Complex Function Approximation Using Two-Dimensional Interpolation

Wang, Dong; Ercegovac, M.D.; Xiao, Yang

doi:10.1109/tc.2013.181

Cited by 5 publications

(2 citation statements)

References 25 publications

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“…Lastly, implementing complex exponential functions is a crucial part of this project, and it has been developed in many research studies in various ways on FPGA, including polynomial approximation, interpolation, lookup-table-based methods [16], CORDIC IP core [17], two-dimensional interpolation [18], and floating-point implementation [19]. However, these methods often consume a significant amount of FPGA logic cells, such as lookup tables (LUTs) and D flip-flops.…”

Section: Related Workmentioning

confidence: 99%

Complex-Exponential-Based Bio-Inspired Neuron Model Implementation in FPGA Using Xilinx System Generator and Vivado Design Suite

Ahmad,

Zhang,

et al. 2023

Biomimetics

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This research investigates the implementation of complex-exponential-based neurons in FPGA, which can pave the way for implementing bio-inspired spiking neural networks to compensate for the existing computational constraints in conventional artificial neural networks. The increasing use of extensive neural networks and the complexity of models in handling big data lead to higher power consumption and delays. Hence, finding solutions to reduce computational complexity is crucial for addressing power consumption challenges. The complex exponential form effectively encodes oscillating features like frequency, amplitude, and phase shift, streamlining the demanding calculations typical of conventional artificial neurons through levering the simple phase addition of complex exponential functions. The article implements such a two-neuron and a multi-neuron neural model using the Xilinx System Generator and Vivado Design Suite, employing 8-bit, 16-bit, and 32-bit fixed-point data format representations. The study evaluates the accuracy of the proposed neuron model across different FPGA implementations while also providing a detailed analysis of operating frequency, power consumption, and resource usage for the hardware implementations. BRAM-based Vivado designs outperformed Simulink regarding speed, power, and resource efficiency. Specifically, the Vivado BRAM-based approach supported up to 128 neurons, showcasing optimal LUT and FF resource utilization. Such outcomes accommodate choosing the optimal design procedure for implementing spiking neural networks on FPGAs.

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Section: Related Workmentioning

confidence: 99%

Complex-Exponential-Based Bio-Inspired Neuron Model Implementation in FPGA Using Xilinx System Generator and Vivado Design Suite

Ahmad,

Zhang,

et al. 2023

Biomimetics

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“…The bivariate approximation methods could be compared to a bivariate interpolation technique used in [14]. The technique used there resorts to two sequential interpolation processes (on x, then on y).…”

Section: A Logic-only Synthesismentioning

confidence: 99%

Hardware Implementations of Fixed-Point Atan2

Dinechin

Istoan

2015

2015 IEEE 22nd Symposium on Computer Arithmetic

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The atan2 function computes the polar angle arctan(y/x) of a point given by its cartesian coordinates. It is widely used in digital signal processing to recover the phase of a signal. This article studies for this context the implementation of atan2 with fixed-point inputs and outputs. It compares the prevalent CORDIC shift-and-add algorithm to two multiplierbased techniques. The first one computes the bivariate atan2 function as the composition of two univariate functions: the reciprocal, and the arctangent, each evaluated using bipartite or polynomial approximation methods. The second technique directly uses piecewise bivariate polynomial approximations of degree 1 or 2. Each of these approaches requires a relevant argument reduction, which is also discussed. All the algorithms are last-bit accurate, and implemented with similar care in the open-source FloPoCo framework. Based on synthesis results on FPGAs, their relevance domains are discussed.

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Complex exponential functions: A high-precision hardware realization

Hosseiny

Jaberipur

2020

Integration

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Complex Function Approximation Using Two-Dimensional Interpolation

Cited by 5 publications

References 25 publications

Complex-Exponential-Based Bio-Inspired Neuron Model Implementation in FPGA Using Xilinx System Generator and Vivado Design Suite

Complex-Exponential-Based Bio-Inspired Neuron Model Implementation in FPGA Using Xilinx System Generator and Vivado Design Suite

Hardware Implementations of Fixed-Point Atan2

Complex exponential functions: A high-precision hardware realization

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