Non-uniform discrete Fourier transform

About: Non-uniform discrete Fourier transform is a research topic. Over the lifetime, 4067 publications have been published within this topic receiving 123952 citations.

Inverse Source Problems for the Helmholtz Equation and the Windowed Fourier Transform

Abstract: We consider the inverse source problem for time-harmonic acoustic or electromagnetic wave propagation in the two-dimensional free space Given the radiated far field pattern of the solution to the Helmholtz equation for a certain source term, we find that the windowed Fourier transform of this far field is related to an exponential Radon transform with purely imaginary exponent of a smoothed approximation of the source Based on this observation we set up a filtered backprojection algorithm to recover information on the unknown source term from a single far field measurement We analyze this algorithm and provide extensive numerical results that illustrate our theoretical findings As one outcome the method is shown to work better the larger the wave number Possible extensions of the reconstruction method to limited aperture data and to inverse obstacle scattering problems are briefly sketched

On the computation of running discrete cosine and sine transform

Abstract: Two algorithms are given for the computation of the updated discrete cosine transform-II (DCT-II), discrete sine transform-II (DST-II), discrete cosine transform-IV (DCT-IV), and discrete sine transform-IV (DST-IV). It is pointed out that the algorithm used for running DCT-IV can also be used for computation for running DST-IV without additional computational overhead. An architecture which is common and suitable for VLSI implementation of the derived algorithms is also presented. Preliminary studies have shown that the architecture can easily be implemented in VLSI form, and, in conjunction with a high-speed digital signal processor (for example ADSP 2100A), it can be used for real-time transform domain LMS adaptive filtering (128 taps) of 8 kHz sample rate speech signals. >

Robust algorithm based on decimated Padè approximant technique for processing sensor data in leak detection in waterworks

Abstract: Although today water is becoming more and more precious, its major waste is caused by transportation. The authorities in charge of the management of water pipes indicate double-digit percentage of waste, sometimes it even exceeds 50% the amount of water mostly lost by inefficiency of distribution waterworks. In this study, the authors present an alternative method of spectral analysis, used for detecting leaks in water pipes, with respect to classical spectral methods as direct Fourier transform/fast Fourier transform. They have used decimated Pade approximant (DPA), where the input time signal points or auto-correlation functions are given via measurements or computations, and the task is to reconstruct the unknown components as the harmonic variables in terms of the fundamental complex frequencies and amplitudes. They have also introduced decimated linear predictor technique as direct consequence of the DPA, since they differ only in one step, namely the calculation of the amplitudes.