Explore chapters and articles related to this topic
On The Number Of Bpc Permutations Admissible To K-Extra-Stage Omega Networks
Published in Amir Hussain, Mirjana Ivanovic, Electronics, Communications and Networks IV, 2015
By using foregoing approach, it is not difficult to find that in general bit reversal for admissibility needs n-1 extra stages, and the same is suitable for butterfly. On the contrary, bit shuffle and shuffle row major need only one extra stage to become admissible. The reader is encouraged to try the rest frequently used BPC permutations. Routing bit reversal permutation on 8×82-Omega is shown in Figure 6.
The Fast Fourier Transform (FFT)
Published in James S. Walker, Fast Fourier Transforms, 2017
Buneman’s algorithm is the simplest method for performing the bit reversal permutation. It is based on a simple pattern. If we have permuted the N numbers {0,1,…,N−1}
Omega multistage interconnection network manages double-pattern traffic with a regulator and high-speed forwarding method
Published in International Journal of Parallel, Emergent and Distributed Systems, 2023
Eleftherios Stergiou, Dimitrios Liarokapis, Spiridoula Margariti, Ilias Bombotsaris
The connections between the nodes in each stage can be represented using a matrix. Let be the connection matrix for stage i, where represents the connection between node j in stage (i) and node k in stage (i + 1). The connection matrix can be defined recursively as follows: , where is the identity matrix of size . The connection matric in stage is: , where is a permutation matrix that defines the connections between the nodes in stage . The permutation matrix can be constructed using the bit-reversal permutation algorithm. Let be the bit-reversed binary representation of , where the least significant bit is first. Then, the matrix can be defined as follows:
Design of a modern fast Fourier transform and cache effective bit-reversal algorithm
Published in International Journal of Parallel, Emergent and Distributed Systems, 2023
In the year 1998, L. Carter and K. S. Gatlin came up with an interesting solution [21] using a square matrix buffer fitting smaller caches like L2 or L1. This algorithm, called Cache Optimized Bit Reversal Algorithm (COBRA), uses the decomposition of a bit-reversed permutation into two parts, from naive FFT, it can be observed that the process of decimation creates bit-reversal in the form of a tree structure and that permutations of the powers of two contain permutation patterns of lower powers of two, then the problem can be cut in chosen depth and reduced into two bit-reversal permutation problems.