scholarly journals A Mathematical Investigation of a Continuous Covariance Function Fitting with Discrete Covariances of an AR Process

2021 ◽  
Vol 5 (1) ◽  
pp. 18
Author(s):  
Johannes Korte ◽  
Till Schubert ◽  
Jan Martin Brockmann ◽  
Wolf-Dieter Schuh
Keyword(s):  
Difference Equation ◽  
Spectral Density ◽  
Power Spectral Density ◽  
Covariance Function ◽  
Second Step ◽  
Function Fitting ◽  
Power Spectral ◽  
Derived Properties ◽  
Ar Process ◽  
Class Of Functions

In this paper, we want to find a continuous function fitting through the discrete covariance sequence generated by a stationary AR process. This function can be determined as soon as the Yule–Walker equations are found. The procedure consists of two steps. At first the inverse zeros of the characteristic polynomial of the AR process must be fixed. The second step is based on the fact that an AR process can also be seen as a difference equation. By solving this difference equation, it is possible to determine a class of functions from which a candidate for a continuous covariance function can be determined. To analyze if this function is applicable as a positive definite covariance function, it is analyzed mathematically in view of the power spectral density compared to the characteristics of the power spectral density for the discrete covariances. Then it is shown that this function is positive semi-definite. At the end, a simulation of a stationary AR(3) process is elaborated to illustrate the derived properties.

Fuzzy Modeling of Multi-Degree-of-Freedom Power Spectral Density Systems

2009 ◽  
Vol 2 (1) ◽  
pp. 40-47
Author(s):  
Montasser Tahat ◽  
Hussien Al-Wedyan ◽  
Kudret Demirli ◽  
Saad Mutasher
Keyword(s):  
Spectral Density ◽  
Power Spectral Density ◽  
Fuzzy Modeling ◽  
Degree Of Freedom ◽  
Power Spectral

scholarly journals Noise power spectral density scaled SNR response estimation with restricted range search for sound source localisation using unmanned aerial vehicles

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Benjamin Yen ◽  
Yusuke Hioka
Keyword(s):  
Spectral Density ◽  
Noise Reduction ◽  
Power Spectral Density ◽  
Sound Source ◽  
Processing Algorithm ◽  
Post Processing ◽  
Time Frequency ◽  
Distance Error ◽  
Rotor Noise ◽  
Power Spectral

Abstract A method to locate sound sources using an audio recording system mounted on an unmanned aerial vehicle (UAV) is proposed. The method introduces extension algorithms to apply on top of a baseline approach, which performs localisation by estimating the peak signal-to-noise ratio (SNR) response in the time-frequency and angular spectra with the time difference of arrival information. The proposed extensions include a noise reduction and a post-processing algorithm to address the challenges in a UAV setting. The noise reduction algorithm reduces influences of UAV rotor noise on localisation performance, by scaling the SNR response using power spectral density of the UAV rotor noise, estimated using a denoising autoencoder. For the source tracking problem, an angular spectral range restricted peak search and link post-processing algorithm is also proposed to filter out incorrect location estimates along the localisation path. Experimental results show the proposed extensions yielded improvements in locating the target sound source correctly, with a 0.0064–0.175 decrease in mean haversine distance error across various UAV operating scenarios. The proposed method also shows a reduction in unexpected location estimations, with a 0.0037–0.185 decrease in the 0.75 quartile haversine distance error.

Numerical and Experimental Studies of Pipe Vibration Generated by Elongated Orifice

2016 ◽  
Author(s):  
Wenjie Bai ◽  
Quan Duan ◽  
Zaoxiao Zhang
Keyword(s):  
Spectral Density ◽  
Power Spectral Density ◽  
Flow Rate ◽  
Vibration Response ◽  
Frequency Range ◽  
Fluctuating Pressure ◽  
Outlet Pressure ◽  
Wall Pressure Fluctuations ◽  
Power Spectral ◽  
Pipe Vibration

Hydraulic tests for elongated orifice-induced wall pressure fluctuations and vibration in pipeline have been carried out. The regulating modes of test system consist of maintaining outlet pressure to increase flow rate and maintaining flow rate to decrease outlet pressure. Both regulating modes would increase the possibility of cavitation within elongated orifice, which has been confirmed by numerical simulation in present study. Statistical characteristics of the fluctuating pressure and structure vibration response have been studied. The standard deviation analyses indicate that the amplitude of fluctuating pressure is mainly determined by flow rate. The power spectral density analyses show that the energy of the fluctuating pressure behind elongated orifice is concentrated in lower frequency range and it can be divided into two parts in this test: the pressure pulsation excited by plunger pump and the random fluctuating pressure produced by elongated orifice’s disturbance. The power spectral density of pipe vibration response shows that the lower frequency of pipe vibration response can be ascribed to the fluctuating pressure behind elongated orifice and the characteristic frequencies corresponding to cavitation within elongated orifice are in the higher frequency range.

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