Bayesian approach to signal modelling

In this paper, an introduction to Bayesian methods in signal processing will be given. The paper starts by considering the important issues of model selection and parameter estimation and derives analytic expressions for the model probabilities of two simple models. The idea of marginal estimation of certain model parameter is then introduced and expressions are derived for the marginal probability densities for frequencies in white Gaussian noise and a Bayesian approach to general changepoint analysis is given. Numerical integration methods are introduced based on Markov chain Monte Carlo techniques and the Gibbs sampler in particular.

Technique for wavelength converting a 2.488 Gb/s signal whilst simultaneously monitoring and replacing a wavelength identifying pilot tone

A wavelength conversion device was demonstrated at the bit rate of 2.488 Gb/s with 2R (reamplification and reshaping) regenerative properties. A low frequency pilot tone was removed during the conversion process and a new one added. The wavelength converter is shown to operate well at 10 Gb/s, and tone identification/replacement should also be possible at this data rate.

1 × 4 space switching and simultaneous all-optical wavelength conversion at 2.488Gbit/s using a single monolithically integrated multiwavelength laser

A novel InGaAs/InGaAsP/InP integrated multiwavelength grating cavity laser is presented, which has been used to demonstrate space switching and simultaneous all-optical wavelength conversion at bit rates of 2.488 Gbit/s. This has been achieved using a single monolithically integrated device without the need for post-filtering to separate the converted signal from the input.

10-Gbits/s all-optical 3R regeneration and format conversion using a gain-switched DFB laser

A strain-compensated multiple quantum well device is used as a DFB laser, this has been optimized for low jitter gain switched operation at 10 GHz. The signal is transmitted down 80 km of standard fiber then amplified, filtered and polarization controlled before being injected into a DFB laser. The purpose of this regeneration process is to gain switch the DFB with the extracted clock signal in order to retime the converted signal. This process also simultaneously converts the input NRZ format to an output RZ data to format and results in a signal whose optical power and extinction ratio are considerably improved by the regeneration process.

Quality enhancement of a WDM signal using dispersion-imbalanced loop mirror

The nonlinear filtering of a 10Gb/s data stream in a dispersion-imbalanced fibre loop mirror has been demonstrated over a wide spectral range of 28nm. A relative extinction ratio of - 30 dB for the cw background has been achieved across the whole spectral range.

The Bayesian Approach to Signal Modelling

In this paper, an introduction to Bayesian methods in signal processing will be given. The paper starts by considering the important issues of model selection and parameter estimation and derives analytic expressions for the model probabilities of two simple models. The idea of marginal estimation of certain model parameter is then introduced and expressions are derived for the marginal probabilitiy densities for frequencies in white Gaussian noise and a Bayesian approach to general changepoint analysis is given. Numerical integration methods are introduced based on Markov chain Monte Carlo techniques and the Gibbs sampler in particular.

Bayesian estimation of simultaneous musical notes based on frequency domain modelling

This paper proposes a Bayesian method for polyphonic music description. The method first divides an input audio signal into a series of sections called snapshots, and then estimates parameters such as fundamental frequencies and amplitudes of the notes contained in each snapshot. The parameter estimation process is based on a frequency domain modelling and Gibbs sampling. Experimental results obtained from audio signals of test note patterns are encouraging; the accuracy is better than 80% for the estimation of fundamental frequencies in terms of semitones and instrument names when the number of simultaneous notes is two.

Bayesian signal processing

The application of Bayes' Theorem to signal processing provides a consistent framework for proceeding from prior knowledge to a posterior inference conditioned on both the prior knowledge and the observed signal data. The first part of the lecture will illustrate how the Bayesian methodology can be applied to a variety of signal processing problems. The second part of the lecture will introduce the concept of Markov Chain Monte-Carlo (MCMC) methods which is an effective approach to overcoming many of the analytical and computational problems inherent in statistical inference. Such techniques are at the centre of the rapidly developing area of Bayesian signal processing which, with the continual increase in available computational power, is likely to provide the underlying framework for most signal processing applications.

TOPS (Task optimization in the presence of signal-dependent noise) model

This paper proposes a movement trajectory planning model, which is a maximum task achievement model in which signal-dependent noise is added to the movement command. In the proposed model, two optimization criteria are combined, maximum task achievement and minimum energy consumption. The proposed model has the feature that the end-point boundary conditions for position, velocity, and acceleration need not be prespecified. Consequently, the method can be applied not only to the simple point-to-point movement, but to any task. In the method in this paper, the hand trajectory is derived by a psychophysical experiment and a numerical experiment for the case in which the target is not stationary, but is a moving region. It is shown that the trajectory predicted from the minimum jerk model or the minimum torque change model differs considerably from the results of the psychophysical experiment. But the trajectory predicted from the maximum task achievement model shows good qualitative agreement with the hand trajectory obtained from the psychophysical experiment. © 2004 Wiley Periodicals, Inc.

Gaussian Process Regression Networks

We introduce a new regression framework, Gaussian process regression networks (GPRN), which combines the structural properties of Bayesian neural networks with the non-parametric flexibility of Gaussian processes. This model accommodates input dependent signal and noise correlations between multiple response variables, input dependent length-scales and amplitudes, and heavy-tailed predictive distributions. We derive both efficient Markov chain Monte Carlo and variational Bayes inference procedures for this model. We apply GPRN as a multiple output regression and multivariate volatility model, demonstrating substantially improved performance over eight popular multiple output (multi-task) Gaussian process models and three multivariate volatility models on benchmark datasets, including a 1000 dimensional gene expression dataset.

Real-time experimental demonstration of low-cost VCSEL intensity-modulated 11.25 Gb/s optical OFDM signal transmission over 25 km PON systems.

The feasibility of utilising low-cost, un-cooled vertical cavity surface-emitting lasers (VCSELs) as intensity modulators in real-time optical OFDM (OOFDM) transceivers is experimentally explored, for the first time, in terms of achievable signal bit rates, physical mechanisms limiting the transceiver performance and performance robustness. End-to-end real-time transmission of 11.25 Gb/s 64-QAM-encoded OOFDM signals over simple intensity modulation and direct detection, 25 km SSMF PON systems is experimentally demonstrated with a power penalty of 0.5 dB. The low extinction ratio of the VCSEL intensity-modulated OOFDM signal is identified to be the dominant factor determining the maximum obtainable transmission performance. Experimental investigations indicate that, in addition to the enhanced transceiver performance, adaptive power loading can also significantly improve the system performance robustness to variations in VCSEL operating conditions. As a direct result, the aforementioned capacity versus reach performance is still retained over a wide VCSEL bias (driving) current (voltage) range of 4.5 mA to 9 mA (275 mVpp to 320 mVpp). This work is of great value as it demonstrates the possibility of future mass production of cost-effective OOFDM transceivers for PON applications.