Frequency-Domain Analysis of Time Series

It should be noted that if the process model is known, then it is relatively easy to obtain the required auto- and cross-correlatiOTis and use them to compute the predictor. 

---

Periodogram and Its Use in Frequency-Domain Analysis of Time Series... 

Clearly, the final MDS diagram is partially dependent on the parameters of the noise imposed on the system. It is possible that frequency domain approaches to time series analysis [10] may help in a study of the role of frequency transfer functions in the control of chemical networks. We have assumed that all species involved in the mechanism may be identified and measured. For systems with many species this may be difficult. When there are missing species, CMC may still be performed on the measurable subset of species. The effects of the other species are subsumed into the correlations among the known species, and a consistent diagram can be constructed. The MDS diagram, then, may not be an obvious representation of the underlying mechanism. In fact, due... 

HRV assesses the modulation of autonomic tone on the sinus node, or simply put, the irregularity of sinus rhythm. Methods of measuring HRV fall under broad categories of being either time domain or frequency domain analyses. Time domain measurements involve statistical analyses of the variability in the R-R interval, while frequency domain measurements use spectral analysis of a series of R-R intervals to classify HRV into ultra-low frequency, very low frequency, low frequency, high frequency, and total power. One method is not better than another as there is no gold standard (65). 

To evaluate HRV, several measures have been proposed. These measures are roughly classifiable into time domain analysis [5], frequency domain analysis, and nonlinear and fractal analysis [5]. Time domain analysis includes tone-entropy method [6]. Nonlinear and fractal analysis include de-trended fluctuation analysis (DFA) [7]. Frequency domain analysis is based on estimation of the power spectrum of RRI series. Depending on the estimation method of power spectrum, frequency domain analysis is classified into FFT method [8], AR model method [9], maximum entropy method [10], and complex de-modulation method [11]. Akselrod et al. [3] investigated the relation between spectral component of HRV and ANS activity [12]. They classified spectral component of HRV into a high-frequency (HF) band of 0.14-0.4 Hz, a low-frequency (LF) band of 0.04-0.14 Hz, a very-low-frequency (VLF) band of 0.003-0.04 Hz, and a ultra-low-frequency (ULF) band under 0.003 Hz. They further show that LF and HF components are affected from both sympathetic and parasympathetic nervous system activity and the parasympathetic nervous system activity, respectively [12]. Furthermore, VLF and ULF components are affected by the thermoregulation system [13],... 

A common technique for measuring noise is frequency domain analysis, such as plotting the acceleration power spectral density (PSD) of the seismic data over some time period. While tmies are readily distinguishable from broadband noise, nonstationary events such as pops have a broadband spectral characteristic (typically proportional to j) that can nuslead the troubleshooter. However, small pops may not be readily identified by examining the time-domain time-series data as they may have amplitudes too small to be distinguished from the background seismic activity. 

At the present time, two methods are in common use for the determination of time-resolved anisotropy parameters—the single-photon counting or pulse method 55-56 and the frequency-domain or phase fluorometric methods. 57 59) These are described elsewhere in this series. Recently, both of these techniques have undergone considerable development, and there are a number of commercially available instruments which include analysis software. The question of which technique would be better for the study of membranes is therefore difficult to answer. Certainly, however, the multifrequency phase instruments are now fully comparable with the time-domain instruments, a situation which was not the case only a few years ago. Time-resolved measurements are generally rather more difficult to perform and may take considerably longer than the steady-state anisotropy measurements, and this should be borne in mind when samples are unstable or if information of kinetics is required. It is therefore important to evaluate the need to take such measurements in studies of membranes. Steady-state instruments are of course much less expensive, and considerable information can be extracted, although polarization optics are not usually supplied as standard. 

However these techniques fall short in detecting soft layers below stiff layers (Kramer and Stewart, 2004). A relatively new technique that can be used to determine subsurface thickness and wave propagation velocities without necessity of borings is the Multi Channel Analysis of Surface Waves (MASW) test (Nazarian and Stokoe, 1983 Suto, 2007). In this test series of vertical receivers are place on the ground in line with an impact source. The output of the receivers are recorded and transformed into the frequency domain. The phase angles between the recoded responses are used to compute an apparent travel time of the surface waves. The surface wave phase velocity is... 

Given the pre-eminence of the transfer function and frequency-domain-based approaches in process and chemical engineering, these two approaches will be discussed in greatest detail in this chapter. Nevertheless, information about the state-space-based approach will also be considered. This chapter will present the basic, univariate approach to time series analysis, which will be extended in Chap. 6 to consider the multivariate case containing both stochastic and deterministic components in order to model complex processes for process control, economic analysis, and simulation development. 

---