Adaptive instantaneous frequency estimation: Techniques and algorithms

This thesis deals with the problem of the instantaneous frequency (IF) estimation of sinusoidal signals. This topic plays significant role in signal processing and communications. Depending on the type of the signal, two major approaches are considered. For IF estimation of single-tone or digitally-modulated sinusoidal signals (like frequency shift keying signals) the approach of digital phase-locked loops (DPLLs) is considered, and this is Part-I of this thesis. For FM signals the approach of time-frequency analysis is considered, and this is Part-II of the thesis. In part-I we have utilized sinusoidal DPLLs with non-uniform sampling scheme as this type is widely used in communication systems. The digital tanlock loop (DTL) has introduced significant advantages over other existing DPLLs. In the last 10 years many efforts have been made to improve DTL performance. However, this loop and all of its modifications utilizes Hilbert transformer (HT) to produce a signal-independent 90-degree phase-shifted version of the input signal. Hilbert transformer can be realized approximately using a finite impulse response (FIR) digital filter. This realization introduces further complexity in the loop in addition to approximations and frequency limitations on the input signal. We have tried to avoid practical difficulties associated with the conventional tanlock scheme while keeping its advantages. A time-delay is utilized in the tanlock scheme of DTL to produce a signal-dependent phase shift. This gave rise to the time-delay digital tanlock loop (TDTL). Fixed point theorems are used to analyze the behavior of the new loop. As such TDTL combines the two major approaches in DPLLs: the non-linear approach of sinusoidal DPLL based on fixed point analysis, and the linear tanlock approach based on the arctan phase detection. TDTL preserves the main advantages of the DTL despite its reduced structure. An application of TDTL in FSK demodulation is also considered. This idea of replacing HT by a time-delay may be of interest in other signal processing systems. Hence we have analyzed and compared the behaviors of the HT and the time-delay in the presence of additive Gaussian noise. Based on the above analysis, the behavior of the first and second-order TDTLs has been analyzed in additive Gaussian noise. Since DPLLs need time for locking, they are normally not efficient in tracking the continuously changing frequencies of non-stationary signals, i.e. signals with time-varying spectra. Nonstationary signals are of importance in synthetic and real life applications. An example is the frequency-modulated (FM) signals widely used in communication systems. Part-II of this thesis is dedicated for the IF estimation of non-stationary signals. For such signals the classical spectral techniques break down, due to the time-varying nature of their spectra, and more advanced techniques should be utilized. For the purpose of instantaneous frequency estimation of non-stationary signals there are two major approaches: parametric and non-parametric. We chose the non-parametric approach which is based on time-frequency analysis. This approach is computationally less expensive and more effective in dealing with multicomponent signals, which are the main aim of this part of the thesis. A time-frequency distribution (TFD) of a signal is a two-dimensional transformation of the signal to the time-frequency domain. Multicomponent signals can be identified by multiple energy peaks in the time-frequency domain. Many real life and synthetic signals are of multicomponent nature and there is little in the literature concerning IF estimation of such signals. This is why we have concentrated on multicomponent signals in Part-H. An adaptive algorithm for IF estimation using the quadratic time-frequency distributions has been analyzed. A class of time-frequency distributions that are more suitable for this purpose has been proposed. The kernels of this class are time-only or one-dimensional, rather than the time-lag (two-dimensional) kernels. Hence this class has been named as the T -class. If the parameters of these TFDs are properly chosen, they are more efficient than the existing fixed-kernel TFDs in terms of resolution (energy concentration around the IF) and artifacts reduction. The T-distributions has been used in the IF adaptive algorithm and proved to be efficient in tracking rapidly changing frequencies. They also enables direct amplitude estimation for the components of a multicomponent

Instantaneous phase of the autocorrelation and robustness to signal-dependent noise

The phase of an analytic signal constructed from the autocorrelation function of a signal contains significant information about the shape of the signal. Using Bedrosian's (1963) theorem for the Hilbert transform it is proved that this phase is robust to multiplicative noise if the signal is baseband and the spectra of the signal and the noise do not overlap. Higher-order spectral features are interpreted in this context and shown to extract nonlinear phase information while retaining robustness. The significance of the result is that prior knowledge of the spectra is not required.

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.

Development of a new signal processing diagnostic tool for vibration signals acquired in transient conditions

The diagnostics of mechanical components operating in transient conditions is still an open issue, in both research and industrial field. Indeed, the signal processing techniques developed to analyse stationary data are not applicable or are affected by a loss of effectiveness when applied to signal acquired in transient conditions. In this paper, a suitable and original signal processing tool (named EEMED), which can be used for mechanical component diagnostics in whatever operating condition and noise level, is developed exploiting some data-adaptive techniques such as Empirical Mode Decomposition (EMD), Minimum Entropy Deconvolution (MED) and the analytical approach of the Hilbert transform. The proposed tool is able to supply diagnostic information on the basis of experimental vibrations measured in transient conditions. The tool has been originally developed in order to detect localized faults on bearings installed in high speed train traction equipments and it is more effective to detect a fault in non-stationary conditions than signal processing tools based on spectral kurtosis or envelope analysis, which represent until now the landmark for bearings diagnostics.

The combination of empirical mode decomposition and minimum entropy deconvolution for roller bearing diagnostics in non-stationary operation

Diagnostics is based on the characterization of mechanical system condition and allows early detection of a possible fault. Signal processing is an approach widely used in diagnostics, since it allows directly characterizing the state of the system. Several types of advanced signal processing techniques have been proposed in the last decades and added to more conventional ones. Seldom, these techniques are able to consider non-stationary operations. Diagnostics of roller bearings is not an exception of this framework. In this paper, a new vibration signal processing tool, able to perform roller bearing diagnostics in whatever working condition and noise level, is developed on the basis of two data-adaptive techniques as Empirical Mode Decomposition (EMD), Minimum Entropy Deconvolution (MED), coupled by means of the mathematics related to the Hilbert transform. The effectiveness of the new signal processing tool is proven by means of experimental data measured in a test-rig that employs high power industrial size components.

Signal Processing Diagnostic Tool for Rolling Element Bearings Using EMD and MED

The signal processing techniques developed for the diagnostics of mechanical components operating in stationary conditions are often not applicable or are affected by a loss of effectiveness when applied to signals measured in transient conditions. In this chapter, an original signal processing tool is developed exploiting some data-adaptive techniques such as Empirical Mode Decomposition, Minimum Entropy Deconvolution and the analytical approach of the Hilbert transform. The tool has been developed to detect localized faults on bearings of traction systems of high speed trains and it is more effective to detect a fault in non-stationary conditions than signal processing tools based on envelope analysis or spectral kurtosis, which represent until now the landmark for bearings diagnostics.

Rapid quantification of methamphetamine: using Attenuated Total Reflectance Fourier Transform Infrared Spectroscopy (ATR-FTIR) and Chemometrics

In Australia and increasingly worldwide, methamphetamine is one of the most commonly seized drugs analysed by forensic chemists. The current well-established GC/MS methods used to identify and quantify methamphetamine are lengthy, expensive processes, but often rapid analysis is requested by undercover police leading to an interest in developing this new analytical technique. Ninety six illicit drug seizures containing methamphetamine (0.1% - 78.6%) were analysed using Fourier Transform Infrared Spectroscopy with an Attenuated Total Reflectance attachment and Chemometrics. Two Partial Least Squares models were developed, one using the principal Infrared Spectroscopy peaks of methamphetamine and the other a Hierarchical Partial Least Squares model. Both of these models were refined to choose the variables that were most closely associated with the methamphetamine % vector. Both of the models were excellent, with the principal peaks in the Partial Least Squares model having Root Mean Square Error of Prediction 3.8, R2 0.9779 and lower limit of quantification 7% methamphetamine. The Hierarchical Partial Least Squares model had lower limit of quantification 0.3% methamphetamine, Root Mean Square Error of Prediction 5.2 and R2 0.9637. Such models offer rapid and effective methods for screening illicit drug samples to determine the percentage of methamphetamine they contain.

Evidence for the adsorption of molecules at special sites located at copper/zinc oxide interfaces. Part 2. -- A fourier-transform infrared spectroscopy study of methanol adsorption on reduced and oxidised Cu/ZnO/SiO2 catalysts

FTIR spectra are reported of methanol adsorbed at 295 K on ZnO/SiO 2, on reduced Cu/ZnO/SiO2 and on Cu/ZnO/SiO2 which had been preoxidised by exposure to nitrous oxide. Methanol on ZnO/SiO2 gave methoxy species on ZnO and SiO, in addition to both strongly and weakly physisorbed methanol on SiO2. The corresponding adsorption of methanol on reduced Cu/ZnO/SiO2 also gave methoxy species on Cu and a small amount of bridging formate. Reaction of methanol with a reoxidised Cu/ZnO/SiO2 catalyst resulted in an enhanced quantity of methoxy species on Cu. Heating adsorbed species on Cu/ZnO/SiO2 at 393 K led to the loss of methoxy groups on Cu and the concomitant formation of formate species on both ZnO and Cu. The comparable reaction on a reoxidised Cu/ZnO/SiO2 catalyst gave an increased amount of formate species on ZnO and this correlated with an increased quantity of methoxy groups lost from Cu. An explanation is given in terms of adsorption of formate and formaldehyde species at special sites located at the copper/zinc oxide interface.

Evidence for the adsorption of molecules at special sites located at copper/zinc oxide interfaces: Part 1. -- A Fourier-transform infrared study of formic acid and formaldehyde adsorption on reduced and oxidised Cu/ZnO/SiO2 catalysts

Fourier-transform infrared (FTIR) spectra are reported of formic acid and formaldehyde on ZnO/SiO2, reduced Cu/ZnO/SiO2 and reoxidised Cu/ZnO/SiO2 catalyst. Formic acid adsorption on ZnO/SiO2 produced mainly bidentate zinc formate species with a lesser quantity of unidentate zinc formate. Formic acid on reduced Cu/ZnO/SiO2 catalyst resulted not only in the formation of bridging copper formate structures but also in an enhanced amount of formate relative to that for ZnO/SiO2 catalyst. Formic acid on reoxidised Cu/ZnO/SiO2 gave unidentate formate species on copper in addition to zinc formate moieties. The interaction of formaldehyde with ZnO/SiO2 catalyst resulted in the formation of zinc formate species. The same reaction on reduced Cu/ZnO/SiO2 catalyst gave bridging formate on copper and a remarkable increase in the quantity of formate species associated with the zinc oxide. Adsorption of formaldehyde on a reoxidised Cu/ZnO/SiO2 catalyst produced bridging copper formate and again an apparent increase in the concentration of zinc formate species. An explanation in terms of the adsorption of molecules at special sites located at the interface between copper and zinc oxide is given.

A combined temperature-programmed reaction spectroscopy and Fourier-transform infrared spectroscopy study of CO2/H2 and CO/CO2/H2 interactions with model ZnO/SiO2, Cu/SiO2 and Cu/ZnO/SiO2 methanol-synthesis catalysts

The reaction of CO2 and H2 with ZnO/SiO2 catalyst at 295 K gave predominantly hydrogencarbonate on zinc oxide and a small quantity of formate was evolved after heating at 393 K. Elevation of the reaction temperature to 503 K enhanced the rate of formation of zinc formate species. Significantly these formate species decomposed at 573 K almost entirely to CO2 and H2. Even after exposure of CO2-H2 or CO-CO2-H2 mixtures to highly defected ZnO/SiO2 catalyst, the formate species produced still decomposed to give CO2 and H2. It was concluded that carboxylate species which were formed at oxygen anion vacancies on polar Zn planes were not significantly hydrogenated to formate. Consequently it was proposed that the non-polar planes on zinc oxide contained sites which were specific for the synthesis of methanol. The interaction of CO2 and H2 with reduced Cu/ZnO/SiO2 catalyst at 393 K gave copper formate species in addition to substantial quantities of formate created at interfacial sites between copper and zinc oxide. It was deduced that interfacial formate species were produced from the hydrogenation of interfacial bidentate carbonate structures. The relevance of interfacial formate species in the methanol synthesis reaction is discussed. Experiments concerning the reaction of CO2-H2 with physical mixtures of Cu/SiO2 and ZnO/SiO2 gave results which were simply characteristic of the individual components. By careful consideration of previous data a detailed proposal regarding the role of spillover hydrogen is outlined. Admission of CO to a gaseous CO2-H2 feedstock resulted in a considerably diminished amount of formate species on copper. This was ascribed to a combination of over-reduction of the surface and site-blockage.