The generalized continuous wavelet transform associated with the fractional Fourier transform

Prasad, Akhilesh; Manna, Santanu; Mahato, Ashutosh; Singh, V. K.

doi:10.1016/j.cam.2013.04.016

Cited by 76 publications

(25 citation statements)

References 6 publications

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“…The signals received by sensors S0 to S3 are shown in Figure 10, which are the results of wavelet denoising [21] . In comparison with S0 and S3, the amplitudes in S1 and S2 are obviously larger, because S1 and S2 are closer to the sound source, which means less sound attenuation in the soil.…”

Section: Experiments Results and Discussionmentioning

confidence: 99%

A novel above-ground marking approach based on the girth weld impact sound for pipeline defect inspection

Li¹,

Liu²,

Dorantes-Gonzalez³

et al. 2014

Insight

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Above-ground marking systems, composed of instrumented pigs and above-ground markers (AGMs), have been widely used to locate defects in long-distance buried pipelines. However, the location error for most of the existing AGMs can be up to several tens of centimetres. In this paper, an innovative marking method based on the girth weld impact sound is proposed. An equally-spaced four-sensor linear array was employed to collect the impact sound between the pig and the girth weld in the pipeline. A time difference of arrival (TDOA) algorithm was applied to locate the weld. Experiments show that this method can clearly locate the position of a weld relative to the linear array in buried pipelines with an error of less than 0.1 m. It is envisioned that the method has great potential to monitor the safe operations of long-range buried pipelines.

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Section: Experiments Results and Discussionmentioning

confidence: 99%

A novel above-ground marking approach based on the girth weld impact sound for pipeline defect inspection

Li¹,

Liu²,

Dorantes-Gonzalez³

et al. 2014

Insight

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show abstract

“…[3] Subsequently, several authors have considered fractional Fourier transform for many different reasons and have investigated a number of properties and applications of it, see, e.g. [4][5][6][7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

“…Note that the convolutions * 1 and * 2 behave like conjugate to each other. Yet another generalized convolution * 3 is known in the literature, see [9,11], defined by…”

Section: Introductionmentioning

confidence: 99%

On fractional convolutions and distributions

Jain

Kumar

2015

Integral Transforms and Special Functions

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The present paper focuses on three types of fractional convolutions. First consideration is to extend the famous Young's inequality in the context of fractional convolution. Then for these convolutions, weighted iterated L p − L q inequalities have been investigated. Finally, the notion of fractional convolutions between functions and distributions and also between distributions has been defined and various corresponding properties have been studied.

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“…Generally, there are four changing features such as trend [ 4 ], periodicity [ 5 ], randomness [ 6 ], and synthesis [ 7 ] in time series and three types of time series prediction including point prediction which offers prediction values, range prediction which offers prediction value within one interval, and density prediction which offers the complete probability distribution of the prediction value.…”

Section: Introductionmentioning

confidence: 99%

Study of Track Irregularity Time Series Calibration and Variation Pattern at Unit Section

Jia

Li-li

Wang

et al. 2014

Computational Intelligence and Neuroscience

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Focusing on problems existing in track irregularity time series data quality, this paper first presents abnormal data identification, data offset correction algorithm, local outlier data identification, and noise cancellation algorithms. And then proposes track irregularity time series decomposition and reconstruction through the wavelet decomposition and reconstruction approach. Finally, the patterns and features of track irregularity standard deviation data sequence in unit sections are studied, and the changing trend of track irregularity time series is discovered and described.

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The generalized continuous wavelet transform associated with the fractional Fourier transform

Cited by 76 publications

References 6 publications

A novel above-ground marking approach based on the girth weld impact sound for pipeline defect inspection

A novel above-ground marking approach based on the girth weld impact sound for pipeline defect inspection

On fractional convolutions and distributions

Study of Track Irregularity Time Series Calibration and Variation Pattern at Unit Section

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