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

The mechanism of maturation of insulin-like growth factor-1

This study, to elucidate the role of des(1-3)IGF-I in the maturation of IGF-I,used two strategies. The first was to detect the presence of enzymes in tissues, which would act on IGF-I to produce des(1-3)IGF-I, and the second was to detect the potential products of such enzymic activity, namely Gly-Pro-Glu(GPE), Gly-Pro(GP) and des(l- 3)IGF-I. No neutral tripeptidyl peptidase (TPP II), which would release the tripeptide GPE from IGF-I, was detected in brain, urine nor in red or white blood cells. The TPPlike activity which was detected, was attributed to a combined action of a dipeptidyl peptidase (DPP N) and an aminopeptidase (AP A). A true TPP II was, however, detected in platelets. Two purified TPP II enzymes were investigated but they did not release GPE from IGF-I under a variety of conditions. Consequently, TPP II seemed unlikely to participate in the formation of des(1-3)IGF-I. In contrast, an acidic tripeptidyl peptidase activity (TPP I) was detected in brain and colostrum, the former with a pH optimum of 4.5 and the latter 3.8. It seems likely that such an enzyme would participate in the formation of des( 1-3 )IGF-I in these tissues in vitro, ie. that des(1-3)IGF-I may have been produced as an artifact in the isolation of IGF-I from brain and colostrum in acidic conditions. This contrasts with suggestions of an in vivo role for des(1-3)IGF-I, as reported by others. The activity of a dipeptidyl peptidase N (DPP N) from urine, which should release the dipeptide GP from IGF-I, was assessed under a variety of conditions and with a variety of additives and potential enzyme stimulants, but there was no release of GP. The DPP N also exhibited a transferase activity with synthetic substrates in the presence of dipeptides, at lower concentrations than previously reported for other acceptors or other proteolytic enzymes. In addition, a low concentration of a product,possibly the tetrapeptide Gly-Pro-Gly-Leu, was detected with the action of the enzyme on IGF-I in the presence of the dipeptide Gly-Leu. As part of attempts to detect tissue production of des(1-3)IGF-I, a monoclonal antibody (MAb ), directed towards the GPE- end ofiGF-I was produced by immunisation with a 10-mer covalently attached to a carrier protein. By the use of indirect ELISA and inhibitor studies, the MAb was shown to selectively recognise peptides with anNterminal GPE- sequence, and applied to the indirect detection of des(1-3)IGF-I. The concentration of GPE in brain, measured by mass spectrometry ( MS), was low, and the concentration of total IGF-I (measured by ELISA with a commercial polyclonal antibody [P Ab]) was 40 times higher at 50 nmol/kg. This also, was not consistent with the action of a tripeptidyl peptidase in brain that converted all IGF-I to des(1-3)IGF-I plus GPE. Contrasting ELISA results, using the MAb prepared in this study, suggest an even higher concentration of intact IGF-I of 150 nmollkg. This would argue against the presence of any des( 1-3 )IGF-I in brain, but in turn, this indicates either the presence of other substances containing a GPE amino-terminus or other cross reacting epitope. Although the results of the specificity studies reported in Chapter 5 would make this latter possibility seem unlikely, it cannot be completely excluded. No GP was detected in brain by MS. No GPE was detected in colostrum by capillary electrophoresis (CE) but the interference from extraneous substances reduced the detectability of GPE by CE and this approach would require further, prior, purification and concentration steps. A molecule, with a migration time equal to that of the peptide GP, was detected in colostrum by CE, but the concentration (~ 10 11mo/L) was much higher than the IGF-I concentration measured by radio-immunoassay using a PAb (80 nmol/L) or using a Mab (300-400 nmolL). A DPP IV enzyme was detected in colostrum and this could account for the GP, derived from substrates other than IGF-1. Based on the differential results of the two antibody assays, there was no indication of the presence of des(1-3)IGF-I in brain or colostrum. In the absence of any enzyme activity directed towards the amino terminus of IGF-I and the absence any potential products, IGF-I, therefore, does not appear to "mature" via des(1-3)IGF-I in the brain, nor in the neutral colostrum. In spite of these results which indicate the absence of an enzymic attack on IGF-I and the absence of the expected products in tissues, the possibility that the conversion of IGF-I may occur in neutral conditions in limited amounts, cannot be ruled out. It remains possible that in the extracellular environment of the membrane, a complex interaction of IGF-I, binding protein, aminopeptidase(s) and receptor, produces des(1- 3)IGF-I as a transient product which is bound to the receptor and internalised.