We demonstrate a 13-fold speed improvement in broadband cantilever-enhanced photoacoustic spectroscopy (CEPAS) by combining it with phase-controlled Fourier-transform (PC-FTS) instead of traditional infrared (FTIR). PC-FTS is modification FTIR and capable fundamentally faster interferogram acquisitions. The speed-improvement beneficial for CEPAS, which an especially sensitive version the backgr...

It is shown that number theoretic transforms (NTT) can be used to compute discrete Fourier transform (DFT) very efficiently. By noting some simple properties of number theory and the DFT, the total number of real multiplications for a length-P DFT is reduced to (P — 1). This requires less than one real multiplication per point. For a proper choice of transform length and NTT, the number of shif...

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...

A mathematical theory on the computational complexity of the Discrete Fourier Transform (DFT) is required, independently of any kind of known Fast Fourier Transform (FFT) algorithm.

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...