An Algorithm for the Evaluation of Finite Trigonometric Series

Goertzel, G.

doi:10.2307/2310304

Cited by 430 publications

(206 citation statements)

References 2 publications

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“…All discrete Fourier transforms were performed using a second order Goertzel algorithm, which is a very efficient method of computing DFT values at specific frequencies. 19 The temperature of the sensor was calculated from the resistance of the heating element and its thermal coefficient of resistance. The total heat capacity C of a sensor with sample was calculated using Eqs.…”

Section: B Data Reduction For Ac Calorimetry Measurementsmentioning

confidence: 99%

Scanning AC nanocalorimetry combined with in-situ x-ray diffraction

Xiao

Gregoire

McCluskey

et al. 2013

Journal of Applied Physics

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Micromachined nanocalorimetry sensors have shown excellent performance for high-temperature and high-scanning rate calorimetry measurements. Here, we combine scanning AC nanocalorimetry with in-situ x-ray diffraction (XRD) to facilitate interpretation of the calorimetry measurements. Time-resolved XRD during in-situ operation of nanocalorimetry sensors using intense, high-energy synchrotron radiation allows unprecedented characterization of thermal and structural material properties. We demonstrate this experiment with detailed characterization of the melting and solidification of elemental Bi, In, and Sn thin-film samples, using heating and cooling rates up to 300 K/s. Our experiments show that the solidification process is distinctly different for each of the three samples. The experiments are performed using a combinatorial device that contains an array of individually addressable nanocalorimetry sensors. Combined with XRD, this device creates a new platform for high-throughput mapping of the composition dependence of solid-state reactions and phase transformations. V C 2013 AIP Publishing LLC.

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Section: B Data Reduction For Ac Calorimetry Measurementsmentioning

confidence: 99%

Scanning AC nanocalorimetry combined with in-situ x-ray diffraction

Xiao

Gregoire

McCluskey

et al. 2013

Journal of Applied Physics

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“…All discrete Fourier transforms were performed using a second order Goertzel algorithm, which is a very efficient method of computing DFT values at specific frequencies [42]. The temperature of the sensor was calculated from the resistance of the heating element and its thermal coefficient of resistance.…”

Section: B Data Reduction For Ac Calorimetry Measurementsmentioning

confidence: 99%

Scanning AC Nanocalorimetry and Its Applications

Xiao

Vlassak

2016

Fast Scanning Calorimetry

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This thesis presents an AC nanocalorimetry technique that enables calorimetry measurements on very small quantities of materials over a wide range of scanning rates (from isothermal to 3×10^3 K/s), temperatures (up to 1200 K), and environments. Such working range bridges the gap between traditional scanning calorimetry of bulk materials and nanocalorimetry. The method relies on a micromachined nanocalorimeter with negligible thermal lags between heater, thermometer, and sample. The ability to perform calorimetry measurements over such a broad range of scanning rates makes it an ideal tool to characterize the kinetics of phase transformations, reactions at elevated temperatures or to explore the behavior of materials far from equilibrium. We By combining scanning DC and AC nano-calorimetry techniques, we study the nucleation behavior of undercooled liquid Bi at cooling rates ranging from 10^1 to 10^4 K/s. Upon initial melting, the Bi thin-film sample breaks up into isolated islands. The number of islands in a typical sample is sufficiently large that highly repeatable nucleation behavior is observed, despite the stochastic nature of the nucleation process.We establish a data reduction technique to evaluate the nucleation rate from DC and AC calorimetry results. The results show that the driving force for the nucleation of melted Bi is well described by classical nucleation theory over a wide range of cooling rates. The proposed technique provides a unique and efficient way to examine nucleation kinetics v with cooling rates over several orders of magnitude. The technique is quite general and can be used to evaluate reaction kinetics in other materials.Lastly, we apply the scanning AC nanocalorimetry technique to study solid-gas phase reactions by measuring the change in heat capacity of a sample during reaction. We apply this approach to evaluate the oxidation kinetics of thin-film samples of zirconium in air. The results confirm parabolic oxidation kinetics with an activation energy of 0.59±0.03 eV. The nano-calorimetry measurements were performed using a device that contains an array of micromachined nano-calorimeter sensors in an architecture designed for combinatorial studies. We demonstrate that the oxidation kinetics can be quantified using a single sample, thus enabling high-throughput mapping of the composition-dependence of the reaction rate.vi

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“…The Goertzel algorithm [1] provides efficent tone detection in a signal. It can be regarded as the evaluation of a single bin of the FFT, or as a narrow-band filter.…”

Section: Introductionmentioning

confidence: 99%

An Evaluation of the Goertzel Algorithm for Low-Power, Embedded Systems

Brown¹,

Timoney²,

Lysaght³

2014

25th IET Irish Signals &Amp; Systems Conference 2014 and 2014 China-Ireland International Conference on Information and Communi

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-The Goertzel Algorithm provides an efficient mechanism for tone detection in signal processing. However, on Wireless Sensor Network nodes, there is often not sufficient processing power to implement this using floating-point arithmetic, so fixed-point implementations are used. In this paper we compare the quality of the results for a typical audio application with different resolutions of fixed-point support using MATLAB. We also provide performance figures based on implementing this on a representative sensor node platform. Our results show that, for this application-space, 16-bit fixed-point arithmetic provides the best tradeoff of accuracy against performance. No previous work has addressed this specific aspect of implementating the Goertzel algorithm.

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An Algorithm for the Evaluation of Finite Trigonometric Series

Cited by 430 publications

References 2 publications

Scanning AC nanocalorimetry combined with in-situ x-ray diffraction

Scanning AC nanocalorimetry combined with in-situ x-ray diffraction

Scanning AC Nanocalorimetry and Its Applications

An Evaluation of the Goertzel Algorithm for Low-Power, Embedded Systems

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