The discrete Fourier transform algorithm for determining decay constants—Implementation using a field programmable gate array

Bostrom, Gregory A.; Atkinson, Dean B.; Rice, A. L.

doi:10.1063/1.4916709

Cited by 5 publications

(4 citation statements)

References 13 publications

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“…For CRD, the APD signal is sent to an oscilloscope (PicoScope 2000 A, Pico Technology, St. Neots, Cambridgeshire, UK), which acquires the decays and stores them in an on-board buffer before sending a block of waveforms to LabVIEW. Once in LabVIEW, the decays are co-added and fit to an exponential function using the discrete Fourier transform method (Mazurenka et al 2005;Everest and Atkinson 2008;Bostrom et al 2015).…”

Section: Electronics and Data Acquisitionmentioning

confidence: 99%

A portable, four-wavelength, single-cell photoacoustic spectrometer for ambient aerosol absorption

Fischer

Smith

2017

Aerosol Science and Technology

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Aerosols directly affect Earth's climate by scattering and absorbing solar radiation. Although they are ubiquitous in Earth's atmosphere, direct, in situ, wavelength-resolved measurements of aerosol optical properties remain challenging. As a result, the so-called aerosol direct effects are one of the largest uncertainties in predictions of Earth's future climate, and new instrumentation is needed to provide measurements of the absorption of sunlight by atmospheric particles. We have developed a portable, four-wavelength, single-cell photoacoustic spectrometer for simultaneous measurement of aerosol absorption at 406, 532, 662, and 785 nm, with an additional extinction measurement at 662 nm via a built-in cavity ringdown spectrometer. The instrument, dubbed MultiPAS-IV, is compact, robust, has low power requirements, and utilizes a multipass optical arrangement to achieve typical detection limits of 0.6-0.7 Mm ¡1 for absorption (2s, 2-min average). Tests with nigrosin aerosols show agreement with Mie theory calculations to within 2%, and comparison with a 7-wavelength aethalometer shows good correlation for ambient (Athens, GA, USA) aerosols. We demonstrate the utility of the broad spectral coverage and sensitivity of the MultiPAS-IV for calculating the absorption A ngstr€ om exponent of black carbon (AAE BC , median value of 0.70) in ambient aerosols and use this value to derive the brown carbon contributions to absorption at 406 nm (43%) and 532 nm (13%) and its wavelength dependence (AAE BrC D 6.3).

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Section: Electronics and Data Acquisitionmentioning

confidence: 99%

A portable, four-wavelength, single-cell photoacoustic spectrometer for ambient aerosol absorption

Fischer

Smith

2017

Aerosol Science and Technology

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“…In previous work [43], it was shown that non-iterative FFT methods have a 200 µs calculation time and that a least squares fitting algorithm requires > 1 ms of calculation time to analyse decaying oscillations of the same length that we consider in this paper using similar computational facilities to the systems used in this present work. Others have shown FPGA-based FFT algorithms for determining the decay constant of decaying signals with analysis rates of 4.4 kHz [40]. Here, we show that trained autoencoder networks are able to analyse incoming signals significantly faster than previously reported methods.…”

Section: B Decaying Oscillationsmentioning

confidence: 52%

“…Different time-and frequency-based computational methods for rapid parameter estimation have been demonstrated, and evaluated, for cavity ring-down (CRD) spectroscopy methods [37][38][39]. Among those, Fourier-transform methods on a field programmable gate arrays (FPGA) have demonstrated data-time analysis rates as high as 4.4 kHz [40]. Several works discuss timeand frequency-domain analysis algorithms for damped sinusoidal signals [41,42] and we recently published a comparative study of three specific analysis methods of discretely sampled damped sinusoidal signals in terms of their speed, and attainable accuracy and precision [43].…”

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confidence: 99%

Rapid parameter estimation of discrete decaying signals using autoencoder networks

Visschers¹,

Budker²,

Bougas³

2021

Preprint

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In this work we demonstrate the use of autoencoder networks for rapid extraction of the signal parameters of discretely sampled signals. In particular, we use dense autoencoder networks to extract the parameters of interest from exponentially decaying signals and decaying oscillations. Using a three-stage training method and careful choice of the neural network size, we are able to retrieve the relevant signal parameters directly from the latent space of the autoencoder network at significantly improved rates compared to traditional algorithmic signal-analysis approaches. We show that the achievable precision and accuracy of this method of analysis is similar to conventional, algorithm-based signal analysis methods, by demonstrating that, the extracted signal parameters are approaching their fundamental parameter estimation limit as provided by the Cramér-Rao lower bound. Furthermore, we demonstrate that autoencoder networks are able to achieve signal analysis, and, hence, parameter extraction, at rates of 75 kHz, orders -of-magnitude faster than conventional techniques with equal precision. Finally, we explore the limitations of our approach, demonstrating that analysis rates of >200 kHz are feasible with further optimization of the transfer rate between the data-acquisition system and data-analysis system. Contents

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“…Time-and frequency-based computational methodologies for rapid parameter estimation have been developed within the context of CRD spectroscopy, and these have been evaluated and compared in terms of their speed and precision [27][28][29]. Most notably, Fourier transform methods have been implemented on FPGAs for fast analysis of exponentially decaying signals [30], with demonstrated analysis rates as high as 4.4 kHz [31]. However, while several works discuss the performance of various time-and frequency-domain analysis algorithms for damped sinusoidal signals [32,33], a direct comparison between their attainable precision and computational speed is currently missing.…”

Section: Introductionmentioning

confidence: 99%

Rapid parameter determination of discrete damped sinusoidal oscillations

Visschers¹,

Wilson²,

Conneely³

et al. 2020

Preprint

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We present different computational approaches for the rapid extraction of the signal parameters of discretely sampled damped sinusoidal signals. We compare time-and frequency-domain-based computational approaches in terms of their accuracy and precision and computational time required in estimating the frequencies of such signals, and observe a general trade-off between precision and speed. Our motivation is precise and rapid analysis of damped sinusoidal signals as these become relevant in view of the recent experimental developments in cavity-enhanced polarimetry and ellipsometry, where the relevant time scales and frequencies are typically within the ∼ 1 − 10 µs and ∼ 1 − 100 MHz ranges, respectively. In such experimental efforts, single-shot analysis with high accuracy and precision becomes important when developing experiments that study dynamical effects and/or when developing portable instrumentations. Our results suggest that online, runningfashion, microsecond-resolved analysis of polarimetric/ellipsometric measurements with fractional uncertainties at the 10 −6 levels, is possible, and using a proof-of-principle experimental demonstration we show that using a frequency-based analysis approach we can monitor and analyze signals at kHz rates and accurately detect signal changes at microsecond time-scales.

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The discrete Fourier transform algorithm for determining decay constants—Implementation using a field programmable gate array

Cited by 5 publications

References 13 publications

A portable, four-wavelength, single-cell photoacoustic spectrometer for ambient aerosol absorption

A portable, four-wavelength, single-cell photoacoustic spectrometer for ambient aerosol absorption

Rapid parameter estimation of discrete decaying signals using autoencoder networks

Rapid parameter determination of discrete damped sinusoidal oscillations

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