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.

Depth Recovery from Noisy Gradient Vector Fields Using Regularization

Abstract: This paper presents a regularization based method for surface reconstruction from noisy gradient vector fields. The algorithm takes as its input a discrete gradient vector field, obtained by applying a Shape from Shading or Photometric Stereo method. To derive this algorithm, we combine the integrability constraint and the surface curvature and area constraints into a single functional, which is then minimized. Therefore, value changes in the height or depth map will be more regular. To solve the minimization problem, we employ the Fourier transform theory rather than variational approach to avoid using the initial and boundary conditions. The Fourier transform of the unknown surface is expressed as a function of the given gradient’s Fourier transforms. The relative depth values can be obtained by an inverse Fourier Transform and by choosing associated weighting parameters. The method is evaluated on gradient data delivered by a shape-from-shading algorithm. Experimental results using both synthetic and real images show that the new algorithm is more robust against noise than existing methods.

Spiral-generated modular FFT algorithms

Abstract: This paper presents an extension of the Spiral system to automatically generate and optimize FFT algorithms for the discrete Fourier transform over finite fields. The generated code is intended to support modular algorithms for multivariate polynomial computations in the modpn library used by Maple. The resulting code provides an order of magnitude speedup over the original implementations in the modpn library, and the Spiral system provides the ability to automatically tune the FFT code to different computing platforms.

The "Invaders' Algorithm: Range of Values Modulation for Accelerated Correlation

Abstract: In this paper, we present an algorithm that allows the simultaneous calculation of several cross correlations. The algorithm works by shifting the range of values of different images/signals to occupy different orders of magnitude and then combining them to form a single composite image/signal. Because additional signals are placed in the space usually occupied by a single signal, we call this the "invaders algorithm," to imply that extra signals invade the space that normally belongs to a single signal. After correlation is performed, the individual results are recovered by performing the inverse operation. The limitations of the algorithm are imposed by the finite length of the mantissa of the hardware used, the precision of the algorithm that performs the cross correlation (e.g., the precision of the fast Fourier transform (FFT)) and by the actual values of the images/signals that are to be combined. The algorithm does not require any special hardware or special FFT algorithm. For typical 250 times 256 images, an acceleration by a factor of at least two in the calculation of their cross correlations is guaranteed using an ordinary PC or a laptop. As for smaller sized templates, tenfold accelerations may be achieved

Multi-dimensional systolic networks, for discrete fourier transform

Abstract: In this paper the problem of computing the Discrete Fourier Transform (DFT) in VLSI is considered. We describe an approach to extend the linear systolic array algorithm to the multidimensional systolic network algorithm. The proposed networks is based on the pipeline design and have regular structure. Among them the mesh-connected network matches, with a small factor, the known theoretical Ω(n2) lower bound to the (area × time2) measure of complexity in the planar VLSI.

Design of a mixed prime factor FFT for portable digital radio mondiale receiver

Abstract: To achieve better sound quality and to improve data reception, digital radio mondiale (DRM) offers a worldwide initiative to bring analog amplitude modulation (AM) radio into the digital era. DRM systems use coded orthogonal frequency division multiplexing (COFDM) modulation with a multilevel coding scheme to get high resistance to the multipath padding and interference. The bandwidth of a DRM passband signal is less than 20 kHz and the number of carriers used in orthogonal frequency division multiplexing (OFDM) modulation is relatively small. For this reason, DRM systems use non-power-of-two Fast Fourier Transforms (FFT) for OFDM demodulation, such processing gives way to more speed and power consumption in critical paths in DRM receivers. In this paper, we propose a mixed radix-2n and prime factor FFT algorithm for portable DRM receivers. Using the proposed architecture, we can reduce the processing time and energy consumption compared to conventional digital signal processor (DSP) based DRM receivers.