# Adaptive instantaneous frequency estimation: Techniques and algorithms

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

## 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 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

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ID Code: | 36137 |
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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, non-stationary signals, communication systems, multicomponent signals, frequency modulated (FM) signals, frequency shift keying (FSK) signals, sinusoidal signals, analytic signals, digital phase-locked loops, Hilbert transform, time-delay, phase shifter, difference equation, sinusoidal digital phase locked loops, digital tanlock loop, tanlock, lock range, independent locking, digital filters, nonuniform sampling, additive Gaussian noise, signal-to-noise-ratio (SNR), locking speed, phase error detector, Cramer-Rao bounds, time-frequency analysis, ambiguity function, time-frequency distribution (TFD), the quadratic class, resolution, cross-terms, 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: | 22 Jun 2017 14:42 |

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