in this article, by using a partial on locally compact semi-direct product groups, we present a compatible extension of the fourier transform. as a consequence, we extend the fundamental theorems of abelian fourier transform to non-abelian case.

Because of mass assignment onto grid points in the measurement of the power spectrum using the Fast Fourier Transform (FFT), the raw power spectrum |δ f (k)| 2 estimated with FFT is not the same as the true power spectrum P (k). In this paper, we derive the formula which relates |δ

Radial sampling of the NMR time domain has recently been introduced to speed up data collection significantly. Here, we show that radially sampled data can be processed directly using Fourier transforms in polar coordinates. We present a comprehensive theoretical analysis of the discrete polar Fourier transform, and derive the consequences of its application to radially sampled data using linea...

In this paper we devise a so-called cylindrical Fourier transform within the Clifford analysis context. The idea is the following: for a fixed vector in the image space the level surfaces of the traditional Fourier kernel are planes perpendicular to that fixed vector. For this Fourier kernel we now substitute a new Clifford-Fourier kernel such that, again for a fixed vector in the image space, ...

The mel-scaled frequency cepstral coefficients (MFCCs) derived from Fourier transform and filter bank analysis are perhaps the most widely used front-ends in state-of-the-art speech recognition systems. One of the major issues with the MFCCs is that they are very sensitive to additive noise. To improve the robustness of speech front-ends with respect to noise, we introduce, in this paper, a new...

Signal processing is an important issue that should be considered prior to recording mechanomyographic (MMG) signals. The first studies in this area found that the fast Fourier transform and maximum entropy spectrum estimation techniques provided MMG frequency spectra that were very similar in shape. The shape of the spectrum from the maximum entropy spectrum estimation technique, however, was ...

The Doppler spectrum estimation of a weather radar signal in a classic way can be made by two methods, temporal one based in the autocorrelation of the successful signals, whereas the other one uses the estimation of the power spectral density PSD by using Fourier transforms. We introduces a new tool of signal processing based on Ramanujan sums cq(n), adapted to the analysis of arithmetical seq...