The classical method of numerically computing the Fourier transform of digitizedfunctions in one or in ddimensions is the so-called discrete Fourier transform ( D F T ) , efficiently implemented as Fast Fourier Transform ( F F T ) algorithms. In m n y cases the D F T is not an adequate appmximation of the continuous Fourier transform. The method presented in this contribution provides accurate ...

We study the windowed Fourier transform in the framework of Clifford analysis, which we call the Clifford windowed Fourier transform (CWFT). Based on the spectral representation of the Clifford Fourier transform (CFT), we derive several important properties such as shift, modulation, reconstruction formula, orthogonality relation, isometry, and reproducing kernel. We also present an example to ...

Time-frequency distributions (TFDs) have proven useful in a wide variety of nonstationary signal processing applications. While sophisticated optimal bilinear TFDs have been developed to extract the maximum possible timefrequency information from signals, certain applications dictate simpler linear, running-FFT processing techniques. In this paper, we propose a signal-dependent short-time Fouri...

This paper compares wavelet and short time Fourier transform based techniques for single channel speech signal noise reduction. Despite success of wavelet denoising of images, it has not yet been widely used for removal of noise in speech signals. We explored how to extend this technique to speech denoising, and discovered some problems in this endeavor. Experimental comparison with large amoun...

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...

A framework for approximate signal processing is introduced which can be used to design novel classes of algorithms for performing DFT and STFT calculations. In particular , we focus on the derivation of multi-stage incremen-tal reenement algorithms that meet a variety of design criteria on the tradeoo achieved at each stage between solution quality and computational cost.

The recent emergence of the discrete fractional Fourier transform (DFRFT) has caused a revived interest in the eigenanalysis of the discrete Fourier transform (DFT) matrix F with the objective of generating orthonormal Hermite-Gaussian-like eigenvectors. The Grünbaum tridiagonal matrix T – which commutes with matrix F – has only one repeated eigenvalue with multiplicity two and simple remaining...

In this paper, the quaternion Bessel-Fourier moments are introduced. The significance of phase information in quaternion Bessel-Fourier moments is investigated and an accurate estimation method for rotation angle is described. Furthermore, a new set of invariant descriptors based on the magnitude and the phase information of quaternion Bessel-Fourier moments is derived. Experimental results sho...