Four Fourier transforms are usually defined, the Integral Fourier transform, the Discrete-Time Fourier transform (DTFT), the Discrete Fourier transform (DFT) and the Integral Fourier transform for periodic functions. However, starting from their definitions, we show that all four Fourier transforms can be reduced to actually only one Fourier transform, the Fourier transform in the distributiona...

This paper is concerned with the approach to teaching an introductory course on Fourier theory for engineers. Commonly called Signals and Systems (or some variation), this course generally introduces four transforms: the Fourier Transform, the Fourier Series, the Discrete-Time Fourier Transform (DTFT), and the Discrete Fourier Transform (DFT). Our concern is that the method and order of topic p...

--The fractional fourier transform(FRFT) which is a generalisation of classical fourier transform, was introduced number of years ago in the mathematics literature but appears to have remained largely unknown to a signal processing community to which it may, however, be a potentially useful. The fractional fourier transform depends on a parameter ‘α’ and can be interpreted as a rotation by an a...

A fast Fourier transform (FFT) is an efficient algorithm to compute the discrete Fourier transform (DFT) of an input vector. Efficient means that the FFT computes the DFT of an n-element vector in O(n logn) operations in contrast to the O(n2) operations required for computing the DFT by definition. FFTs exist for any vector length n and for real and higher-dimensional data. Parallel FFTs have b...

cisplatin is a common chemotherapeutic agent that used for treatment of many solid cancers. rapid identification of chemotherapy resistance is very important and may lead to effective treatment plan. spectroscopy techniques, such as infrared spectroscopy, which are sensitive to biochemical composition of samples, have shown potentials to discriminate tissues. developing in fourier transform inf...

introduction: the aim of this in vitro study was to evaluate the setting time, flow, film thickness, solubility, radiopacity and characterization analysis of three epoxy resin based sealers including two experimental sealers and ah-26. methods and materials: five samples of each material were evaluated for setting time, flow, film thickness, solubility and radiopacity according to iso 6876 stan...

The combination of gas chromatography (GC) with Fourier transform infrared spectroscopy (FTIR) has gradually become the important analytical tool for qualitative and quantitative analysis of complex mixtures. Numerous applications have been reported in previous reviews. Separation and identification of components in complex mixtures can be a daunting task. GC is the most common technique for se...

Infrared spectroscopy is a widely used method of analysis to monitor various characteristics in the honey products analysis, highlight these changes and detect fraudulent modifications. In this way could not be avoided. This article reviews some most important applications spectroscopic procedures order discriminate different types other published between 2015–2022.

A novel and automated technique is described for removing fMRI image artifacts resulting from motion outside of the imaging field of view. The technique is based on the Stockwell transform (ST), a mathematical operation that provides the frequency content at each time point within a time-varying signal. Using this technique, 1D Fourier transforms (FTs) are performed on raw image data to obtain ...