Statistical Methods in Spectral Estimation
نویسنده
چکیده
Suppose a certain variable Xt is measured at discrete equally spaced time points t = 1, ... , T and we want to make assertions on the energy distribution of the frequencies in a harmonic analysis. This energy distribution may for example be used to code the data if Xt is a speech signal or to make a prediction if the Xt are economic data. Instead of using a deterministic approach applied scientists usually use a stochastic approach to model the data and to estimate the energy distribution (e.g. in electrical engineering, geophysics, economics or neurophysiology). One reason is that in a stochastic setup certain fluctuations of the Fourier-transform of the data can be interpreted more naturally (cp. section 2). In this paper we discuss the estimation of the energy distribution in a stochastic model and, more generally, the use of the energy distribution for other purposes, such as the detection of hidden frequencies, the estimation of parameters in parametric models and the prediction of the series. The stochastic framework of this paper is the theory of stationary processes. A stationary process is a stochastic process whose finite dimensional distributions are time invariant (c.f. Brillinger, 1981, section 2.4). In particular the mean and the correlation of neighbouring values of a stationary process remain constant over time. An important feature of stationary processes is the following spectral representation (cf. Brockwell and Davies, 1991, Theorem 4.8.2).
منابع مشابه
Spectral Estimation of Stationary Time Series: Recent Developments
Spectral analysis considers the problem of determining (the art of recovering) the spectral content (i.e., the distribution of power over frequency) of a stationary time series from a finite set of measurements, by means of either nonparametric or parametric techniques. This paper introduces the spectral analysis problem, motivates the definition of power spectral density functions, and reviews...
متن کاملPerformances of classic and weighted versions of some selected methods in estimation of spectral data from camera responses
متن کامل
A Novel Sampling Approach in GNSS-RO Receivers with Open Loop Tracking Method
Propagation of radio occultation (RO) signals through the lower troposphere results in high phase acceleration and low signal to noise ratio signal. The excess Doppler estimation accuracy in lower troposphere is very important in receiving RO signals which can be estimated by sliding window spectral analysis. To do this, various frequency estimation methods such as MUSIC and ESPRIT can be adopt...
متن کاملTarget Detection Improvements in Hyperspectral Images by Adjusting Band Weights and Identifying end-members in Feature Space Clusters
Spectral target detection could be regarded as one of the strategic applications of hyperspectral data analysis. The presence of targets in an area smaller than a pixel’s ground coverage has led to the development of spectral un-mixing methods to detect these types of targets. Usually, in the spectral un-mixing algorithms, the similar weights have been assumed for spectral bands. Howe...
متن کاملWheat Leaf Rust Disease Severity Estimation Using Reflectance Spectrum Coding Methods
Using spectroradiometry and remote sensing techniques is an effective and rapid method in diagnosing vegetation diseases which enforced mostly by using spectral vegetation indices and statistical methods. The present study aimed to deploy encoding technique for the reflectance spectrum of the wheat leaves to assess the severity of the Rust disease. This is unlike to the spectral vegetation ind...
متن کاملSPOT-5 Spectral and Textural Data Fusion for Forest Mean Age and Height Estimation
Precise estimation of the forest structural parameters supports decision makers for sustainable management of the forests. Moreover, timber volume estimation and consequently the economic value of a forest can be derived based on the structural parameter quantization. Mean age and height of the trees are two important parameters for estimating the productivity of the plantations. This research ...
متن کامل