Adaptive instantaneous frequency estimation: Techniques and algorithms
Hussain, Zahir M (2002) Adaptive instantaneous frequency estimation: Techniques and algorithms. PhD thesis, Queensland University of Technology.

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Abstract
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 singletone or digitallymodulated sinusoidal signals (like frequency shift keying signals) the approach of digital phaselocked loops (DPLLs) is considered, and this is PartI of this thesis. For FM signals the approach of timefrequency analysis is considered, and this is PartII of the thesis.
In partI we have utilized sinusoidal DPLLs with nonuniform 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 signalindependent 90degree phaseshifted 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 timedelay is utilized in the tanlock scheme of DTL to produce a signaldependent phase shift. This gave rise to the timedelay 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 nonlinear 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 timedelay may be of interest in other signal processing systems. Hence we have analyzed and compared the behaviors of the HT and the timedelay in the presence of additive Gaussian noise.
Based on the above analysis, the behavior of the first and secondorder 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 nonstationary signals, i.e. signals with timevarying spectra. Nonstationary signals are of importance in synthetic and real life applications. An example is the frequencymodulated (FM) signals widely used in communication systems. PartII of this thesis is dedicated for the IF estimation of nonstationary signals. For such signals the classical spectral techniques break down, due to the timevarying nature of their spectra, and more advanced techniques should be utilized.
For the purpose of instantaneous frequency estimation of nonstationary signals there are two major approaches: parametric and nonparametric. We chose the nonparametric approach which is based on timefrequency 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 timefrequency distribution (TFD) of a signal is a twodimensional transformation of the signal to the timefrequency domain. Multicomponent signals can be identified by multiple energy peaks in the timefrequency 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 PartH.
An adaptive algorithm for IF estimation using the quadratic timefrequency distributions has been analyzed. A class of timefrequency distributions that are more suitable for this purpose has been proposed. The kernels of this class are timeonly or onedimensional, rather than the timelag (twodimensional) 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 fixedkernel TFDs in terms of resolution (energy concentration around the IF) and artifacts reduction. The Tdistributions 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
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ID Code:  36137 

Item Type:  QUT Thesis (PhD) 
Supervisor:  Boashash, Boualem, Mesbah, Mostefa, & Senadji, Bouchra 
Additional Information:  Presented to the Signal Processing Research Centre, Queensland University of Technology. 
Keywords:  Signal processing, Time series analysis, Frequency spectra, instantaneous frequency, stationary signals, nonstationary signals, communication systems, multicomponent signals, frequency modulated (FM) signals, frequency shift keying (FSK) signals, sinusoidal signals, analytic signals, digital phaselocked loops, Hilbert transform, timedelay, phase shifter, difference equation, sinusoidal digital phase locked loops, digital tanlock loop, tanlock, lock range, independent locking, digital filters, nonuniform sampling, additive Gaussian noise, signaltonoiseratio (SNR), locking speed, phase error detector, CramerRao bounds, timefrequency analysis, ambiguity function, timefrequency distribution (TFD), the quadratic class, resolution, crossterms, Fourier transform, estimation, amplitude estimation, instantaneous frequency estimation, mean square error, simulation, algorithms, adaptive algorithms, adaptive estimation, bias, variance, asymptotic analysis, thesis, doctoral 
Institution:  Queensland University of Technology 
Copyright Owner:  Copyright Zahir M Hussain 
Deposited On:  22 Sep 2010 13:04 
Last Modified:  07 Jan 2016 06:46 
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