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.

Discrete Cosine Transform for 8x8 Blocks with CUDA

Abstract: In this whitepaper the Discrete Cosine Transform (DCT) is discussed. The two-dimensional variation of the transform that operates on 8x8 blocks (DCT8x8) is widely used in image and video coding because it exhibits high signal decorrelation rates and can be easily implemented on the majority of contemporary computing architectures. The key feature of the DCT8x8 is that any pair of 8x8 blocks can be processed independently. This makes possible fully parallel implementation of DCT8x8 by definition. Most of CPU-based implementations of DCT8x8 are firmly adjusted for operating using fixed point arithmetic but still appear to be rather costly as soon as blocks are processed in the sequential order by the single ALU. Performing DCT8x8 computation on GPU using NVIDIA CUDA technology gives significant performance boost even compared to a modern CPU. The proposed approach is accompanied with the sample code " DCT8x8 " in the NVIDIA CUDA SDK.

Effects of Noise, Time-Domain Damping, Zero-Filling and the FFT Algorithm on the “Exact” Interpolation of Fast Fourier Transform Spectra:

Abstract: A frequency-domain Lorentzian spectrum can be derived from the Fourier transform of a time-domain exponentially damped sinusoid of infinite duration. Remarkably, it has been shown that even when such a noiseless time-domain signal is truncated to zero amplitude after a finite observation period, one can determine the correct frequency of its corresponding magnitude-mode spectral peak maximum by fitting as few as three spectral data points to a magnitude-mode Lorentzian spectrum. In this paper, we show how the accuracy of such a procedure depends upon the ratio of time-domain acquisition period to exponential damping time constant, number of time-domain data points, computer word length, and number of time-domain zero-fillings. In particular, we show that extended zero-filling (e.g., a "zoom" transform) actually reduces the accuracy with which the spectral peak position can be determined. We also examine the effects of frequency-domain random noise and round-off errors in the fast Fourier transformation (FFT) of time-domain data of limited discrete data word length (e.g., 20 bit/word at single and double precision). Our main conclusions are: (1) even in the presence of noise, a three-point fit of a magnitude-mode spectrum to a magnitude-mode Lorentzian line shape can offer an accurate estimate of peak position in Fourier transform spectroscopy; (2) the results can be more accurate (by a factor of up to 10) when the FFT processor operates with floating-point (preferably double-precision) rather than fixed-point arithmetic; and (3) FFT roundoff errors can be made negligible by use of sufficiently large (> 16 K) data sets.

General multifractional Fourier transform method based on the generalized permutation matrix group

Abstract: The paper studies the possibility of giving a general multiplicity of the fractional Fourier transform (FRFT) with the intention of combining existing finite versions of the FRFT. We introduce a new class of FRFT that includes the conventional fractional Fourier transforms (CFRFTs) and the weighted-type fractional Fourier transforms (WFRFTs) as special cases. The class is structurally well organized because these new FRFTs, which are called general multifractional Fourier transform (GMFRFTs), are related with one another by the Generalized Permutation Matrix Group (GPMG), and their kernels are related with that of CFRFTs as the finite combination by the recursion of matrix. In addition, we have computer simulations of some GMFRFTs on a rectangular function as a simple application of GMFRFTs to signal processing.