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

Removal of the phase noise in the autocorrelation estimates with data windowing

13th European Signal Processing Conference, EUSIPCO 2005; Antalya; Turkey; 4 September 2005 through 8 September 2005The sinusoidal frequency estimation from short data records based on Toeplitz autocorrelation (AC) matrix estimates suffer from phase noise. This effect becomes prominent especially when additive noise vanishes becoming a nuisance, that is at high signal-to-noise ratios (SNR). Based on both analytic derivation of the AC lag terms and simulation experiments, we show that data windowing can mitigate the limitations caused by the phase noise. Thus with proper windowing, the variance of the frequency estimate is no more limited by phase noise, but it continues to decrease linearly with the SNR. The cases of the Pisarenko frequency estimator and of MUSIC, both for the single sinusoid case, are analyzed in detail

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 Estimation Of Single-Tone Sinusoids Under Additive And Phase Noise

We investigate the performance of main frequency estimation methods for a single-component complex sinusoid under complex additive white Gaussian noise (AWGN) as well as phase noise (PN). Two methods are under test: Maximum Likelihood (ML) method using Fast Fourier Transform (FFT), and the autocorrelation method (Corr). Simulation results showed that FFT-method has superior performance as compared to the Corr-method in the presence of additive white Gaussian noise (affecting the amplitude) and phase noise, with almost 20dB difference

On Kalman smoothing with random packet loss

The abstract is included in the text

An evaluation of the broadband direction finding capabilities of array signal processing techniques

The objective of this study was to determine and compare the direction finding capabilities of high resolution spectral analysis techniques applied to the signals from an antenna array. The maintenance of acceptable resolution over a broad operating frequency range was of particular concern. The comparison was accomplished by computer simulation of the performance of a linear array of eleven isotropic elements, spaced 15 cm apart, over the frequency range from 100 MHz to 1.0 GHz;The two-signal resolution of three linear prediction based algorithms was compared. The variation in performance with signal-to-noise ratio, frequency, and center angle of arrival was also evaluated;An algorithm due to Tufts and Kumaresan which reduces the effects of noise by replacing the noisy signal correlation matrix by a smoothed, least-squares fit to it gave the best performance at the cost of the highest computational complexity. A special case of this method which is easy to compute exhibited blind angles, where performance was severely degraded in spite of wide spacing of the sources;The ratio of the physical length of the array to the length of the modulation envelope set up by the interference of the two incoming signals was found to be a constant at the point of resolution. This led to an expression for the two-signal resolution as a function of look angle, array length, frequency, and this algorithm dependent constant

Contribution of an interharmonic component to the sine- wave parameters estimators returned by the interpolated Discrete Fourier transform algorithm

This article investigates the contribution of a small-amplitude interharmonic component to the sine-wave parameter estimators returned by the classical interpolated discrete Fourier transform (IpDFT) algorithm. The analytical expressions for the frequency, amplitude, and phase estimation errors are derived herein by considering the IpDFT algorithm based on the maximum sidelobe decay (MSD) windows and by assuming the interharmonic frequency located at least one bin apart the unknown sine-wave frequency. The derived expressions allow us to analyse the impact of an interharmonic on the accuracies of the IpDFT frequency, amplitude, and phase estimators. The accuracies of the derived expressions are verified by means of both computer simulations and experimental results.</p

Induction machine faults detection using stator current parametric spectral estimation

International audienceCurrent spectrum analysis is a proven technique for fault diagnosis in electrical machines. Current spectral estimation is usually performed using classical techniques such as periodogram (FFT) or its extensions. However, these techniques have several drawbacks since their frequency resolution is limited and additional post-processing algorithms are required to extract a relevant fault detection criterion. Therefore, this paper proposes a new parametric spectral estimator that fully exploits the faults sensitive frequencies. The proposed technique is based on the maximum likelihood estimator (MLE) and offers high-resolution capabilities. Based on this approach, a fault criterion is derived for detecting several fault types.The proposed technique is assessed using simulation signals, issued from a coupled electromagnetic circuits approach-based simulation tool for mechanical unbalance and electrical asymmetry faults detection. It is afterward validated using experiments on a 0.75-kW induction machine test bed for the particular case of bearing faults