A Review of the Frequency Estimation and Tracking Problems

This report presents a concise review of some frequency estimation and frequency tracking problems. In particular, the report focusses on aspects of these problems which have been addressed by members of the Frequency Tracking and Estimation project of the Centre for Robust and Adaptive Systems. The report is divided into four parts: problem specification and discussion, associated problems, frequency estimation algorithms and frequency tracking algorithms. Part I begins with a definition of the various frequency estimation and tracking problems. Practical examples of where each problem may arise are given. A comparison is made between the frequency estimation and tracking problems. In Part II, block frequency estimation algorithms, fast block frequency estimation algorithms and notch filtering techniques for frequency estimation are dealt with. Frequency tracking algorithms are examined in Part III. Part IV of this report examines various problems associated with frequency estimation. Associated problems include Cramer-Rao lower bounds, theoretical algorithm performance, frequency resolution, use of the analytic signal and model order selection

On Kalman smoothing with random packet loss

The abstract is included in the text

Statistical Spectral Parameter Estimation of Acoustic Signals with Applications to Byzantine Music

Digitized acoustical signals of Byzantine music performed by Iakovos Nafpliotis are used to extract the fundamental frequency of each note of the diatonic scale. These empirical results are then contrasted to the theoretical suggestions and previous empirical findings. Several parametric and non-parametric spectral parameter estimation methods are implemented. These include: (1) Phase vocoder method, (2) McAulay-Quatieri method, (3) Levinson-Durbin algorithm,(4) YIN, (5) Quinn & Fernandes Estimator, (6) Pisarenko Frequency Estimator, (7) MUltiple SIgnal Characterization (MUSIC) algorithm, (8) Periodogram method, (9) Quinn & Fernandes Filtered Periodogram, (10) Rife & Vincent Estimator, and (11) the Fourier transform. Algorithm performance was very precise. The psychophysical aspect of human pitch discrimination is explored. The results of eight (8) psychoacoustical experiments were used to determine the aural just noticeable difference (jnd) in pitch and deduce patterns utilized to customize acceptable performable pitch deviation to the application at hand. These customizations [Acceptable Performance Difference (a new measure of frequency differential acceptability), Perceptual Confidence Intervals (a new concept of confidence intervals based on psychophysical experiment rather than statistics of performance data), and one based purely on music-theoretical asymphony] are proposed, discussed, and used in interpretation of results. The results suggest that Nafpliotis\u27 intervals are closer to just intonation than Byzantine theory (with minor exceptions), something not generally found in Thrasivoulos Stanitsas\u27 data. Nafpliotis\u27 perfect fifth is identical to the just intonation, even though he overstretches his octaveby fifteen (15)cents. His perfect fourth is also more just, as opposed to Stanitsas\u27 fourth which is directionally opposite. Stanitsas\u27 tendency to exaggerate the major third interval A4-F4 is still seen in Nafpliotis, but curbed. This is the only noteworthy departure from just intonation, with Nafpliotis being exactly Chrysanthian (the most exaggerated theoretical suggestion of all) and Stanitsas overstretching it even more than Nafpliotis and Chrysanth. Nafpliotis ascends in the second tetrachord more robustly diatonically than Stanitsas. The results are reported and interpreted within the framework of Acceptable Performance Differences

Frequency synchronization techniques in wireless communication

In this thesis various iterative channel estimation and data detection techniques for time-varying frequency selective channels with multiple frequency offsets are proposed. Firstly, a maximum likelihood approach for the estimation of complex multipath gains (MGs) and real Doppler shifts (DSs) for a single input "single output (SISO) frequency selective channel is proposed. In a time di vision multiple access (TDMA) system, for example the third-generation global system, or mobile GSM communications, the pilot symbols are generally inadequate to provide enough resolution to estimate frequency offsets. Therefore, our approach is to use the pilot sequence for the estimation and equalization of the channel without consideration to frequency offsets, and then to use the soft estimates of the transmitted signal as a long pilot sequence to determine iteratively the multiple frequency offsets and refine the channel estimates. Inter-symbol interference (ISI) is removed with a linear structure turbo equalizer where the filter coefficients are chosen based on the minimum mean square error (MMSE) criterion. The detection performance is verified using the bit error rate (BER) curves and the frequency offset estimation performance through comparison with appropriate Cramer-Rao lower bounds. This work is then extended for a multi-user transmission system where the channel is modelled as a multi input multi output (MIMO) TDMA system. For the iterative channel estimation, the MIMO frequency selective channel is decoupled into multiple SISO flat fading sub-channels through appropriately cancelling both inter-symbol-interference (ISI) and inter-user-interference (IUI) from the received signal. The refined channel estimates and the corresponding frequency offset estimates are then obtained for each resolved MIMO multipath tap. Simulation results confirm a superior BER and estimation performance. Finally, these iterative equalization and estimation techniques are ex tended to orthogonal frequency division multiplexing (OFDM) based SISO and MIMO systems. For OFDM, the equalization is performed in two stages. In the first stage, the channel and the frequency offsets are estimated in the time domain, while in the second stage, the transmitted symbols are estimated in the frequency domain and the mean values and the variances of the symbols are determined in the frequency domain. These two procedures interact in an iterative manner, exchanging information between the time and frequency domains. Simulation studies show that the proposed iterative scheme has the ability to track frequency off sets and provide a superior BER performance as compared to a scheme that does not track frequency offsets.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Frequency synchronization techniques in wireless communication

In this thesis various iterative channel estimation and data detection techniques for time-varying frequency selective channels with multiple frequency offsets are proposed. Firstly, a maximum likelihood approach for the estimation of complex multipath gains (MGs) and real Doppler shifts (DSs) for a single input "single output (SISO) frequency selective channel is proposed. In a time di vision multiple access (TDMA) system, for example the third-generation global system, or mobile GSM communications, the pilot symbols are generally inadequate to provide enough resolution to estimate frequency offsets. Therefore, our approach is to use the pilot sequence for the estimation and equalization of the channel without consideration to frequency offsets, and then to use the soft estimates of the transmitted signal as a long pilot sequence to determine iteratively the multiple frequency offsets and refine the channel estimates. Inter-symbol interference (ISI) is removed with a linear structure turbo equalizer where the filter coefficients are chosen based on the minimum mean square error (MMSE) criterion. The detection performance is verified using the bit error rate (BER) curves and the frequency offset estimation performance through comparison with appropriate Cramer-Rao lower bounds. This work is then extended for a multi-user transmission system where the channel is modelled as a multi input multi output (MIMO) TDMA system. For the iterative channel estimation, the MIMO frequency selective channel is decoupled into multiple SISO flat fading sub-channels through appropriately cancelling both inter-symbol-interference (ISI) and inter-user-interference (IUI) from the received signal. The refined channel estimates and the corresponding frequency offset estimates are then obtained for each resolved MIMO multipath tap. Simulation results confirm a superior BER and estimation performance. Finally, these iterative equalization and estimation techniques are ex tended to orthogonal frequency division multiplexing (OFDM) based SISO and MIMO systems. For OFDM, the equalization is performed in two stages. In the first stage, the channel and the frequency offsets are estimated in the time domain, while in the second stage, the transmitted symbols are estimated in the frequency domain and the mean values and the variances of the symbols are determined in the frequency domain. These two procedures interact in an iterative manner, exchanging information between the time and frequency domains. Simulation studies show that the proposed iterative scheme has the ability to track frequency off sets and provide a superior BER performance as compared to a scheme that does not track frequency offsets

Autoregressive Spectral Estimation in Noise with Application to Speech Analysis

Electrical Engineerin

Compressive Sensing Applications in Measurement: Theoretical issues, algorithm characterization and implementation

At its core, signal acquisition is concerned with efficient algorithms and protocols capable to capture and encode the signal information content. For over five decades, the indisputable theoretical benchmark has been represented by the wellknown Shannon’s sampling theorem, and the corresponding notion of information has been indissolubly related to signal spectral bandwidth. The contemporary society is founded on almost instantaneous exchange of information, which is mainly conveyed in a digital format. Accordingly, modern communication devices are expected to cope with huge amounts of data, in a typical sequence of steps which comprise acquisition, processing and storage. Despite the continual technological progress, the conventional acquisition protocol has come under mounting pressure and requires a computational effort not related to the actual signal information content. In recent years, a novel sensing paradigm, also known as Compressive Sensing, briefly CS, is quickly spreading among several branches of Information Theory. It relies on two main principles: signal sparsity and incoherent sampling, and employs them to acquire the signal directly in a condensed form. The sampling rate is related to signal information rate, rather than to signal spectral bandwidth. Given a sparse signal, its information content can be recovered even fromwhat could appear to be an incomplete set of measurements, at the expense of a greater computational effort at reconstruction stage. My Ph.D. thesis builds on the field of Compressive Sensing and illustrates how sparsity and incoherence properties can be exploited to design efficient sensing strategies, or to intimately understand the sources of uncertainty that affect measurements. The research activity has dealtwith both theoretical and practical issues, inferred frommeasurement application contexts, ranging fromradio frequency communications to synchrophasor estimation and neurological activity investigation. The thesis is organised in four chapters whose key contributions include: • definition of a general mathematical model for sparse signal acquisition systems, with particular focus on sparsity and incoherence implications; • characterization of the main algorithmic families for recovering sparse signals from reduced set of measurements, with particular focus on the impact of additive noise; • implementation and experimental validation of a CS-based algorithmfor providing accurate preliminary information and suitably preprocessed data for a vector signal analyser or a cognitive radio application; • design and characterization of a CS-based super-resolution technique for spectral analysis in the discrete Fourier transform(DFT) domain; • definition of an overcomplete dictionary which explicitly account for spectral leakage effect; • insight into the so-called off-the-grid estimation approach, by properly combining CS-based super-resolution and DFT coefficients polar interpolation; • exploration and analysis of sparsity implications in quasi-stationary operative conditions, emphasizing the importance of time-varying sparse signal models; • definition of an enhanced spectral content model for spectral analysis applications in dynamic conditions by means of Taylor-Fourier transform (TFT) approaches