Bit synchronization algorithms based on signal zero-crossing analysis are investigated. Their performance is compared to conventional maximum-likelihood-type techniques for symbol timing recovery. The zero-crossing bit synchronizers are shown to be superior for bandlimited pulses such as raised cosine and double-jump frequency rolloff, except for very low signal-to-noise ratios.>

Measurements of a process described by t(i)=k/sub i/T+ tau + eta (i), (i=1, 2, . . .), where k/sub i/ are unknown integers and ( eta (i)) is a white noise, are considered. The estimation of the 'period' T and 'phase' tau of such processes is often required in communications and radar. Popular linear regression techniques for this estimation problem are shown to fail and new algorithms are derived. Statistical properties of the estimators are presented, under reasonable assumptions. The suggested procedure is illustrated in the digital communications symbol timing recovery from eye-diagram zero crossings. The new bit synchronizer obtained is shown to be superior in many practical situations to known maximum-likelihood-type algorithms.>

The fundamental difficulty in the resolution of closely spaced modes using parametric spectral estimation techniques is shown to be a numerical one. Using the condition number of the sampled covariance matrix, an optimal sampling rate for the covariance function is derived. It is shown that by employing the optimal sampling rate, frequency resolution can be significantly improved. The optimization of the sampling rate is subsequently extended to rates smaller than the Nyquist rate. This yields a "zoom in" procedure which enables the resolution of very close modes in high noise.

A non-statistical approach to parameter estimation is presented. Assuming bounded noise, two algorithms are developed to obtain membership sets in the parameter space which are consistent with the set of measurements. The set theoretic approach enables the evaluation of information pertaining to the estimation problem as a new measurement is obtained. The proposed algorithms are shown to converge at least as fast as the least squares procedure. This performance is obtained while only about 10% of the data is actually used in the identification. The proposed algorithms are thus very attractive in the context of speach analysis where the assumption of bounded noise is easy to justify.