Multirate digital adaptive control

A design method is developed which involves the use of several adaptive controllers working in parallel at different sampling rates while maintaining the asymptotic stability of the overall adaptive scheme, as well as the boundedness of all the signals within the system. The use of adaptive sampling is considered as an additional loop in a hierarchical organization of the scheme. This strategy allows the designer to take advantage of the suitable properties of such schemes which are well known in classical multirate control designs. These advantages arise from the need for alleviating control computer throughput requirements of accommodating sensor information available at multiple rates and for compensating excitations of the fast modes of the plant in the presence of high-frequency disturbances. As a direct consequence of the involved methodology, the transient behaviour of the adaptive system becomes in some cases greatly improved.     

Multirate digital control system design

Methods for multirate digital control system design are discussed. A simple method for sampling rate selection based on control bandwidths is proposed. Methods for generating a discrete-time state model of a sampled-data plant and a discrete-time equivalent to an analog cost function for a sampled-data plant are described. The successive loop closures and linear quadratic Gaussian synthesis methods are reviewed, and a constrained optimization synthesis method is introduced. The proposed sampling rate selection, discretization, and synthesis methods are applied to two example design problems. Multirate and single-rate compensators synthesized by the different methods are compared based on closed-loop responses with compensators having the same real-time computation load     

From special analogous crystal filters to digital impacting filters

The implementation of high-speed and high-efficiency wireless communications, or Ultra Narrow Band (UNB) modulation, depends on the design of a special digital filter, which needs to not only maintain or even enlarge the minute differences in modulated waveforms, but also weaken noise or interference. This paper proposes a novel but simple digital impacting filter produced by exploiting the mechanism of zero group delay crystal filters. The proposed filter can cooperate with the usual small-angle modulation of UNB modulation, especially with Extended Binary Phase Shift Keying (EBPSK) modulation, which can convert the signal characteristics in noise into high-amplitude impacting at the phase jump points, such that the UNB signal is easy to detect. A computer simulation illustrates the validity of the proposed filter.     

Synthesis of recursive digital filters

The coefficients of a parallel programmed recursive digital filter are obtained using the nonlinear optimization algorithms described by Fletcher and Powell and Fletcher and Reeves. The technique is based on least square error criterion. The strategy adopted is the same as that of Steiglitz. The flowchart is given and the frequency responses for this filter obtained from the optimized values are compared. The Fletcher and Powell algorithm is found to give better results.     

From switched-capacitors to digital filters

Digital filters have been realized with inexpensive reverse switched capacitors and expensive special purpose digital computers. Analysis shows that the semi-null inherent in any switched capacitor can be eliminated with an analog-to-digital converter realization which is intermediate in cost. The main emphasis is on band-pass filter realization by means of the overlapping spectra method and a preferred ordering of the cascaded filter sections. Band-rejection filter realization is considered for completeness.     

Multirate digital control design of an optimal regulator via singular perturbation theory

In this paper a multirate digital control design of an optimal regulator is investigated via singular perturbation theory. It is shown that the singularity perturbed continuous-time regulator leads, under slow and fast sampling rates, to two different discrete-time versions. They are decomposed into slow and fast subsystems, and then these solutions are combined in a proper way. Within the framework of such a decomposition-coordination principle, a multirate control design is developed naturally. Furthermore, the problem of the asymptotic stability of a multirate controlled system is investigated and the relationship between the original continuous-time version and the multirate controlled version is discussed.     

Minimax design of recursive digital filters

The application of two new algorithms for minimax optimization due to Charalambous and Bandler is investigated. The application is to the problem of finding the coefficients of a recursive digital filter to meet arbitrary specifications of the magnitude or the group delay characteristics. Unlike the original minimax algorithm due to Bandler and Charalambous in which a sequence of least $\text{p}\text{th}$ optimizations as $\text{p}$ tends to infinity is taken, the two new algorithms do not require the value of $\text{p}$ to do this. Instead, a sequence of least $\text{p}\text{th}$ optimization problems is constructed with finite values of $\text{p}$ in the range $\text{1 < p < ∞}$. A criterion is given under which the order of the filter can be increased by growing filter sections. A general computer program has been developed, based on the ideas presented.     

Optimal mean-square N-observation digital morphological filters: I. Optimal binary filters

The present paper places binary morphological filtering into the framework of statistical estimation, the intent being to develop the theory of mean-square (MS) optimization. Classical binary morphological operations are interpreted as numerical functionals on binary N-vectors, so that in the random setting they can be treated as estimators dependent on N binary observation random variables. For single-erosion filters, optimization is achieved by finding the structuring element that minimizes MS error. Using the Matheron representation as a guide, we generalize the analysis to morphological filters given by unions of multiple erosions and optimize by minimizing MS error over all collections of erosions, or over a prefixed number of erosions. In all cases, MS error is relative to the estimation of an unobserved variable by a morphological function of observed variables. A key element in the method is use of the basis form of the Matheron expansion to reduce significantly the structuring-element search. The technique is adapted to special morphological filters by constraining the basis representation in accordance with the class of interest. It is demonstrated that optimization in terms of erosions is equivalent to optimization in terms of dilations.     

Recursive algorithms for implementing digital image filters

The B-spline functions are used to develop recursive algorithms for the efficient implementation of two-dimensional linear digital image filters. These filters may be spatially varying. The B-splines are used in a representation of the desired point spread function. We show that this leads to recursive algorithms and hardware implementations which are more efficient than either direct spatial domain filter realizations or FFT implementations. The Z-transform is used to develop a discrete version of Duhamel's theorem. A computer architecture for B-spline image filters is proposed and a complexity analysis and comparison to other approaches is provided.     

Hybrid method for designing digital Butterworth filters

A procedure for designing digital Butterworth filters is proposed. The procedure determines the denominator and the numerator of the filter transfer function based on the positions of the poles in the s-plane and zeros in the z-plane, respectively, and calculates the gain factor using a maximum point normalization method. In contrast to some conventional algorithms, the presented procedure is much simpler by directly obtaining the filter with 3-dB frequencies. This makes the presented algorithm a useful tool for determining the boundaries in electronic or communication systems’ frequency responses. Moreover, the proposed algorithm is compatible with high-order transformations which are the limitations of general pole-zero placement techniques. The proposed method is illustrated by the examples of designing the low-pass, high-pass, band-pass, and band-stop filter.     

Stability criterion forN-dimensional digital filters

The stability requirement for one-dimensional recursive filters is well known. A stability theorem forn-dimensional recursive filters is proved wherein the denominator of the filter is ann-dimensional power series. A Tauberian theorem due to Wiener yields the desired result in the general case.     

Digital formant speech synthesis utilizing wave digital filters

Digital computer processing of speech is of much current interest. This paper examines the synthesis of speech utilizing the wave digital filter which has been shown to have low coefficient sensitivity properties and to generate smaller roundoff error than conventional filters. Also examined is the coefficient quantization in the digital formant speech synthesis model and how implementation with the wave filter may serve as a better alternative. Simulation and generation of speech confirm the feasibility and corresponding advantages of implementation with the wave digital filter compared to conventional filters.     

A nearly optimum linear-phase digital FIR filters design

A new simple method to design linear-phase finite impulse response (FIR) digital filters, based on the steepest-descent optimization method, is presented in this paper. Starting from the specifications of the desired frequency response and a maximum approximation error a nearly optimum digital filter is obtained. Tests have shown that this method is alternative to other traditional ones such as Frequency Sampling and Parks–McClellan, mainly when other than brick wall frequency response is required as a desired frequency response.     

Parallel merged multiplier-accumulator coprocessor optimized for digital filters

In an attempt to improve the speed of VLSI signal processing systems, a new architecture for a high-speed multiply-accumulate (MAC) unit optimized for digital filters is proposed. This unit is designed as a coprocessor for the LEON2 RISC processor [LEON2 Processor; 2005 [Online]. <http://www.gaisler.com/products/leon2/leon.html>]. In this work, four parallel MAC units with two dual-port coefficient register-files, a three-port general register-file and a control unit are included in the coprocessing block. With the existence of four parallel units, several SIMD format instructions have been added to LEON2 instruction set. Each MAC unit has two 16-bit inputs, 32-bit output register and a programmable round-saturate block. The MAC unit uses a new architecture which embeds the accumulate module within the partial products summation tree of the multiplier with minimum overhead. A central control unit controls inputs of the four MACs and loading of the output registers. Our experimental results demonstrate a high performance in implementation of digital filters at elevated speeds of up to 33 millions of input samples per second in a 0.18 μm technology.     

Microcomputer program for the design of digital filters

The program presented here is intended to be a design device and learning tool for digital filters. Digital filters designed with the program can be implemented by incorporation within the data analysis programs of the user. The program is written in BASIC for use with the IBM-PC, is intended to be user-friendly, and includes a great deal of filter assistance not found in other programs. An example of program use shows how one filter can be used to remove noise from respiratory waveform data.     

Parallel digital models of continuous systems and their application to digital filters synthesis

A method of parallel digital models of continuous systems and their use to digital filtering is discussed. Parallel digital models are based on the approximation of an input sampled function. The spline function is used instead of real sampled one. Convenient methods how to build parallel models are described. In addition, two particular methods for synthesis of digital filters are presented. Theoretical results have been veryfied on concrete applications.