| Some applications of the Discrete Fourier Transform (DFT) in coding and in cryptography are described. The DFT over general commutative rings is introduced and the condition for its existence given. Blahut's Theorem, which relates the DFT to linear complexity, is shown to hold unchanged in general commutative rings. I. The (Usual) Discrete Fourier Transform Let be a primitive N th root of uni...

In this paper we consider optimal estimators for speech enhancement in the Discrete Fourier Transform (DFT) domain. We derive an analytical solution for estimating complex DFT coefficients in the MMSE sense when the clean speech DFT coefficients are Laplacian distributed and the DFT coefficients of the noise are Gaussian or Laplacian distributed. We show that these estimators have a number of i...

FFTW is an implementation of the discrete Fourier transform (DFT) that adapts to the hardware in order to maximize performance. This paper shows that such an approach can yield an implementation that is competitive with handoptimized libraries, and describes the software structure that makes our current FFTW3 version flexible and adaptive. We further discuss a new algorithm for real-data DFTs o...

This research paper describes an image change detection method based upon the Discrete Fractional Fourier transform (DFrFT) along with intensity normalization and thresholding. DFrFT is used as it provides extra degree of freedom to detect accurate changed regions. The use of intensity normalization and thresholding ensure that change is based on appearance or disappearance of objects only, wit...

The Spectral decomposition of seismic data was incepted earlier in the second half of the 19th century, howeverlimited research work has been done in this filed because of lack of availability of advancetools/ techniques for analysis of transient signal like earthquake time historyrecords. Although, there are several conventional techniques like Fourier Transform (FT),Fourier Series (FS)that ar...

self-association of alcohols; including ethanol, methanol, cyclopentanol and octanol in separate mixtures with inert solvents have been studied using ft-ir spectroscopy. except for the band at 3640 cm–1 in the ir spectrum of the alcohols which is due to the monomer species, the presence of other bands in the region of stretching vibrational frequencies of oh (3100-3700 cm–1) are attributed to t...

a new fourier transform-infra red (ft-ir) spectrometric method was developed for assaying hydrochlorothiazide (hct) and enalapril maleate (enm) in binary solid pharmaceutical formulations. multivariate partial least squares (pls) method was used for calibration of derivative spectral data. acetonitrile was used as solvent due to its spectral transparency and adequate solubility of analytes in i...

It is well-known that the discrete Fourier transform (DFT) can be characterized as decomposition matrix for the polynomial algebra C [x℄=(xn 1). This property gives deep insight into the DFT and can be used to explain and derive its fast algorithms. In this paper we present the polynomial algebras associated to the 16 discrete cosine and sine transforms. Then we derive important algorithms by m...

This paper presents a novel approach to achieving high spatial resolution in the demodulation of images produced by a two-dimensional X-ray Talbot interferometry (XTI) system. Currently, demodulation of XTI images is mainly performed by either phase-stepping (PS) or Fourier transform (FT) methods. However, the PS method for two-dimensional XTI demodulation requires a larger number of exposures ...