Hans-Peter Bernhard

Nonlinear long-term prediction of speech signals

This paper presents an in-depth study of nonlinear long-term prediction of speech signals. While previous studies of nonlinear prediction focused on short-term prediction (with only moderate performance advantage over adaptive linear prediction in most cases), successful long-term prediction strongly depends on the nonlinear oscillator framework for speech modeling. This hypothesis has been confirmed in a series of experiments run on a voiced speech database. We provide results for the prediction gain as a function of the prediction delay using two methods. One is based on an extended form of radial basis function networks and is intended to show what performance can be reached using a nonlinear predictor. The other relies on calculating the mutual information between multiple signal samples. We explain the role of this mutual information function as the upper bound on the achievable prediction gain. We show that with matching memory and dimension, the two methods yield nearly the same value for the achievable prediction gain. We try to make a fair comparison of these values against those obtained using optimized linear predictors of various orders. It turns out that the nonlinear predictors gain is significantly higher than that for a linear predictor using the same parameters.

Performance analysis of the mutual information function for nonlinear and linear signal processing

Nonlinear signal processing is now well established both in theory and applications. Nevertheless, very few tools are available for the analysis of nonlinear systems. We introduce the mutual information function (MIF) as a nonlinear correlation function and describe the practicalities of estimating it from data. Even if an estimator is consistent, it is of great interest to check what the bias and variance are with a finite sample. We discuss these questions, as well as the computational efficiency, for two estimators. Both algorithms are of complexity Nlog/sub 2/N, where N is the sample length, but they use different methods to find the histogram for the estimation of the mutual information. An efficient implementation makes it possible to apply the algorithm on real time signal processing problems where the linear correlation analysis breaks down. Examples involving linear and nonlinear channels are discussed.

Timing synchronization of low power wireless sensor nodes with largely differing clock frequencies and variable synchronization intervals

In this paper a novel synchronization method for wireless sensor networks with star topology is presented. We address timing synchronization using low frequency real-time clocks in all nodes. A beacon-driven TDMA-protocol for bidirectional node/base communication is used. Between the beacons, which are sent by the base station, lie the superframe time intervals to handle data transmission from node to base. We discuss the protocol and its energy saving advantages including the challenges of synchronization. We reduce the required communication for synchronization based on long term synchronicity of the node to save energy. Due to the individual node clock, the accurate superframe time interval usually will consist of a rational number of clock ticks. We propose to use a ΔΣ-converter to generate a sequence of superframes with different time durations, but each consisting of integer multiples of clock ticks, which - on average - achieve the accurate superframe duration for any rational number of clock ticks. We show by theory and measurements that our novel approach leads to a variance of the synchronization error which is constant at a value of 0.25 clock cycles. The variance is independent of the rate at which the nodes listen to the beacon of the base station.

Analysis of ΔΣ-synchronization in wireless sensor nodes

We analyse the use of a ΔΣ-modulator in the nodes of a wireless sensor network, which is a new method to achieve long term synchronization. We consider star topology WSNs (Wireless Sensor Networks) with a central base station and address timing synchronization using low frequency realtime clocks. The WSN uses a beacon driven TDMA-protocol for bidirectional node/base communication. Between the beacons, which are sent by the base station, lie the superframe time intervals to handle data transmission from node to base. The ΔΣ-modulator is used to generate - at average - the accurate superframe duration for any rational number of clock ticks, by generating a sequence of superframes with different time durations, but each consisting of integer multiples of clock ticks. We discuss the synchronization accuracy based on the internal arithmetic of the ΔΣ-modulator and show by theory a relation between synchronization accuracy and word length of the internal arithmetic. Additionally the fractional part of a crystal clock module is responsible for variations in the synchronization quality. We present an equation that allows us to interpret measurements showing periodic variations of synchronization quality.

Life cycle of wireless sensor nodes in industrial environments

We present the design of a suite of protocols for wireless sensor networks (WSNs) with respect to a complete life cycle of a WSN node from warehouse to the end of operation. While there are numerous publications on various, usually isolated, aspects of WSNs, the whole life cycle of a node from registration in an automation system via warehouse, calibration, mounting, performing measurements to finally unmounting, has not yet been sufficiently addressed as compound survey. Our application example is a WSN to be used in automotive test beds in which a large amount of testing with many different sensors is performed in controlled environments. While there is published work on WSNs for performing the measurements focusing on node hardware and MAC protocol, we now extend this work by accounting for the whole life cycle of operation of such a WSN and its nodes. This is mainly achieved by introducing optimized MAC protocols for wireless communication in all life cycle phases. Right from beginning of the life cycle the nodes are synchronized with a base node. Even during long offline periods nodes stay synchronized. The life cycle is modeled via a set of states, instantiated in state machines, which control operation in the base station and the nodes. Besides, considering the whole life cycle of the sensor nodes, our design minimizes energy consumption, largely avoids collisions due to suitable multiple access protocols, and allows tight synchronization even during long sleep periods. A demonstrator concludes the presentation and shows functionality and benefits of the concept.

Determining the predictability of signals

In case of signal or time series prediction, it is important to know if there is any chance for prediction or not. Therefore, the maximum achievable prediction gain is the desired measure used to characterize the future knowledge of a signal. We present a method to evaluate the maximum prediction gain based on the observed signal only. Hence, the presented method does not rely on a special prediction function, therefore it is suitable for a decision whether any given predictor is good enough or could be improved. To aid system identification tasks the progress of the prediction gain is used as an additional model selection rule. Considering different signal types the predictability behaves differently, i.e., it keeps constant; for periodic signals or vanishes in the case of chaotic or random signals.

Linear complex iterative frequency estimation of sparse and non-sparse pulse and point processes

Clock frequency estimation is a key issue in many signal processing applications, e.g. network clock estimation in wireless sensor networks. In wireless systems or harsh environments, it is likely that clock events can be missed and, therefore, the observed process has to be treated as a sparse periodic process. To parameterize the clock, current research is applying periodogram estimators at a complexity of at least O(N log N). We introduce a highly accurate iterative frequency estimator for pulse signals with low computational complexity. An unbiased frequency estimator is presented with a complexity of O(N). Furthermore the mean square error (MSE), which is proportional to O(N−3) is derived and it is shown by theory and simulation that this estimator performs as well as periodogram based methods. The work concludes with simulations on sparse and non-sparse processes including a discussion of the application of the method.

Error characterization of duty cycle estimation for sampled non-band-limited pulse signals with finite observation period

In many applications the pulse duration of a periodic pulse signal is the parameter of interest. Thereby, the non-band-limited pulse signal is sampled during a finite observation period yielding to aliasing and windowing effects, respectively. In this work, the pulse duration estimation based on the mean value of the samples is considered, and an exact expression of the mean squared estimation error (averaged over all possible time shifts) is derived. The resulting mean squared error expression depends on the observation period, the pulse period and the pulse duration. Analyzing the effect of these parameters shows that the mean squared error can be reduced (i) if the observation period is a multiple of the pulse period, (ii) if the pulse period is not a multiple of the sampling period, and (iii) if the total number of samples is a prime number. All results were validated with simulation results.

An environmentally powered wireless sensor node for high precision temperature measurements

Wireless measurement systems will provide significant benefits to industrial applications, for production facilities as well as in mobile or R&D scenarios. However, in order to exploit the improvements by flexibility, scalability and easy reconfigurability brought by wireless sensor networks (WSN), industrial use cases often require a sustainable autonomous energy supply, while providing the reliability which is comparable with todays wired systems. In this work we introduce a sensor node implementation with a temperature measurement circuit design, optimized for low energy consumption, while providing industry-grade accuracy and resolution. A first implementation realizing the concept of a switched signal acquisition circuitry is discussed, demonstrating the impact of the energy harvesting and storage unit. In a second implementation, a coordinated signal conditioning and power management concept is introduced.

Estimation of Time Variant System Clock Period for Wireless Sensor Network Applications

In industrial applications synchronized sensor nodes are vital for many tasks like multi parameter sampling of complex machinery behavior. The wirelessly connected nodes are usually synchronized to a base station. Therefore, frequency or period estimation of the reference clock is a key issue for all connected tasks like sampling, localization or applying energy optimized communication protocols. In wireless systems and especially in harsh industrial environments, it is likely to miss one or more synchronization events. The available data for clock estimations is therefore sparse and periodogramm estimators, at a complexity of at least O(N log N), are commonly used for accurate clock estimation. We introduce a period estimator for sparse clock signals with O(N) complexity. Furthermore, we present an equation for the observation time necessary to estimate the clock period at a certain quality. Mostly due to temperature influences, the crystal frequency at the nodes are varying. Our iterative period estimator follows those changes with a given estimation accuracy. We analyze an equation, which allows to calculate the accuracy of the estimator given a certain change rate of time variant system clock. The work is concluded with simulations considering sparse and time varying processes, including a discussion of the application of the method.