of these ideas to all the major fast Fourier transform (FFT) algorithms is discussed, and the various algorithms are compared. We present a new implementation of the real-valued split-radix FFT, an algorithm that uses few...

PURPOSE Analysis of the uterine contractility in the nonpregnant states has provided information about physiological changes during menstrual cycle. There is need to develop methods of recording uterine activity as well as mathematical interpretation of recorded time series. Wavelets are a new powerful tool for signal and image processing. The aim of this study is an introductory view of Fourie...

In this paper modified variants of the sparse Fourier transform algorithms from [32] are presented which improve on the approximation error bounds of the original algorithms. In addition, simple methods for extending the improved sparse Fourier transforms to higher dimensional settings are developed. As a consequence, approximate Fourier transforms are obtained which will identify a near-optima...

Heart rate variability (HRV) power spectrum analysis is a well-known technique used to study the activity of the autonomic nervous system. It is performed by calculating the spectral power of certain bands of the RR time series. There are several tools that perform this type of analysis: Kubios HRV, PhysioNet's HRV toolkit for MatLab and aHRV, among others. All these tools use the Short Fourier...