The Fast Fourier Transform and Its Applications

Cooley, James W.; Lewis, Peter; Welch, Peter D.

doi:10.1109/te.1969.4320436

Cited by 404 publications

(169 citation statements)

References 10 publications

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“…This is supported by Figure 4a,c, which show a comparison between observed and normalised hourly demands, respectively, for a one-week period in DMA1. Furthermore, a fast Fourier transform (FFT) algorithm [31] was applied to compute the amplitude of sinusoidal components, as a function of the frequency, characterising the original (Figure 4b) and normalised (Figure 4d) time series. In order to make the results of the analysis comparable, both the time series were preliminary scaled to belong to the [0 1] interval.…”

Section: Case Studiesmentioning

confidence: 99%

A Probabilistic Short-Term Water Demand Forecasting Model Based on the Markov Chain

Gagliardi

Alvisi

Kapelan

et al. 2017

Water

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This paper proposes a short-term water demand forecasting method based on the use of the Markov chain. This method provides estimates of future demands by calculating probabilities that the future demand value will fall within pre-assigned intervals covering the expected total variability. More specifically, two models based on homogeneous and non-homogeneous Markov chains were developed and presented. These models, together with two benchmark models (based on artificial neural network and naïve methods), were applied to three real-life case studies for the purpose of forecasting the respective water demands from 1 to 24 h ahead. The results obtained show that the model based on a homogeneous Markov chain provides more accurate short-term forecasts than the one based on a non-homogeneous Markov chain, which is in line with the artificial neural network model. Both Markov chain models enable probabilistic information regarding the stochastic demand forecast to be easily obtained.

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Section: Case Studiesmentioning

confidence: 99%

A Probabilistic Short-Term Water Demand Forecasting Model Based on the Markov Chain

Gagliardi

Alvisi

Kapelan

et al. 2017

Water

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“…Wave-frequency spectra were calculated using a Fast Fourier Transform (FFT) algorithm (Cooley et al 1969) and smoothed following the averaging procedure described by Otnes and Enochsen (1972, p. 302-306). The spectrum estimates were corrected for water-pressure filtering using the procedures of Kim and Simons (1974).…”

Section: Analysis Of Field Datamentioning

confidence: 99%

Wave-energy distribution and hurricane effects on Margarita Reef, southwestern Puerto Rico

1994

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Abstract. Wave measurements at Margarita Reef in southwestern Puerto Rico show that wave height decreases as waves travel across the forereef and into the backreef. Wave spectra reveal the presence of two wave trains impinging on the reef during the study: trade-wind waves and locally generated seas. Significant wave height calculated from the spectra show an average reduction of 19.5% from 20-to 10-m isobaths and 26% from 20-to 5-m isobaths. The significant wave height decreases an average of 82% for waves traveling across the reefcrest and into the backreef. Wave-energy reduction is 35% from 20-to 10-m isobaths and 45% from 20-to 5-m isobaths. Energy loss across the reef crest is 97% which translates into the formation of strong across-the-reef currents capable of moving coarse sediment. Refraction diagrams of waves impinging on the reef from the SE provide a display of wave energy distribution around the reef. The transmission coefficients calculated for trade-wind waves and locally generated seas have means of 18% and 39%, respectively. A wave height model with negligible energy dissipation, produces wave height estimates that are, in general, within the f 15% error bands. Results of wave-energy changes from this study were applied to waves representative of hurricane conditions at the reef. Aerial photographs of the reef before and after the passage of hurricanes were compared to assess the reef changes. Changes observed in the photographs are interpreted as products of sediment transport by hurricane-generated waves. The patterns of change agree with the refraction diagrams suggesting that waves were the main agents of change at Margarita Reef during severe storms.

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“…The Fast Fourier Transform (FFT) is a digital computer algorithm for fast and efficient computation of the Discrete Fourier Transform (DFT) [61,62]. The DFT is defined by…”

Section: The Fast Fourier Transformmentioning

confidence: 99%

“…A distortion due to aliasing occurs in the frequency domain for real functions which are not sampled at sufficiently high rates [62,63].…”

Section: The Approximation Of the Fourier Transform Or Fourier Series Bymentioning

confidence: 99%

On the Statistical Modeling of Radar Targets

Wright¹,

Haddad²

1972

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The Fast Fourier Transform and Its Applications

Cited by 404 publications

References 10 publications

A Probabilistic Short-Term Water Demand Forecasting Model Based on the Markov Chain

A Probabilistic Short-Term Water Demand Forecasting Model Based on the Markov Chain

Wave-energy distribution and hurricane effects on Margarita Reef, southwestern Puerto Rico

On the Statistical Modeling of Radar Targets

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