U-model enhanced control of non-minimum phase systems

Repeaters equipped with on-board digital baseband processing in a time division duplex (TDD) demand short processing time in order to alleviate inter-symbol interference resulting from having a time delay that is greater than the guard time. To accomplish this, the total system delay of the repeater should be minimized as much as possible without distorting signal quality. Conventionally, the finite impulse response (FIR) type of filter is deployed as a channelization filter, but due to the necessity of large numbers of coefficients to fulfill a prerequisite filter response with a sharp transition band characteristic, an unwanted excessive time delay intrinsically occurs. To make the processing delay as low as possible, this paper proposes a method employing a minimum-phase characterized infinite impulse response (IIR) filter whose magnitude response is almost identical to that of the original FIR filter. Furthermore, in order to linearize the phase response of the designed IIR filter, this paper also introduces an all-pass filter cascaded with the IIR filter for digital down-conversion as well as up-conversion. To achieve further simplicity, this paper introduces polyphase-style IIR filters transformed from conventional single IIR filters that have their own all-pass filters in order to linearize the phase response. The computer simulation results verify that the proposed integrated IIR filter exhibits a relatively short processing delay with a minor deterioration in signal quality-like error vector magnitude (EVM) performance.

Infinite impulse response (IIR) filters are used in applications where the computational efficiency is the highest priority. It is well known that an IIR filter transfer function is of a considerably lower order than the transfer function of an FIR equivalent. The drawbacks of an IIR filter are the nonlinear phase characteristic and sensitivity to quantization errors. In multirate applications, the computational requirements for FIR filters can be reduced by the sampling rate conversion factor as demonstrated in Chapter IV. However, such a degree of computation savings cannot be achieved in multirate implementations of IIR filters. This is due to the fact that every sample value computed in the recursive loop is needed for evaluating an output sample. Based on the polyphase decomposition, several techniques have been developed which improve the efficiency of IIR decimators and interpolators as will be shown later on in this chapter. In this chapter, we consider first the direct implementation structures for IIR decimators and interpolators. In the sequel, we demonstrate the computational requirements for direct form IIR decimators and interpolators. The polyphase decomposition of an IIR transfer function is explained with its application to decimation and interpolation. Then, we demonstrate an efficient IIR polyphase structure based on all-pass subfilters, which is applicable to a restricted class of decimators and interpolators. In this chapter, we discuss the application of the elliptic minimal Q factor (EMQF) filter transfer function in constructing high-performance decimators and interpolators. The chapter concludes with a selection of MATLAB exercises for the individual study.

In this paper, a unified theory is proposed for the fractional control of the non-minimum phase plus dead time systems via the introduction of the fractional filter-PID control and stability inequality. More precisely, three Theorems from a fractional system-theoretic viewpoint are developed. The first Theorem deals with the controller design through the notion of generalised internal model control. That embeds the fractional filter-PID controller coupled with the unified form of the Smith predictor and the inverse compensator. The second Theorem designs a bound on the fractional filter parameter that leads to a stable feedback system. The third Theorem deals with the stability of a fractional quasi-characteristic polynomial of the commensurate order arising from the control of non-minimum phase systems with dead time. Two illustrative second-order plus dead time non-minimum phase systems are presented to test the efficacy of the resulting fractional filter-PID controller that obeys the stability bound. Controller and sensitivity performance indices for the nominal as well as mismatch cases reveal the effectiveness and robustness of the proposed method for enhanced closed-loop performance. Thus, the generalised inverse compensator, the fractional filter-PID controller and the stability inequality in corroboration with numerical simulations demonstrate the better control of non-minimum phase systems with dead time.

Recursive structures are introduced for implementing long linear-phase finite impulse response (FIR) filters using a very small number of multipliers. The implementation uses the principle of switching and resetting between two identical copies of the same infinite impulse response (IIR) filter. The impulse response of the resulting filters is a truncated and shifted version of the response of a filter G(z)G(z/sup -1/) where G(z) is a stable IIR stable and G(z/sup -1/) is the corresponding unstable IIR filter. The filters are implemented as a parallel connection of several branches, each branch generating a truncated response corresponding to a complex conjugate pole pair and its mirror-image pair. The truncation is performed using a feedforward term which provides pole-zero cancellations. To stabilize the pole-zero cancellations, and to avoid the quantization error from growing too much, the branch filters are implemented by applying the principle of switching and resetting. It is shown, by means of an example, that by using this approach a nearly optimum FIR filter of order larger than 500 using just 17 adjustable parameters can be designed. >

The advantage of infinite-impulse response (IIR) filters over finite-impulse response (FIR) ones is that the former require a much lower order (much fewer multipliers and adders) to obtain the desired response specifications. However, in contrast with well-developed FIR filter bank design theory, there is no satisfactory methodology for IIR filter bank design. The well-known IIR filters are mostly derived by rather heuristic techniques, which work in only narrow design classes. The existing deterministic techniques usually lead to too high order IIR filters and thus cannot be practically used. In this paper, we propose a new method to solve the low-order IIR filter bank design, which is based on tractable linear-matrix inequality (LMI) optimization. Our focus is the quadrature mirror filter bank design, although other IIR filter related problems can be treated and solved in a similar way. The viability of our theoretical development is confirmed by extensive simulation.

An investigation is conducted of the acceleration of the iterative implementation of the two-dimensional infinite impulse response (IIR) filter proposed by D.E. Dudgeon (IEEE Trans. Acoust. Speech Signal Proc., vol.ASSP-28, no.6, p.666-71, 1980). The conventional procedure results in a sequence of estimations that converge linearly to the desired filter output. Applying an accelerated convergence algorithm for linearly distorted signal reconstruction problems, the authors use a product expansion of the denominator of the transfer function of an IIR filter to derive a class of iterative algorithms that have a pth-order rate of convergence. Specifically, k iterations of the proposed pth-order algorithm are equal to the p/sup k/ iterations of the linear algorithm. Therefore, the number of iterations required to obtain a given approximation is reduced from p/sup k/ to k. The authors show that the spatial truncation error does not affect the computation of the desired result in the region of interest, provided that the boundary values outside the area of interest are known. Finally, the authors present two examples in order to compare the convergence rates for the linear and the accelerated algorithms. >

Generally, the process industry is affected by unwanted fluctuations in control loops arising due to external interference, components with inherent nonlinearities or aggressively tuned controllers. These oscillations lead to production of substandard products and thus affect the overall profitability of a plant. Hence, timely detection of oscillations is desired for ensuring safety and profitability of the plant. In order to achieve this, a control loop oscillation detection and quantification algorithm using Prony method of infinite impulse response (IIR) filter design and deep neural network (DNN) has been presented in this work. Denominator polynomial coefficients of the obtained IIR filter using Prony method were used as the feature vector for DNN. Further, DNN is used to confirm the existence of oscillations in the process control loop data. Furthermore, amplitude and frequency of oscillations are also estimated with the help of cross-correlation values, computed between the original signal and estimated error signal. Experimental results confirm that the presented algorithm is capable of detecting the presence of single or multiple oscillations in the control loop data. The proposed algorithm is also able to estimate the frequency and amplitude of detected oscillations with high accuracy. The Proposed method is also compared with support vector machine (SVM) and empirical mode decomposition (EMD) based approach and it is found that proposed method is faster and more accurate than the later.

This paper describes a new approach to the design of multidimensional (M-D) finite-wordlength digital filters with specifications in the frequency and spatial domains. The approach is based on stochastic optimization and extends previous work on finite impulse response (FIR) filters in two ways: by inclusion of spatial constraints and by application to the case of infinite impulse response (IIR) filters. The formulation proposed is based on a multiple-term objective function that, in addition to magnitude constraints, also includes step response, group delay and stability constraints. Our attention to these characteristics stems from the application of such filters to video processing that we are actively pursuing. Since filter coefficients are of finite precision and since the objective function is multivariable, nondifferentiable and likely to have multiple minima, we use simulated annealing for optimization. We show numerous examples of the design of practical filters such as channel and luminance/chrominance separation filters used in the NTSC system. We demonstrate the impact of coefficient precision as well as of group delay and step response constraints on filter parameters. >

Filters are used to implement signal transforms, and filter design is a very important part of the signal processing field. There are currently 2 types of filters available: the finite impulse response (FIR) filter, and the infinite impulse response (IIR) filter. While FIR filters have desirable traits such as stability (an absence of poles), IIR filters are able to generate outputs more efficiently. This paper combines the two types of filters by introducing an output slope trigger, to make a hybrid impulse response (HIR) filter with desirable traits from both FIR and IIR filters

As a generalization of the fundamental Levinson algorithm to linear modeling of control systems and IIR (infinite impulse response) filters, the fast order recursive algorithm (ORA) and the time and order recursive algorithm (TORA) have been developed. However, only the ORA and TORA which operate recursively in the order of the autoregressive part of system outputs have been presented. The authors give a detailed description of the ORA which operates recursively in the order of the moving-average part of the system inputs. In addition, a numerical example is given which illustrates how the ORA operates. >

Orthogonal frequency division multiplexing (OFDM) is widely implemented in high data rate wireless applications due to its favourable properties. The main disadvantage associated with OFDM is high peak to average power ratio (PAPR). Although numerous schemes have been proposed to solve the PAPR problem, no specific PAPR reduction scheme can be considered as the best solution. The aim of this paper is to review the performance and effectiveness of the filtering technique as a PAPR reduction method focusing on the filter's performance. To achieve this, investigations are performed using various infinite impulse response (IIR) filters. The simulation results provide a clearer picture on the OFDM systems performance, with the two key areas of focus being peak power reduction and error performance.

Development of equation-error adaptive IIR-filter-based active noise control system

Digital infinite impulse response (IIR) filter have become the target of growing interest, because they often provide a much better performance and less computational cost than finite impulse response (FIR) filters. Since the problem of error surface of designing Digital IIR filters is generally nonlinear and multimodal, global optimization techniques are required in order to avoid local minima. In this paper, an evolutionary method based on Imperialist Competitive Algorithm (ICA) has been proposed to design Digital IIR filters. By adding a step to the standard ICA algorithm, its performance has been improved in searching solution space and convergence to the global minima. Simulation results show the efficiency of the proposed method to design Digital IIR filter.

In this letter, a new broadband beamformer using infinite impulse response (IIR) filters is proposed. The unique feature of our letter is that by replacing all the delay elements with tap-to-tap IIR filters under some structural restrictions, the Frost processor is naturally extended from the finite impulse response (FIR) beamformer to the IIR beamformer. In the new beamformer, the feedforward and feedback weights are computed with the constrained and unconstrained least-mean-squares algorithms, respectively. The stability of the IIR filters in the proposed beamformer could be monitored easily. Simulation results demonstrate the improved performance of the new IIR beamformer relative to the Frost beamformer.

In the present paper, we give the parametrization of all stabilizing modified repetitive controllers for non-minimum phase systems. The basic idea to obtain the parametrization of all modified repetitive controllers for non-minimum phase systems is very simple. If the repetitive controller stabilizes the plant, then the repetitive controller must be included in the class of all stabilizing controllers for the plant. The parametrization of all stabilizing controllers for the plant, which is not necessarily repetitive controllers, are obtained by Youla et al. and Vidyasagar. The parametrization of all stabilizing controllers includes a free parameter, which is stable. That is, stabilizing repetitive controllers for non-minimum phase systems can be designed using the free parameterin the parametrization by Youla et al. and Vidyasagar. Using this idea, we obtain the parametrization of all stabilizing modified repetitive controllers for non-minimum phase systems. Next, a numerical example is illustrated to show the effectiveness of the proposed parametrization.