Abstract Fast (sub-second) spectroscopy with high spectral resolution is of vital importance for revealing quantum chemistry kinetics complex chemical and biological reactions. Fourier transform (FT) spectrometers can achieve operate at hundreds ms time scales in rapid-scan mode. However, the linear translation a scanning mirror imposes stringent time-resolution limitations to these systems, wh...

Fast algorithms for a wide class of non–separable n–dimensional (nD) discrete unitary K– transforms (DKT) are introduced. They need less 1D DKTs than in the case of the classical radix–2 FFT–type approach. The method utilizes a decomposition of the nDK–transform into the product of a new nD discrete Radon transform and of a set of parallel/independ 1D K–transforms. If the nD K–transform has a s...

An optical implementation of the fractional Fourier transform (FRT) with broadband illumination is proposed by use of a single imaging element, namely, a blazed diffractive lens. The setup displays an achromatized version of the FRT of order P of any two-dimensional input function. This fractional order can be tuned continuously by shifting of the input along the optical axis. Our compact and f...

In this paper we will discuss the version of the Fourier analysis and pseudodifferential operators on the torus. Using the toroidal Fourier transform we will show several simplifications of the standard theory. We will also discuss the corresponding toroidal version of Fourier integral operators. To distinguish them from those defined using the Euclidean Fourier transform, we will call them Fou...

An FT-IR Spectrometer is an instrument which acquires broadband NIR to FIR spectra. Unlike a dispersive instrument, i.e. grating monochromator or spectrograph, an FT-IR Spectrometer collects all wavelengths simultaneously. This feature, called the Multiplex or Felgett Advantage, is discussed in detail on page 3. FT-IR Spectrometers are often simply called FT-IRs. But for the purists, an FT-IR (...

Most reported work on transient ̄uid/structure interaction (FSI) in liquid®lled pipes has been carried out in the time domain. When needed, information in the frequency domain (e.g., frequency responses) has been deduced by discrete Fourier transforms. In this paper, the analysis is undertaken directly in the frequency domain and has the advantage of enabling (linear) dispersive terms to be incl...

Toxicity bioassays are important tools to determine biological effects of chemical agents on species. The questions remained on, what effects have been imposed on each of the different molecular site of cells by chemical exposure and how to find a pattern for chemical toxicity. To address the questions, HepG2 cell lines were exposed to the different concentrations of cisplatin for 24 hours to r...