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

Theory of radar imaging using time-frequency distribution

The concept of radar was developed for the estimation of the distance (range) and velocity of a target from a receiver. The distance measurement is obtained by measuring the time taken for the transmitted signal to propagate to the target and return to the receiver. The target's velocity is determined by measuring the Doppler induced frequency shift of the returned signal caused by the rate of change of the time- delay from the target. As researchers further developed conventional radar systems it become apparent that additional information was contained in the backscattered signal and that this information could in fact be used to describe the shape of the target itself. It is due to the fact that a target can be considered to be a collection of individual point scatterers, each of which has its own velocity and time- delay. DelayDoppler parameter estimation of each of these point scatterers thus corresponds to a mapping of the target's range and cross range, thus producing an image of the target. Much research has been done in this area since the early radar imaging work of the 1960s. At present there are two main categories into which radar imaging falls. The first of these is related to the case where the backscattered signal is considered to be deterministic. The second is related to the case where the backscattered signal is of a stochastic nature. In both cases the information which describes the target's scattering function is extracted by the use of the ambiguity function, a function which correlates the backscattered signal in time and frequency with the transmitted signal. In practical situations, it is often necessary to have the transmitter and the receiver of the radar system sited at different locations. The problem in these situations is 'that a reference signal must then be present in order to calculate the ambiguity function. This causes an additional problem in that detailed phase information about the transmitted signal is then required at the receiver. It is this latter problem which has led to the investigation of radar imaging using time- frequency distributions. As will be shown in this thesis, the phase information about the transmitted signal can be extracted from the backscattered signal using time- frequency distributions. The principle aim of this thesis was in the development, and subsequent discussion into the theory of radar imaging, using time- frequency distributions. Consideration is first given to the case where the target is diffuse, ie. where the backscattered signal has temporal stationarity and a spatially white power spectral density. The complementary situation is also investigated, ie. where the target is no longer diffuse, but some degree of correlation exists between the time- frequency points. Computer simulations are presented to demonstrate the concepts and theories developed in the thesis. For the proposed radar system to be practically realisable, both the time- frequency distributions and the associated algorithms developed must be able to be implemented in a timely manner. For this reason an optical architecture is proposed. This architecture is specifically designed to obtain the required time and frequency resolution when using laser radar imaging. The complex light amplitude distributions produced by this architecture have been computer simulated using an optical compiler.

A life jacket with holes- : a case study of 'temporary engagement' : a strategy used by Education Queensland to employ beginning secondary teachers

This research investigated the impact of Education Queensland's employment policy and practices for beginning secondary teachers appointed on temporary engagement. The context was the public secondary school sector within the state of Queensland, Australia. The study was set within a context of the changing nature of work from full-time permanent employment towards casual, fixed-term contracts, temporary and part-time employment, a trend reflected in the employment patterns for teachers within Australia. Two broad categories of literature relating to the research problem of this thesis were reviewed, namely the beginning teacher and permanency or tenure. The focus in the research literature on beginning teachers was the professional experiences of teachers within the classroom and school. There was a paucity of research that considered the working and industrial conditions of temporary employment for beginning teachers or the personal and professional implications of this form of employment. The review of the context and literature was conceptualised as a Beginning Temporary Teacher Theoretical Framework which served to inform the study. Using a qualitative case study methodology, the research techniques employed for the thesis were semi-structured interview and document analysis. A simultaneously conducted research project in which the researcher participated entitled 'Winning the Lottery? Beginning Teachers on Temporary Engagement' foregrounded this thesis in terms of refining the research question, contributing to the literature and in the selection of the participants. For this case study the perspectives of four distinct yet inter-related categories of professionals were sought. These included four beginning secondary teachers, three school administrators, a Senior Personnel Officer with Education Queensland, and a representative from the Queensland Teachers' Union. The research findings indicated that none of the beginning teachers or other professionals viewed starting a career in teaching on temporary engagement as the ideal. The negative features identified were the differential treatment received and the high level of uncertainty associated with temporary employment. Differential treatment tended to indicate 'less' entitlements, in terms of access to induction and professional development, recreational and sick leave, acceptance by and expectations of other colleagues, and avenues of redress in grievance cases. Moreover, interviews indicated a high level of uncertainty in terms of starting within the teaching profession, commencing at a new school, and a regular income. In addition, frequent changes in schools and/or cohorts of students exacerbated levels of uncertainty. The beginning teachers reported significantly decreased motivation, self-esteem and sense of belonging, and increased stress levels. There was an even more marked negative impact on those beginning teachers who had experienced a higher number of temporary engagements and schools in their first year of teaching. Conversely, strong staff support and a reasonable length of time in the one school improved the quality of the beginning teachers' experiences. The overall impact of being on temporary engagement resulted in delayed permanent position appointments, decreased commitment to particular schools and to Education Queensland as the employing authority, and for two of the beginning teachers, it produced a desire to seek alternative employment. The implementation of Education Queensland's policies relating to working conditions and entitlements for these temporary beginning teachers at the school level was revealed to be less than satisfactory. There was a tendency towards 'just-in- time' management of the beginning teacher on temporary engagement. The beginning teachers received 'less-than-messages' about access to and use of departmental documentation, support through induction and professional development, and their transition from temporary to permanent employment. To ensure a more systematic, supportive and inclusive process for managing the temporary beginning teacher, a conceptual framework entitled 'Continuums of Tension' was developed. The four continuums included permanent employment - temporary employment; system perspective - individual perspective; teaching as a profession - teaching as a job; and the permanent beginning teacher - university graduate. The general principles of the human resource policies of Education Queensland were based on a commitment to permanent employment, a system's perspective, viewing teaching as a profession and a homogeneous group of permanent beginning teachers. Contrasting with this, the beginning teacher on temporary engagement tended to operate from the position of temporary employment and a perspective that was individually based. Their priorities therefore included the 'occupational' aspects of being a temporary teacher striving to become permanent. Thus there existed a tension or contradiction between the general principles of human resource policies within Education Queensland and the employment experiences of beginning teachers on temporary engagement. The study proposed three actions for resolution to address the aforementioned tensions. The actions included: (a) the effective provision and targeted communication of information; (b) support, induction and professional development; and (c) a coordinated approach between Education Queensland, Queensland Teachers' Union, the Universities and the beginning teacher. These actions are fm1her refined to include: (a) an induction kit to suppm1 the individual through the pre-employment to permanent employee phases, (b) an extrapolation of the roles and responsibilities of Education Queensland personnel charged with supporting the beginning temporary teacher, and (c) a series of recommendations to effect a coordinated approach amongst the key stakeholders. The theoretical and conceptual frameworks have provided a means of addressing the identified needs of the beginning teacher on temporary engagement. As such, this study has contributed to the research literature on teacher employment and professionalism and aims to provide a beginning temporary teacher with managed professional and occupational support.