Low Power Implementation of Non Power-of-Two FFTs on Coarse-Grain Reconfigurable Architectures

The DRM standard for digital radio broadcast in the AM band requires integrated devices for radio receivers at very low power. A System on Chip (SoC) call DiMITRI was developed based on a dual ARM9 RISC core architecture. Analyses showed that most computation power is used in the Coded Orthogonal Frequency Division Multiplexing (COFDM) demodulation to compute Fast Fourier Transforms (FFT) and inverse transforms (IFFT) on complex samples. These FFTs have to be computed on non power-of-two numbers of samples, which is very uncommon in the signal processing world. The results obtained with this chip, lead to the objective to decrease the power dissipated by the COFDM demodulation part using a coarse-grain reconfigurable structure as a coprocessor. This paper introduces two different coarse-grain architectures: PACT XPP technology and the Montium, developed by the University of Twente, and presents the implementation of a\ud Fast Fourier Transform on 1920 complex samples. The implementation result on the Montium shows a saving of a factor 35 in terms of processing time, and 14 in terms of power consumption compared to the RISC implementation, and a\ud smaller area. Then, as a conclusion, the paper presents the next steps of the development and some development issues

Generating and Searching Families of FFT Algorithms

A fundamental question of longstanding theoretical interest is to prove the lowest exact count of real additions and multiplications required to compute a power-of-two discrete Fourier transform (DFT). For 35 years the split-radix algorithm held the record by requiring just 4n log n - 6n + 8 arithmetic operations on real numbers for a size-n DFT, and was widely believed to be the best possible. Recent work by Van Buskirk et al. demonstrated improvements to the split-radix operation count by using multiplier coefficients or "twiddle factors" that are not n-th roots of unity for a size-n DFT. This paper presents a Boolean Satisfiability-based proof of the lowest operation count for certain classes of DFT algorithms. First, we present a novel way to choose new yet valid twiddle factors for the nodes in flowgraphs generated by common power-of-two fast Fourier transform algorithms, FFTs. With this new technique, we can generate a large family of FFTs realizable by a fixed flowgraph. This solution space of FFTs is cast as a Boolean Satisfiability problem, and a modern Satisfiability Modulo Theory solver is applied to search for FFTs requiring the fewest arithmetic operations. Surprisingly, we find that there are FFTs requiring fewer operations than the split-radix even when all twiddle factors are n-th roots of unity.Comment: Preprint submitted on March 28, 2011, to the Journal on Satisfiability, Boolean Modeling and Computatio

Field-Programmable Gated Array Implementation of Split-Radix Fast Fourier Transform for High Throughput

As the signal processing required in electronic warfare (EW) domain is complex and the sample rates to be handled are very high, IP cores which are freely available are not of much use. A study of various fast fourier transform (FFT) algorithms has been carried out and spit-radix FFT has been chosen to be implemented due to fewer multiplications3.This algorithm is attractive to be implemented using field-programmable gated array (FPGA). This paper presents split-radix FFT algorithm for implementation of 512-pt FFT on FPGA platform for EW applications. The algorithm is such designed that it can achieve a throughput of up to 1500 MSPS. 512-pt SRFFT is implemented using parallel pipelined architecture in order to maximize processing speed and thus achieve a throughput of 1500 MSPS with area optimization. The pipeline structure is partitioned to balance the input throughput and to optimize the available FPGA resources. The standard Cooley-Tukey radix-2 FFT algorithm requires N/2 log2 N (for N=512, 2304 multiplications)multiplications and N log2 N additions where as radix-4 FFT requires N/2 log4 N multiplications and N log2 N additions. The SRFFT presented in this paper has a multiplicative complexity of only about two-thirds that of the radix-2 FFT, and is better than the radix-4 FFT or any higher power-of-two radix as well. The initial latency is less than N clock cycles.Defence Science Journal, 2013, 63(2), pp.210-213, DOI:http://dx.doi.org/10.14429/dsj.63.426

Design of High Speed Memory-Based FFT Processor Using 90nm Technology

In order to enhance performance, the Fast Fourier Transformation is a important operation in Digital Signal Processing (DSP) systems had been extensively studied. State-of-the-art transmission technology uses Orthogonal frequency division multiplexing (OFDM), which primary operation is the Fast fourier transform (FFT). This analysis presents the design of a high-speed memory-based FFT processor using 90nm technology. The novel hybrid multiplier and hybrid adder is used in this analysis. The main objective of this method is to develop an efficient, memory-efficient FFT processor that requires less area.  Using 90nm CMOS (Complementary Metal Oxide Semiconductor) technology, the proposed FFT processor was created and implemented in process. With reduced processing time, this means that the proposed FFT processor performs better than the prior memory-based FFT processors in terms of performance and the number of LUTs required which reduces area and memory utilization

Overview of Parallel Platforms for Common High Performance Computing

The paper deals with various parallel platforms used for high performance computing in the signal processing domain. More precisely, the methods exploiting the multicores central processing units such as message passing interface and OpenMP are taken into account. The properties of the programming methods are experimentally proved in the application of a fast Fourier transform and a discrete cosine transform and they are compared with the possibilities of MATLAB's built-in functions and Texas Instruments digital signal processors with very long instruction word architectures. New FFT and DCT implementations were proposed and tested. The implementation phase was compared with CPU based computing methods and with possibilities of the Texas Instruments digital signal processing library on C6747 floating-point DSPs. The optimal combination of computing methods in the signal processing domain and new, fast routines' implementation is proposed as well