scholarly journals Nonparametric and parametric methods of spectral analysis

2019 ◽  
Vol 283 ◽  
pp. 07002 ◽  
Author(s):  
Hangfang Zhao ◽  
Lin Gui
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
High Resolution ◽  
Spectral Estimation ◽  
Estimation Method ◽  
Parametric Estimation ◽  
Stationary Time Series ◽  
Estimation Methods ◽  
Practical Applications ◽  
Small Variance

Spectral Analysis is one of the most important methods in signal processing. In practical application, it is critical to discuss the power spectral density estimation of finite data sampled from some stationary time series. A spectral estimator is expected to have good statistical properties such as consistency, high resolution and small variance. For one spectral estimation method, there exists a trade-off between high resolution and small variance. The paper provides a comparison of several popular spectral methods from both theoretical properties and practical applications. We first address several basic nonparametric methods, whose statistical characters are analysed. Then we explain the connections and differences between temporal windowing and lag windowing. Thereafter, the confidence intervals of both windows are given and used to evaluate the estimated results. Besides, several different parametric estimation methods of autoregressive time series are compared, and whose properties and effects are also introduced. Building on our understanding of these studies, we then apply parametric and nonparametric spectral estimation methods on the data of ocean surface wave height.

scholarly journals Multi-Scene Building Height Estimation Method Based on Shadow in High Resolution Imagery

2021 ◽  
Vol 13 (15) ◽  
pp. 2862
Author(s):  
Yakun Xie ◽  
Dejun Feng ◽  
Sifan Xiong ◽  
Jun Zhu ◽  
Yangge Liu
Keyword(s):  
Remote Sensing ◽  
High Resolution ◽  
Estimation Method ◽  
Absolute Error ◽  
Large Error ◽  
Estimation Methods ◽  
Height Estimation ◽  
Building Height ◽  
Remote Sensing Imagery ◽  
High Resolution Imagery

Accurately building height estimation from remote sensing imagery is an important and challenging task. However, the existing shadow-based building height estimation methods have large errors due to the complex environment in remote sensing imagery. In this paper, we propose a multi-scene building height estimation method based on shadow in high resolution imagery. First, the shadow of building is classified and described by analyzing the features of building shadow in remote sensing imagery. Second, a variety of shadow-based building height estimation models is established in different scenes. In addition, a method of shadow regularization extraction is proposed, which can solve the problem of mutual adhesion shadows in dense building areas effectively. Finally, we propose a method for shadow length calculation combines with the fish net and the pauta criterion, which means that the large error caused by the complex shape of building shadow can be avoided. Multi-scene areas are selected for experimental analysis to prove the validity of our method. The experiment results show that the accuracy rate is as high as 96% within 2 m of absolute error of our method. In addition, we compared our proposed approach with the existing methods, and the results show that the absolute error of our method are reduced by 1.24 m-3.76 m, which can achieve high-precision estimation of building height.

scholarly journals Quantile spectral analysis for locally stationary time series

2017 ◽  
Vol 79 (5) ◽  
pp. 1619-1643 ◽  
Author(s):  
Stefan Birr ◽  
Stanislav Volgushev ◽  
Tobias Kley ◽  
Holger Dette ◽  
Marc Hallin
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Stationary Time Series ◽  
Stationary Time ◽  
Locally Stationary Time Series

Integrated processes and the discrete cosine transform

2001 ◽  
Vol 38 (A) ◽  
pp. 105-121
Author(s):  
Robert B. Davies
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Brownian Motion ◽  
White Noise ◽  
Discrete Cosine Transform ◽  
Unit Root ◽  
Stationary Time Series ◽  
Cosine Transform ◽  
Stationary Time ◽  
Integrated Processes

A time-series consisting of white noise plus Brownian motion sampled at equal intervals of time is exactly orthogonalized by a discrete cosine transform (DCT-II). This paper explores the properties of a version of spectral analysis based on the discrete cosine transform and its use in distinguishing between a stationary time-series and an integrated (unit root) time-series.

scholarly journals SOC Estimation of Lead Carbon Batteries Based on the Operating Conditions of an Energy Storage System in a Microgrid System

Energies ◽  
2019 ◽  
Vol 13 (1) ◽  
pp. 33
Author(s):  
Yuanyuan Chen ◽  
Zilong Yang ◽  
Yibo Wang
Keyword(s):  
Wavelet Transform ◽  
Energy Storage ◽  
Storage System ◽  
Estimation Method ◽  
Energy Storage System ◽  
Operating Conditions ◽  
Estimation Methods ◽  
Extend Kalman Filter ◽  
Practical Applications ◽  
Soc Estimation

The environment for practical applications of an energy storage system (ESS) in a microgrid system is very harsh, and therefore actual operating conditions become complex and changeable. In addition, the signal of the ESS sampling process contains a great deal of system and measurement noise, the sampled current fluctuates significantly, and also has high frequency. In this case, under such conditions, it is difficult to accurately estimate the state of charge (SOC) of the batteries in the ESS by common estimation methods. Therefore, this study proposes a compound SOC estimation method based on wavelet transform. This algorithm is very suitable for microgrid systems with large current, frequent fluctuating conditions, and high noise interference. The experimental results and engineering data show that the relative error of the method is 0.5%, which is much lower than the extend Kalman filter (EKF) based on wavelet transform.

scholarly journals Change Detection within Remotely Sensed Satellite Image Time Series via Spectral Analysis

2020 ◽  
Vol 12 (23) ◽  
pp. 4001
Author(s):  
Ebrahim Ghaderpour ◽  
Tijana Vujadinovic
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Change Detection ◽  
Satellite Image ◽  
Remotely Sensed ◽  
Stationary Time Series ◽  
Atmospheric Effects ◽  
Landsat 8 ◽  
Temporal Segmentation ◽  
Jump Detection

Jump or break detection within a non-stationary time series is a crucial and challenging problem in a broad range of applications including environmental monitoring. Remotely sensed time series are not only non-stationary and unequally spaced (irregularly sampled) but also noisy due to atmospheric effects, such as clouds, haze, and smoke. To address this challenge, a robust method of jump detection is proposed based on the Anti-Leakage Least-Squares Spectral Analysis (ALLSSA) along with an appropriate temporal segmentation. This method, namely, Jumps Upon Spectrum and Trend (JUST), can simultaneously search for trends and statistically significant spectral components of each time series segment to identify the potential jumps by considering appropriate weights associated with the time series. JUST is successfully applied to simulated vegetation time series with varying jump location and magnitude, the number of observations, seasonal component, and noises. Using a collection of simulated and real-world vegetation time series in southeastern Australia, it is shown that JUST performs better than Breaks For Additive Seasonal and Trend (BFAST) in identifying jumps within the trend component of time series with various types. Furthermore, JUST is applied to Landsat 8 composites for a forested region in California, U.S., to show its potential in characterizing spatial and temporal changes in a forested landscape. Therefore, JUST is recommended as a robust and alternative change detection method which can consider the observational uncertainties and does not require any interpolations and/or gap fillings.

scholarly journals Method Consideration of Variation Diagnosis and Design Value Calculation of Flood Sequence in Yiluo River Basin, China

Water ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 2722
Author(s):  
Xinxin Li ◽  
Xixia Ma ◽  
Xiaodong Li ◽  
Wenjiang Zhang
Keyword(s):  
Climate Change ◽  
Time Series ◽  
Human Activities ◽  
Extreme Values ◽  
Frequency Estimation ◽  
Synthesis Method ◽  
Estimation Method ◽  
Stationary Time Series ◽  
Distribution Model ◽  
Design Flood

The conventional approaches of the design flood calculation are based on the assumption that the hydrological time series is subject to the same distribution in the past, present, and future, i.e., the series should be consistent. However, the traditional methods may result in overdesign in the water conservancy project since the series has non-stationary variations due to climate change and human activities. Therefore, it is necessary to develop a new approach for frequency estimation of non-stationary time series of extreme values. This study used four kinds of mutation test methods (the linear trend correlation coefficient, Mann–Kendall test, sliding t-test, and Pettitt test) to identify the trend and mutation of the annual maximum flow series (1950–2006) of three hydrological stations in the Yiluo River Basin. Then we evaluated the performance of two types of design flood methods (the time series decomposition-synthesis method, the mixed distribution model) under the impacts of climate change and human activities on hydro-meteorological conditions. The results showed that (a) the design flood value obtained by the time series decomposition-synthesis method based on the series of the backward restore is larger than that obtained by the decomposition synthesis method based on the series of the forward restore; (b) when the return period is 100 years or less, the design flood value obtained by the mixed distribution model using the capacity ratio parameter estimation method is less than that obtained by the hybrid distribution model with simulated annealing parameter estimation method; and (c) both methods can overcome sequence inconsistency in design frequencies. This study provides insight into the frequency estimation of non-stationary time series of extreme values under the impacts of climate change and human activities on hydro-meteorological conditions.

Time-Local Spectral Analysis for Non-Stationary Time Series: The S-Transform for Noisy Signals

2003 ◽  
Vol 03 (03) ◽  
pp. L357-L364 ◽  
Author(s):  
C. R. Pinnegar ◽  
L. Mansinha
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Wavelet Transforms ◽  
Gaussian White Noise ◽  
Stationary Time Series ◽  
Time Frequency ◽  
S Transform ◽  
Undesirable Characteristic ◽  
Noisy Signals ◽  
Short Time

The S-transform is a method of time-local spectral analysis (also known as time-frequency analysis), a modified short-time Fourier Transform, in which the width of the analyzing window scales inversely with frequency, in analogy with continuous wavelet transforms. If the time series is non-stationary and consists of a mix of Gaussian white noise and a deterministic signal, though, this type of scaling leads to larger apparent noise amplitudes at higher frequencies. In this paper, we introduce a modified S-transform window with a different scaling function that addresses this undesirable characteristic.

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