Design of ternary signals for MIMO identification in the presence of noise and nonlinear distortion

A new approach to designing sets of ternary periodic signals with different periods for multi-input multi-output system identification is described. The signals are pseudo-random signals with uniform nonzero harmonics, generated from Galois field GF(q), where q is a prime or a power of a prime. The signals are designed to be uncorrelated, so that effects of different inputs can be easily decoupled. However, correlated harmonics can be included if necessary, for applications in the identification of ill-conditioned processes. A design table is given for q les 31. An example is presented for the design of five uncorrelated signals with a common period N = 168 . Three of these signals are applied to identify the transfer function matrix as well as the singular values of a simulated distillation column. Results obtained are compared with those achieved using two alternative methods

Study of the best linear approximation of nonlinear systems with arbitrary inputs

System identification is the art of modelling of a process (physical, biological, etc.) or to predict its behaviour or output when the environment condition or parameter changes. One is modelling the input-output relationship of a system, for example, linking temperature of a greenhouse (output) to the sunlight intensity (input), power of a car engine (output) with fuel injection rate (input). In linear systems, changing an input parameter will result in a proportional increase in the system output. This is not the case in a nonlinear system. Linear system identification has been extensively studied, more so than nonlinear system identification. Since most systems are nonlinear to some extent, there is significant interest in this topic as industrial processes become more and more complex. In a linear dynamical system, knowing the impulse response function of a system will allow one to predict the output given any input. For nonlinear systems this is not the case. If advanced theory is not available, it is possible to approximate a nonlinear system by a linear one. One tool is the Best Linear Approximation (Bla), which is an impulse response function of a linear system that minimises the output differences between its nonlinear counterparts for a given class of input. The Bla is often the starting point for modelling a nonlinear system. There is extensive literature on the Bla obtained from input signals with a Gaussian probability density function (p.d.f.), but there has been very little for other kinds of inputs. A Bla estimated from Gaussian inputs is useful in decoupling the linear dynamics from the nonlinearity, and in initialisation of parameterised models. As Gaussian inputs are not always practical to be introduced as excitations, it is important to investigate the dependence of the Bla on the amplitude distribution in more detail. This thesis studies the behaviour of the Bla with regards to other types of signals, and in particular, binary sequences where a signal takes only two levels. Such an input is valuable in many practical situations, for example where the input actuator is a switch or a valve and hence can only be turned either on or off. While it is known in the literature that the Bla depends on the amplitude distribution of the input, as far as the author is aware, there is a lack of comprehensive theoretical study on this topic. In this thesis, the Blas of discrete-time time-invariant nonlinear systems are studied theoretically for white inputs with an arbitrary amplitude distribution, including Gaussian and binary sequences. In doing so, the thesis offers answers to fundamental questions of interest to system engineers, for example: 1) How the amplitude distribution of the input and the system dynamics affect the Bla? 2) How does one quantify the difference between the Bla obtained from a Gaussian input and that obtained from an arbitrary input? 3) Is the difference (if any) negligible? 4) What can be done in terms of experiment design to minimise such difference? To answer these questions, the theoretical expressions for the Bla have been developed for both Wiener-Hammerstein (Wh) systems and the more general Volterra systems. The theory for the Wh case has been verified by simulation and physical experiments in Chapter 3 and Chapter 6 respectively. It is shown in Chapter 3 that the difference between the Gaussian and non-Gaussian Bla’s depends on the system memory as well as the higher order moments of the non-Gaussian input. To quantify this difference, a measure called the Discrepancy Factor—a measure of relative error, was developed. It has been shown that when the system memory is short, the discrepancy can be as high as 44.4%, which is not negligible. This justifies the need for a method to decrease such discrepancy. One method is to design a random multilevel sequence for Gaussianity with respect to its higher order moments, and this is discussed in Chapter 5. When estimating the Bla even in the absence of environment and measurement noise, the nonlinearity inevitably introduces nonlinear distortions—deviations from the Bla specific to the realisation of input used. This also explains why more than one realisation of input and averaging is required to obtain a good estimate of the Bla. It is observed that with a specific class of pseudorandom binary sequence (Prbs), called the maximum length binary sequence (Mlbs or the m-sequence), the nonlinear distortions appear structured in the time domain. Chapter 4 illustrates a simple and computationally inexpensive method to take advantage this structure to obtain better estimates of the Bla—by replacing mean averaging by median averaging. Lastly, Chapters 7 and 8 document two independent benchmark studies separate from the main theoretical work of the thesis. The benchmark in Chapter 7 is concerned with the modelling of an electrical Wh system proposed in a special session of the 15th International Federation of Automatic Control (Ifac) Symposium on System Identification (Sysid) 2009 (Schoukens, Suykens & Ljung, 2009). Chapter 8 is concerned with the modelling of a ‘hyperfast’ Peltier cooling system first proposed in the U.K. Automatic Control Council (Ukacc) International Conference on Control, 2010 (Control 2010)

Design of Truncated Maximum Length Ternary Signals Where Their Squared Versions Have Uniform Even Harmonics

The design of pseudo-random maximum length (PRML) ternary signals with properties suitable for identification of generalized quadratic. Hammerstein models is considered. For such an application, it is desirable for the signal to have odd harmonics uniform and even harmonics suppressed, with its squared version having odd harmonics suppressed and even harmonics uniform. To date, the only class of signal known to possess such harmonic properties comprises of PRML ternary signals based on Galois field GF(3), and its extension fields. In this note, theoretical conditions for a PRML signal to possess these properties are derived and imposed on the design of signals based on higher odd fields to generate truncated PRML signals that fulfill the required specifications

The development of speech coding and the first standard coder for public mobile telephony

This thesis describes in its core chapter (Chapter 4) the original algorithmic and design features of the ??rst coder for public mobile telephony, the GSM full-rate speech coder, as standardized in 1988. It has never been described in so much detail as presented here. The coder is put in a historical perspective by two preceding chapters on the history of speech production models and the development of speech coding techniques until the mid 1980s, respectively. In the epilogue a brief review is given of later developments in speech coding. The introductory Chapter 1 starts with some preliminaries. It is de- ??ned what speech coding is and the reader is introduced to speech coding standards and the standardization institutes which set them. Then, the attributes of a speech coder playing a role in standardization are explained. Subsequently, several applications of speech coders - including mobile telephony - will be discussed and the state of the art in speech coding will be illustrated on the basis of some worldwide recognized standards. Chapter 2 starts with a summary of the features of speech signals and their source, the human speech organ. Then, historical models of speech production which form the basis of di??erent kinds of modern speech coders are discussed. Starting with a review of ancient mechanical models, we will arrive at the electrical source-??lter model of the 1930s. Subsequently, the acoustic-tube models as they arose in the 1950s and 1960s are discussed. Finally the 1970s are reviewed which brought the discrete-time ??lter model on the basis of linear prediction. In a unique way the logical sequencing of these models is exposed, and the links are discussed. Whereas the historical models are discussed in a narrative style, the acoustic tube models and the linear prediction tech nique as applied to speech, are subject to more mathematical analysis in order to create a sound basis for the treatise of Chapter 4. This trend continues in Chapter 3, whenever instrumental in completing that basis. In Chapter 3 the reader is taken by the hand on a guided tour through time during which successive speech coding methods pass in review. In an original way special attention is paid to the evolutionary aspect. Speci??cally, for each newly proposed method it is discussed what it added to the known techniques of the time. After presenting the relevant predecessors starting with Pulse Code Modulation (PCM) and the early vocoders of the 1930s, we will arrive at Residual-Excited Linear Predictive (RELP) coders, Analysis-by-Synthesis systems and Regular- Pulse Excitation in 1984. The latter forms the basis of the GSM full-rate coder. In Chapter 4, which constitutes the core of this thesis, explicit forms of Multi-Pulse Excited (MPE) and Regular-Pulse Excited (RPE) analysis-by-synthesis coding systems are developed. Starting from current pulse-amplitude computation methods in 1984, which included solving sets of equations (typically of order 10-16) two hundred times a second, several explicit-form designs are considered by which solving sets of equations in real time is avoided. Then, the design of a speci??c explicitform RPE coder and an associated eÆcient architecture are described. The explicit forms and the resulting architectural features have never been published in so much detail as presented here. Implementation of such a codec enabled real-time operation on a state-of-the-art singlechip digital signal processor of the time. This coder, at a bit rate of 13 kbit/s, has been selected as the Full-Rate GSM standard in 1988. Its performance is recapitulated. Chapter 5 is an epilogue brie y reviewing the major developments in speech coding technology after 1988. Many speech coding standards have been set, for mobile telephony as well as for other applications, since then. The chapter is concluded by an outlook

Synchronization Techniques for Burst-Mode Continuous Phase Modulation

Synchronization is a critical operation in digital communication systems, which establishes and maintains an operational link between transmitter and the receiver. As the advancement of digital modulation and coding schemes continues, the synchronization task becomes more and more challenging since the new standards require high-throughput functionality at low signal-to-noise ratios (SNRs). In this work, we address feedforward synchronization of continuous phase modulations (CPMs) using data-aided (DA) methods, which are best suited for burst-mode communications. In our transmission model, a known training sequence is appended to the beginning of each burst, which is then affected by additive white Gaussian noise (AWGN), and unknown frequency, phase, and timing offsets. Based on our transmission model, we derive the Cramer-Rao bound (CRB) for DA joint estimation of synchronization parameters. Using the CRB expressions, the optimum training sequence for CPM signals is proposed. It is shown that the proposed sequence minimizes the CRB for all three synchronization parameters asymptotically, and can be applied to the entire CPM family. We take advantage of the simple structure of the optimized training sequence in order to design a practical synchronization algorithm based on the maximum likelihood (ML) principles. The proposed DA algorithm jointly estimates frequency offset, carrier phase and symbol timing in a feedforward manner. The frequency offset estimate is first found by means of maximizing a one dimensional function. It is then followed by symbol timing and carrier phase estimation, which are carried out using simple closed-form expressions. We show that the proposed algorithm attains the theoretical CRBs for all synchronization parameters for moderate training sequence lengths and all SNR regions. Moreover, a frame synchronization algorithm is developed, which detects the training sequence boundaries in burst-mode CPM signals. The proposed training sequence and synchronization algorithm are extended to shaped-offset quadrature phase-shift keying (SOQPSK) modulation, which is considered for next generation aeronautical telemetry systems. Here, it is shown that the optimized training sequence outperforms the one that is defined in the draft telemetry standard as long as estimation error variances are considered. The overall bit error rate (BER) plots suggest that the optimized preamble with a shorter length can be utilized such that the performance loss is less than 0.5 dB of an ideal synchronization scenario

Window Functions and Their Applications in Signal Processing

Window functions—otherwise known as weighting functions, tapering functions, or apodization functions—are mathematical functions that are zero-valued outside the chosen interval. They are well established as a vital part of digital signal processing. Window Functions and their Applications in Signal Processing presents an exhaustive and detailed account of window functions and their applications in signal processing, focusing on the areas of digital spectral analysis, design of FIR filters, pulse compression radar, and speech signal processing. Comprehensively reviewing previous research and recent developments, this book: Provides suggestions on how to choose a window function for particular applications Discusses Fourier analysis techniques and pitfalls in the computation of the DFT Introduces window functions in the continuous-time and discrete-time domains Considers two implementation strategies of window functions in the time- and frequency domain Explores well-known applications of window functions in the fields of radar, sonar, biomedical signal analysis, audio processing, and synthetic aperture rada

Window Functions and Their Applications in Signal Processing

Window functions—otherwise known as weighting functions, tapering functions, or apodization functions—are mathematical functions that are zero-valued outside the chosen interval. They are well established as a vital part of digital signal processing. Window Functions and their Applications in Signal Processing presents an exhaustive and detailed account of window functions and their applications in signal processing, focusing on the areas of digital spectral analysis, design of FIR filters, pulse compression radar, and speech signal processing. Comprehensively reviewing previous research and recent developments, this book: Provides suggestions on how to choose a window function for particular applications Discusses Fourier analysis techniques and pitfalls in the computation of the DFT Introduces window functions in the continuous-time and discrete-time domains Considers two implementation strategies of window functions in the time- and frequency domain Explores well-known applications of window functions in the fields of radar, sonar, biomedical signal analysis, audio processing, and synthetic aperture rada

Algorithms and VLSI architectures for parametric additive synthesis

A parametric additive synthesis approach to sound synthesis is advantageous as it can model sounds in a large scale manner, unlike the classical sinusoidal additive based synthesis paradigms. It is known that a large body of naturally occurring sounds are resonant in character and thus fit the concept well. This thesis is concerned with the computational optimisation of a super class of form ant synthesis which extends the sinusoidal parameters with a spread parameter known as band width. Here a modified formant algorithm is introduced which can be traced back to work done at IRCAM, Paris. When impulse driven, a filter based approach to modelling a formant limits the computational work-load. It is assumed that the filter's coefficients are fixed at initialisation, thus avoiding interpolation which can cause the filter to become chaotic. A filter which is more complex than a second order section is required. Temporal resolution of an impulse generator is achieved by using a two stage polyphase decimator which drives many filterbanks. Each filterbank describes one formant and is composed of sub-elements which allow variation of the formant’s parameters. A resource manager is discussed to overcome the possibility of all sub- banks operating in unison. All filterbanks for one voice are connected in series to the impulse generator and their outputs are summed and scaled accordingly. An explorative study of number systems for DSP algorithms and their architectures is investigated. I invented a new theoretical mechanism for multi-level logic based DSP. Its aims are to reduce the number of transistors and to increase their functionality. A review of synthesis algorithms and VLSI architectures are discussed in a case study between a filter based bit-serial and a CORDIC based sinusoidal generator. They are both of similar size, but the latter is always guaranteed to be stable