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.

Fast OPED algorithm for reconstruction of images from Radon data

Abstract: A fast implementation of the OPED algorithm, a reconstruction algorithm for Radon data introduced recently, is proposed and tested The new implementation uses FFT for discrete sine transform and an interpolation step The convergence of the fast implementation is proved under the condition that the function is mildly smooth The numerical test shows that the accuracy of the OPED algorithm changes little when the fast implementation is used

Autofocus algorithm using one-dimensional Fourier transform and Pearson correlation

Abstract: A new autofocus algorithm based on one-dimensional Fourier transform and Pearson correlation for Z automatized microscope is proposed. Our goal is to determine in fast response time and accuracy, the best focused plane through an algorithm. We capture in bright and dark field several images set at different Z distances from biological organism sample. The algorithm uses the one-dimensional Fourier transform to obtain the image frequency content of a vectors pattern previously defined comparing the Pearson correlation of these frequency vectors versus the reference image frequency vector, the most out of focus image, we find the best focusing. Experimental results showed the algorithm has fast response time and accuracy in getting the best focus plane from captured images. In conclusions, the algorithm can be implemented in real time systems due fast response time, accuracy and robustness. The algorithm can be used to get focused images in bright and dark field and it can be extended to include fusion techniques to construct multifocus final images beyond of this paper.

Reconstruction of magnetic resonance images using one-dimensional techniques

Abstract: Whenever DFT (discrete Fourier transform) processing of a multidimensional discrete signal is required, one can apply either a multidimensional FFT (fast Fourier transform) algorithm, or a single-dimension FFT algorithm, both using the same number of points. That is, the dimensions of a "multidimensional" signal, and of its spectrum, are a matter of choice. Every multidimensional sequence is completely equivalent to a one-dimensional function in both "time" and "frequency" domains. This statement applied to MRI (magnetic resonance imaging) explains why one can reconstruct the slice by using either one-dimensional or two-dimensional methods, as it is already done in echo planar methods. In the commonly used spin warp methods, the image can be also reconstructed by either one- or two-dimensional processing. However, some artifacts in the images reconstructed from the original "zig-zag" echo planar trajectory, are shown to be due to the wrong dimensionality of the FFT applied. >

On fast Fourier transform

Abstract: Fast Fourier transform (FFT) is an efficient algorithm for computing the discrete Fourier transform. The discovery of the FFT algorithm paved the way for widespread use of digital methods of spectrum estimation which influenced the research in almost every field of engineering and science. In this article, we will first introduce the continuous-time Fourier transform (CFT), discretetime Fourier transform and discrete Fourier transform (DFT) and then present an example to illustrate the relation between CFT and DFT. In particular, we bring out the fact that the DFT is a tool to estimate the samples of the CFT at uniformly spaced frequencies. Next, we introduce the FFT algorithm giving certain key steps in its development.

Speech coding system which uses MPEG/audio layer III encoding algorithm

Abstract: A speech coding system is shown, which comprises a linear transform unit 50 for executing linear transform on an input signal Si with a predetermined block length Sb and an FFT unit 10, 30 for executing Fast Fourier transform on the input signal Si with two different, i.e., large and small, block lengths, a block length setting unit 20 for calculating a predetermined block length Sb to be set in the linear transform unit 50 according to an FFT signal generated in the FFT unit 10, 30 and setting this block length in the linear transform unit 50, and a coding unit 80 for coding an intermediate signal Sm generated in the linear transform unit 50 to form and output a bit stream So. The FFT unit has a function of selecting a block length used for the Fast Fourier transform among two, i.e., large and small, block lengths according to a continuous portion of the input signal Si.