Frequency Sampling Filter Research Articles

Design of Identification Experiments for Step Response Models: Open Loop Case

This paper examines the problem of input signal design for open-loop identification experiments. The objective is to obtain an accurate step response model for the process by minimizing the area enclosed by the statistical confidence bounds surrounding the step response estimate. The approach used to study this problem is based on the frequency sampling filter (FSF) model structure. The results provide the optimal distribution or percentage of energy in the input signal that should be present at the FSF centre frequencies.

Real-time estimation of process frequency response and step response from relay feedback experiments

This paper describes two new methods for obtaining frequency response and step response models for processes operating under relay feedback control. Both methods are based on the frequency sampling filter (FSF) model structure and a recursive least-squares (RLS) estimator. With the first method, a standard relay feedback experiment is performed and the FSF/RLS algorithm is used along with the generated input–output data to provide real-time estimates of the process frequency response at the dominant harmonics of the limit cycle. In the second method, a novel relay experiment is proposed that involves switching the error signal back-and-forth between a standard relay element and an integrator in series with a relay. The FSF/RLS algorithm is then applied to the generated process input–output data to obtain a real time estimate of the process step response.

A design technique for 2-D linear-phase frequency-sampling filters with fourfold symmetry

A two-dimensional (2-D) frequency-sampling filter approximates a desired frequency response by interpolating a frequency response through set frequency samples which are samples taken from the filter's frequency response. In this brief, a technique for designing 2-D Type 1-1, Type 1-2, Type 2-1, and Type 2-2 frequency-sampling filters that have real impulse responses, linear phase, and fourfold symmetry is developed that controls interpolation errors and approximates a desired frequency response by minimizing a weighted mean-square error over the passbands and stopbands subject to constraints on the filter's amplitude response.

Design of Frequency Sampling Filters Using Cyclotomic Polynomials

Frequency sampling filters (FSFs) are of interest to designers of filter banks due, in part, to their intrinsic low complexity and linear phase behavior. FSF designs rely on exact pole-zero annihilation and are often found in embedded applications. Exact FSF pole-zero annihilation can be guaranteed by using polynomial filters defined over an integer ring in the residue number system (RNS) along with algebraic integers. An FPGA implementation example is presented which offers an 86% complexity reduction compared with standard nonrecursive FIR designs.

Automatic design of frequency sampling filters by hybrid genetic algorithm techniques

A new method of designing recursive and nonrecursive frequency sampling filters is presented. We investigate the use of a hybrid real-coded genetic algorithm (GA) for optimising transition sample values to give the maximum stopband attenuation. A modification allows the coefficient wordlength to be optimized concurrently, thereby reducing the overall number of design steps and simplifying the design process. The technique is able to consistently optimize filters with up to six transition samples. Designing digital filters is a complex process involving optimization at several discrete design steps. The techniques presented could form the basis for integrating several of the optimizations. Investigations into increasing this integration by using a binary-coded GA to optimize nonlinear phase, quantized coefficient FIR filters are introduced, with an analysis of the difficulty of the problem from a GA perspective.

Application of the Frequency Sampling Filter Model in Process Identification: An Industrial Cast Study

Abstract This paper examines the application of the frequency sampling filter (FSF) model in process identification. The study has been performed on a refinery distillation train with the objective being to obtain step response models from plant dynamic test data for model predictive controller design. The results focus on: (a) selection of the FSF model-based multivariable system structure using the sum of squared true prediction errors (PRESS): (b) development of noise models for use in prefiltering to remove the effect of any feedback on the step response estimates and to produce white residuals for estimation of the covariance matrix; and (c) presentation of statistical confidence bounds for the step response models. The FSF results are compared with those obtained using the finite impulse response (FIR) model structure and with results obtained from a commercially available identification software package.

Frequency-sampling filters: An improved model structure for step-response identification

This paper presents a new methodology for step-response identification using the frequency-sampling filter (FSF) model. The advantages of the FSF model structure over the popular finite-impulse-response (FIR) model are (i) the number of parameters to be estimated is independent of the choice of sampling interval, and is generally far fewer than the number required by the FIR model to obtain an accurate estimate of the step response, and (ii) the general conditioning of the correlation matrix is better with the FSF model because of the reduction in the number of parameters that need to be estimated and to the narrow-bandpass nature of the frequency sampling filters.

Development of quality bounds for time and frequency domain models: application to the Shell distillation column

Statistical confidence bounds are developed for frequency response and step response models estimated from process input-output data using the frequency sampling filter model structure. The frequency domain bound is an extension of earlier work by the authors (Arifin et al., Journal of Process Control, 1995, 5, 71–76) and the time domain bound is a new result. These bounds provide the engineer with a measure of the quality of the estimated model, and therefore an indication of which aspects of the model are reliable and which aspects require further improvement. The Shell distillation column benchmark problem introduced by Cott (Journal of Process Control, 1995, 5, 60–70) is used for illustrative purposes.

A computationally efficient technique for designing frequency sampling filters

In a recent paper, a technique for designing linear phase frequency sampling filters was proposed that approximates a desired frequency response by minimizing the mean square error over the stopbands subject to constraints on the filters amplitude response. This technique results in a large number of simultaneous linear equations the solution of which determines the filter's impulse response. The filter's frequency samples which are used to implement the filter are then determined by computing the discrete Fourier transform of this impulse response. In this brief, a modification of this technique is developed. This modified technique also approximates a desired frequency response by minimizing the mean square error over the stopbands subject to constraints on the filter's amplitude response. Additionally, however, it allows passbands to be approximated by a weighted mean square error. This modified technique results in a set of simultaneous linear equations, the solution of which directly determines the filter's nonzero frequency samples. Because the number of nonzero frequency samples is typically much less than the number of impulse response elements, this technique requires a significantly smaller number of simultaneous linear equations than the other technique.

Frequency Sampling Filters: An Improved Model Structure for Step Response Identification

This paper presents a new methodology for step response identification using the frequency sampling filter (FSF) model. The advantages of the FSF model structure over the popular finite impulse response (FIR) model are: (1) the number of parameters to be estimated is independent of the choice of sampling interval and is generally far fewer than the number required by the FIR model to obtain an accurate estimate of the step response, and (2) the general conditioning of the correlation matrix is better with the FSF model due to the reduction in the number of parameters that need to be estimated and to the narrow bandpass nature of the frequency sampling filters.

A new approach to the identification of pH processes based on the Wiener model

This paper presents a new approach to the identification of pH processes based on the Wiener model structure (a dynamic linear element in series with a static nonlinearity). A frequency sampling filter model is used to represent the dynamic linear element and a simple least-squares algorithm is applied to simultaneously estimate the parameters of the linear subsystem and the inverse static nonlinearity. Experimental results obtained from a pilot-scale pH process are presented to illustrate the performance of this new scheme. A key benefit of using this approach is that an estimate of the pH titration curve can be obtained in significantly less time as compared to more traditional approaches.

Adaptive Feedforward Control Schemes in Time-Domain, Frequency-Domain and Wavelet Transform Domain

In the present paper, we investigate a stability-guaranteed adaptive algorithm for an adaptive feedforward controller, which is implemented by three kinds of approach: a time-domain approach using an IIR type of adaptive filter, a frequency-domain approach using an adaptive frequency sampling filter (FSF), and a wavelet transform domain approach using an adaptive wavelet packet futer bank (WPFB). In a case when an external signal has power spectrum localized in low frequency range as in active noise control, the adaptive WPFB based algorithm can attain fast and stable convergency. Comparison among three proposed algorithms is made in adaptive active noise control.

Fixed point roundoff noise in frequency sampling filters

A frequency sampling filter which is a finite impulse response digital filter uses a recursive structure that requires exact pole zero cancellation on the unit circle. When implemented with digital technology, errors due to finite length registers and finite precision arithmetic can prevent exact pole zero cancellation making the filter unstable. To guarantee stability, the poles and zeros on the unit circle are moved to a circle of radius r where 0 < r < 1. Most frequency sampling filter design techniques determine optimal frequency responses for r = 1 and then chose a value of r, 0 < r < 1, near to 1 so that the filter's frequency response does not differ significantly. Recently, other techniques have been presented that determine optimal frequency responses for 0 < r < 1. In this paper, the fixed point roundoff noise of Type 1 and Type 2 frequency sampling filters is determined as a function of register length, time and the value of r. An example demonstrates that for a fixed register length and output noise level, a frequency sampling filter designed with 0 < r < 1 can approximate a linear phase filter better than a frequency sampling filter designed with r = 1.

A method of designing filter banks with alias‐free characteristics at equally spaced frequency points

AbstractIt is known that the quadrature mirror filter (QMF) bank used for subband coding cannot avoid the aliasing effect for adaptive signal processing or spectral estimation, etc. A new class of filter banks is desired for these applications where the effect of aliasing should also be considered.In this paper, a new class of filter bank is reported which has alias‐free characteristics at equally spaced frequency points. This filter bank is called frequency sampling filter bank, and it consists of nonrecursive FIR filters. This paper also reports design methods for two types of the filter banks, keeping in mind the reduction in amount of calculation for practical implementation. In one method, all channel filters of the filter bank are determined by complex exponential modulation of a prototype filter. the other method determines the channel filters by cosine or sine modulation of a prototype filter. Both designs have the forementioned aliasing characteristics, and an efficient structure based on polyphase configuration is possible.

Summary of the process identification workshop at the 1992 Canadian chemical engineering conference

Abstract The highlights of the workshop can be summarized as follows: (1) The workshop reaffirmed that data prefiltering is a necessary step in the model building process in order to ensure nonstationary disturbances are not modelled as part of the process; (2) In addition, the workshop confirmed that improvements in the steady-state gain are seen if input test signals are carefully designed using the disturbance dynamics and the expected movement of the manipulated variables while under control as guides. As a result, the majority of input test signals should have significantly more power at low frequencies in order to improve the steady-state gain estimates; (3) Data prefiltering and input signal design decisions appear to affect the final model quality much more than the type of model structure used (Box-Jenkins, finite impulse response, frequency sampling filter); (4) Although the newer techniques presented by some of the university groups do not necessarily yield better quality models, they simplify the model building process by automating model building selections, or by providing better descriptions of model inadequacies.

Identification of the Shell distillation column using the frequency sampling filter model

Abstract This paper illustrates the application of the frequency sampling filter model to the identification of the Shell distillation column. The approach presented here produces an estimate of the process frequency response matrix along with probabilistic confidence bounds on the modelling error, and also an estimate of the process step responses. The role of disturbance models in the design of the identification experiment is emphasized.

On the realization of minimum noise and low noise frequency sampling FIR filters

In this work the finite precision effects issue connected to the frequency sampling realization of FIR filters is considered. In particular, the performance of the frequency sampling filters is evaluated in terms of noise gain for the following three different realizations of the second-order elementary sections: the canonical direct form, the minimum roundoff noise structure, and the suboptimal state-space structure introduced by Bomar (1985). An interesting property on the design of minimum noise second-order sections embedded in the frequency sampling structure, is given. The results obtained show that the realizations via minimum noise structures and Bomar's structures greatly outperform the realizations via canonical direct form structures, and, for very narrow-band filters, have noise gain comparable to that of nonrecursive direct realization.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A frequency sampling filter design method which accounts for finite word length effects

System functions of frequency sampling filters require pole-zero cancellations on the unit circle. For practical implementations, finite word length effects usually prevent pole-zero cancellations which can result in filter instability. The article develops an optimization method for designing a modified frequency sampling filter which is guaranteed to be stable. >

A subband adaptive filter allowing maximally decimation

Conventional subband adaptive filters (ADF) using filter banks have shown degradation in performance because of the nonideal nature of filter banks. For this problem, the authors propose an alias free subband structure for adaptive filtering using polyphase frequency sampling filter (FSF) banks. As a preliminary, they make it clear that the conventional polyphase discrete Fourier transform (DFT) bank is equivalent to a class of the FSF bank. Then, they propose a new class of ADF using the FSF banks based on the frequency sampling theorem. As a result, the proposed technique enables subband adaptive filtering without the degradation effect of both the aliasing and cross terms, even if one chooses critical subsampling.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Optimization approach to the design of frequency sampling filters

Many digital signal processing applications require linear phase filtering. For applications that require narrow-band linear phase filtering, frequency sampling filters can implement linear phase filters more efficiently than the commonly used direct convolution filter. In this paper, a technique is developed for designing linear phase frequency sampling filters. A frequency sampling filter approximates a desired frequency response by interpolating a frequency response through a set of frequency samples taken from the desired frequency response. Although the frequency response of a frequency sampling filter passes through the frequency samples, the frequency response may not be well behaved between the specific samples. Linear programming is commonly used to control the interpolation errors between frequency samples. The design method developed in this paper controls the interpolation errors between frequency samples by minimizing the mean square error between the desired and actual frequency responses in the stopband and passband. This design method describes the frequency sampling filter design problem as a constrained optimization problem which is solved using the Lagrange multiplier optimization method. This results in a set of linear equations which when solved determine the filter's coefficients.