Analysis of twiddle factor memory complexity of radix-2i pipelined FFTs (original) (raw)
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Twiddle factor memory switching activity analysis of radix-22 and equivalent FFT algorithms
Circuits and Systems (ISCAS), …, 2010
In this paper, we propose equivalent radix-2 2 algorithms and evaluate them based on twiddle factor switching activity for a single delay feedback pipelined FFT architecture. These equivalent pipeline FFT algorithms have the same number of complex multipliers with the same resolution as the radix-2 2 . It is shown that the twiddle factor switching activity of the equivalent algorithms is reduced with up to 40% for some of the equivalent algorithms derived for N = 256.
4k-point FFT algorithms based on optimized twiddle factor multiplication for FPGAs
2010 Asia Pacific Conference on Postgraduate Research in Microelectronics and Electronics (PrimeAsia), 2010
In this paper, we propose higher point FFT (fast Fourier transform) algorithms for a single delay feedback pipelined FFT architecture considering the 4096-point FFT. These algorithms are different from each other in terms of twiddle factor multiplication. Twiddle factor multiplication complexity comparison is presented when implemented on Field-Programmable Gate Arrays(FPGAs) for all proposed algorithms. We also discuss the design criteria of the twiddle factor multiplication. Finally it is shown that there is a trade-off between twiddle factor memory complexity and switching activity in the introduced algorithms.
Hardware-Efficient Twiddle Factor Generator for Mixed Radix-2/3/4/5 FFTs
2016 IEEE International Workshop on Signal Processing Systems (SiPS), 2016
Twiddle factors are an integral part of FFT computations. Conventionally, they are either computed in run-time, hence increasing computational complexity, or pre-calculated and stored in RAM memory, which requires large memory footprint and increases power consumption. We created a systematic approach for designing digital circuits that generate twiddle factors based on reduced ROM tables. The approach supports radix-2, radix-3, radix-4, radix-5, and mixed radix-2/3/4/5 algorithms and several transform lengths. Number of complex twiddle factors stored in the memory equals only Nmax 8 + 1 for transform lengths up to Nmax.
Microprocessors and Microsystems, 2018
The fast Fourier transform (FFT) algorithm is widely used in digital signal processing systems (DSPs); hence, the development of a high-performance and resource-efficient FFT processor that conforms to the processing and precision requirements of real-time signal processing is highly desirable. We propose an FFT processor for field programmable gate array (FPGA) devices, based on the radix-2-decimation-in-frequency (R2DIF) algorithm. An appropriately modified parallel doublepath delay commutator (DDC) architecture for radix-2 with continuous dual-input and dual-output streams (CoDIDOS) is proposed to increase throughput and reduce latency in FFT computation. The chip-area of the proposed design is reduced by decreasing the memory footprint of the complex twiddle factor multipliers. A multiplication scheme based on a combination of the unrolled coordinate rotation digital computer (CORDIC) and the canonical signed digit-based binary expression (CSDBE) is used to multiply the complex twiddle factors without requiring memory blocks for their storage. The CSDBE technique is proposed to optimize the multiplication of constants in the architecture. The proposed FFT processor is implemented as an intellectual property (IP) core and tested on a Xilinx Virtex-7 FPGA. Experimental results confirm that the proposed design improves the speed, latency, throughput, accuracy, and resource utilization of computation on FPGA devices over existing designs.
FPGA implementation of Radix-2^2 pipelined FFT processor
The Fast Fourier Transform (FFT) is very important algorithm in signal processing, softwaredefined radio, and wireless communication. This paper explains the realization of radix-2 2 single-path delay feedback pipelined FFT processor. This architecture has the same multiplicative complexity as radix-4 algorithm, but retains the simple butterfly structure of radix-2 algorithm. The implementation was made on a Field Programmable Gate Array (FPGA) because it can achieve higher computing speed than digital signal processors (DSPs), and also can achieve cost effectively ASIC-like performance with lower development time, and risks. The processor has been developed using hardware description language VHDL and simulated up to 465 MHz on an Xilinx xc5vsx35t for transformation length 256-point.
Low-Power Twiddle Factor Unit for FFT Computation
Lecture Notes in Computer Science, 2007
An integral part of FFT computation are the twiddle factors, which, in software implementations, are typically stored into RAM memory implying large memory footprint and power consumption. In this paper, we propose a novel twiddle factor generator based on reduced ROM tables. The unit supports both radix-4 and mixed-radix-4/2 FFT algorithms and several transform lengths. The unit operates at a rate of one factor per clock cycle.
Fast fourier transform processor implementation for high inputs on field programmable gates array
2018
In the past few years, fast Fourier transform (FFT) proved to be an efficient method to accomplish the discrete Fourier transform (DFT) with less number of operations. FFT has been vastly applied for many applications, such as image processing technique, network data transmission (XDSL, WiMAX, and WLAN), orthogonal frequency-division multiplexing (OFDM), digital signal processing (DSP) and numerous applications that require high input data (1024 and up) processing. Low power and low complexity are the main concerns in high input FFT. Therefore, this research aims to investigate the power consumption, hardware resources usage and speed for radix-(2, 4 and 8) FFT processor, using the same device and environment to investigate the performance of each. Memory-based architecture chosen to use for FFT processors, due to the reduction in the number of butterflies and rotators, as they are reused for different stages of the FFT, were implemented on Cyclone II Field Programmable Gate Arrays (FPGA). Verilog Hardware Description Language (Verilog HDL) and VHDL Languages are used to program the algorithms into the FPGA. FFT algorithms will be implemented for up to 4096 points to measure the high load processing capability. The results show that for the 4096 points FFT, the radix-4 is the best trade-off in term of speed, resources and power consumption, which requires only 36% of the power required by the 4069 points radix-8 FFT and 58% of the power required by the 4069 points radix-2 FFT. On another hand, for the hardware resources, the result shows that the 4096 points radix-4 FFT used 30% of hardware resources furthermore; radix-8 FFT uses approximately 45%, in the meanwhile radix-2 require 20% only. For speed, the results shows that a 4096 points radix-4 FFT is 70% faster than 4096 points radix-2 FFT and 62% slower than 4096 points radix-8 FFT. While the radix-2 may be preferred, when it comes to power saving because it only need to consume 28% less
Compact and high‐throughput parameterisable architectures for memory‐based FFT algorithms
IET Circuits, Devices & Systems, 2019
Designers must carefully choose the best-suited fast Fourier transform (FFT) algorithm among various available techniques for the custom implementation that meets their design requirements, such as throughput, latency, and area. This article, to the best of authors' knowledge, is the first to present a compact and yet high-throughput parameterisable hardware architecture for implementing different FFT algorithms, including radix-2, radix-4, radix-8, mixed-radix, and split-radix algorithms. The designed architectures are fully parameterisable to support a variety of transform lengths and variable word-lengths. The FFT algorithms have been modelled and simulated in double-precision floating-point and fixed-point representations using authors' custom-developed library of numerical operations. The designed FFT architectures are modelled in Verilog hardware description language and their cycle-accurate and bit-true simulation results are verified against their fixed-point simulation models. The characteristics and implementation results of various FFT architectures on a Xilinx Virtex-7 FPGA are presented. Compared to recently published works, authors' memory-based FFT architectures utilise less reconfigurable resources while maintaining comparable or higher operating frequencies. The ASIC implementation results in a standard 45-nm CMOS technology are also presented for the designed memory-based FFT architectures. The execution times of FFTs on a workstation and a graphics processing unit are compared against authors' FPGA implementations.
On the efficient computation of single-bit input word length pipelined FFTs
IEICE Electronics Express, 2011
This letter describes an efficient architecture for the computation of fast Fourier transform (FFT) algorithms with single-bit input. The proposed architecture is aimed for the first stages of pipelined FFT architectures, processing one sample per clock cycle, hence making it suiable for real-time FFT computation. Since natural input order pipeline FFTs use large memories in the early stages, it is important to keep the word length shorter in the beginning of the pipeline. By replacing the initial butterflies and rotators of an architecture with that of the proposed block, the memory requirements can be significantly reduced. Comparisons with the commonly used single delay feedback (SDF) architecture show that more than 50% of the required memory can be saved in some cases.
FPGA Implementation for the Multiplexed and Pipelined Building Blocks of Higher Radix-2k FFT
2020 IEEE 11th Latin American Symposium on Circuits & Systems (LASCAS), 2020
Fast Fourier transform (FFT) is one of the fundamental processing block used in many signal processing applications (i.e. for orthogonal frequency division multiplexing in wireless telecommunication). Therefore, every proposal to reduced latency, resources or accuracy errors of FFT implementation counts. This paper proposes the implementation of the butterfly processing elements (BPE) where the concept of the radix-r butterfly computation has been formulated as the combination of α radix-2 butterflies implemented in parallel. An efficient FFT implementation is feasible using our proposed multiplexed and pipelined BPE. Compared to a state-of-the-art reference based on pipelined and parallel structure FFTs, and FPGA based implementation reveals that the maximum throughput is improved by a factor of 1.3 for a 256-point FFT and reach a throughput of 2680 MSps on Virtex-7. The analysis extends to touch on key performance measurements metrics such as throughput, latency and resource utilization.