Prime-factor FFT algorithm

About: Prime-factor FFT algorithm is a research topic. Over the lifetime, 2346 publications have been published within this topic receiving 65147 citations. The topic is also known as: Prime Factor Algorithm.

Exact image representation via a number-theoretic radon transform

Abstract: This study presents an integer-only algorithm to exactly recover an image from its discrete projected views that can be computed with the same computational complexity as the fast Fourier transform (FFT). Most discrete transforms for image reconstruction rely on the FFT, via the Fourier slice theorem (FST), in order to compute reconstructions with lowcomputational complexity. Consequently, complex arithmetic and floating point representations are needed, the latter of which is susceptible to round-off errors. This study shows that the slice theorem is valid within integer fields, via modulo arithmetic, using a circulant theory of the Radon transform (RT). The resulting number-theoretic RT (NRT) provides a representation of images as discrete projections that is always exact and real-valued. The NRT is ideally suited as part of a discrete tomographic algorithm, an encryption scheme or for when numerical overflow is likely, such as when computing a large number of convolutions on the projections. The low-computational complexity of the NRT algorithm also provides an efficient method to generate discrete projected views of image data.

Multifunctional signal transform engine

Abstract: A technique involves using a fast Fourier transform (FFT) module to transform multiple different types of signals. This may be accomplished using one or more of three techniques: logic within the FFT module can enable different processing depending upon a processing state, the FFT module can be called iteratively to transform a signal that is larger than the FFT implemented in the FFT module, the FFT module can be used for parallel transformation of multiple signals that are smaller than the FFT implemented in the FFT module. Thus, a single FFT module can be used to transform a first type of signal (e.g., WIFI) and a second type of signal (e.g., GPS) if configured according to the technique.

Arithmetic complexity of the split-radix FFT algorithms

Abstract: A radix-2/16 decimation-in-frequency (DIF) fast Fourier transform (FFT) algorithm and its higher radix version, namely radix-4/16 DIF FFT algorithm, are proposed by suitably mixing the radix-2, radix-4 and radix-16 index maps, and combing some of the twiddle factors. It is shown that the proposed algorithms and the existing radix-2/4 and radix-2/8 FFT algorithms require exactly the same number of arithmetic operations (multiplications+additions). Moreover, by using techniques similar to these, it can be shown that all the possible split-radix FFT algorithms of the type radix-2/sup r//2/sup rs/ for computing a 2/sup m/-point DFT require exactly the same number of arithmetic operations.