Impulse Response Digital Filters Research Articles

Design of a class of time-constrained FIR digital filters by successive projections

Successive projection onto convex sets method is used to design a class of time-constrained finite impulse response (FIR) digital filters. This class includes Nyquist filters, partial-response FIR filters and Nth-band filter. This method is fast and very effective for filters with some time- and frequency-domain constraints, however the well-known Parks-McClellan filter design program is not suitable for designing these kinds of time-constrained FIR filters. >

Realization of IIR LDM digital filters

A method is presented of realizing an infinite impulse response (IIR) digital filter (DF) using linear delta modulation (LDM) as a simple analog/digital (A/D) converter. This method makes the realization of IIR digital filters much simpler than that of conventional ones because it does not require hardware multipliers or a pulse code modulation (PCM) A/D converter. Compared to the finite impulse response (FIR) LDMDF, this IIR LDMDF requires significantly less computation time. >

Implementation of digital filters via VLSI array processors

This paper describes the implementation of infinite impulse response (IIR) digital filters via VLSI array processors. The IIR digital filter is described by the general state-space model of a multiple-input, multiple-output discrete linear system. The implementation of the associated block parallel state-space model is also described. Finally, the implementation of a single-input, single-output time-varying digital filter is given. The throughput rate and the latency of all the above implementations are considered.

A Fast Multiplierless Architecture for General Purpose VLSI FIR Digital Filters

A multiplierless algorithm for calculating the convolution of a Finite Impulse Response (FIR) digital filter is presented. The algorithm is based on the partial slicing of input data vector words and performing the convolution in a distributed fashion. A fast, flexible and hardware efficient architecture for implementing the algorithm is described. Simulation results of the prototype one tap filter are presented, demonstrating the high speed capability of the architecture.

WMMSE design of digital filter banks with specified composite response

A new method for designing uniform and nonuniform digital filter banks with a specified composite response is presented. The composite response of the filter bank can be met either exactly or to within a given tolerance. We focus on filter banks in which the individual filters are finite impulse response (FIR) digital filters of possibly nonequal length, although the new method is applicable even to more general structures as well. The new method minimizes the weighted sum of the mean square errors in the response of the individual filters, subject to the composite response specifications. Sufficient conditions for either real, ness or phase linearity of the optimal individual filters are presented. The new weighted minimum mean square error (WMMSE) design method is interpreted from a statistical viewpoint as a maximization of the harmonic mean of the output signal-to-noise ratio (SNR) of the individual filters. The complexity of the new method is analyzed, and the design process is demonstrated via a design example.

Digital Filtering — An Interactive Computer Program for the Design and Simulation of a Finite Impulse Response (F.I.R.) Digital Filter

Digital filtering techniques have become an important part of the curriculum of electronic engineering courses. This paper details a computer-based teaching aid, for the popular BBC model B microcomputer, which may be used to design and display the characteristics of a low-pass finite impulse response (FIR) digital filter.

A design algorithm for optimal low-pass nonlinear phase FIR digital filters

The transfer function of the low-pass nonlinear phase finite impulse response (NLPFIR) digital filter is decomposed into a nonlinear phase part and a linear phase part. An algorithm is proposed to iteratively design the magnitude of the linear phase part and the squared magnitude of the nonlinear phase part by directly calling the Remez algorithm of McClellan, et al. [1]. In the design of the nonlinear phase part, we assume that the linearity constraint on the phase is dropped but the phase response is not specified. A scheme is incorporated into our algorithm so that it can design the filter with the desired ripple ratio. This approach also leads to a method for finding the minimum ripple ratio for the given orders of the two parts and band edges of the filters. The filters with ripple ratio larger than this minimum value can be designed by our algorithm and neither passband nor stopband ripples are required to be prescribed. Analysis of roundoff noise reveals that the cascade filter implementation usually needs higher wordlengths than its direct for counterpart for the same roundoff noise performance.

Design of finite-duration impulse response digital and charge-coupled device filters with arbitrary attenuation characteristics

A novel analytic technique is given, for the derivation of finite duration impulse response transfer functions which satisfy arbitrary attenuation characteristics, with or without exact linear phase at all frequencies. The method uses a parameter for the determination of the stopband attenuation at the outset, and the rate of cutoff and the passband performance can be improved by increasing the order of the filter. The resulting solutions provide a marked improvement over the available analytic solutions, particularly where monotonic passband behaviour is required. The technique is also characterised by its simplicity and gives explicit expressions for the coefficients of the transfer function in the z-domain. This obviates the need for the various transformations commonly employed, and consequently improves the accuracy in determining the filter coefficients. The realisation of the resulting functions can be accomplished in either digital or charge-coupled device form.

Two-Dimensional FIR ADM Digital Filters

In this paper the realization and performance of a twodimensional finite impulse response (FIR) digital filter using adaptive delta modulation (ADM) have been studied. The analytical results have been verified by computer simulation. Also, it has been shown that onedimensional DM is adequate in the realization of a two-dimensional FIR ADM digital filter. Since the ADM digital filter requires no multiplication, it offers many advantages over conventional PCM filters in cost reduction, hardware simplicity, and reduced size.

Generalization of the window method for FIR digital filter design

A generalization of the conventional window method for the design of finite impulse response (FIR) digital filters is presented by including nonequal passband and stopband ripple specifications in the design process. Typically, this results in a savings of up to 30 percent in filter length in comparison to the conventional approach.

A pipelined recursive residue number system digital filter

The well-known advantages of pipelining as applied to Finite Impulse Response (FIR) Residue Number System (RNS) arithmetic digital filters is extended to the important area of Infinite Impulse Response (IIR) digital filters through a new technique based on augmentation of the IIR transfer function. Through this technique, pipelined IIR filters based on RNS Read-Only-Memory (ROM) table look-up techniques can be designed which offer throughput rates equal to the table look-up time of the ROM's. This high-speed realization can be achieved even though the recursive filter algorithm requires multiple delays in realizing the output of the filter. For the example of a typical second-order IIR filter, the pipelined structure represents a five-fold increase in speed over standard techniques. Higher order realizations will yield proportionately higher speed improvements. Although the new technique does increase somewhat the hardware complexity of the filter, the increase in speed will often justify the additional hardware. The paper discusses the basic technique, stability considerations, and hardware realizations.

An efficient iterative algorithm for designing optimal recursive digital filters

A new iterative algorithm is presented for the efficient design of unconstrained and constrained infinite impulse response (IIR) digital filters. Both in the unconstrained and constrained cases, the numerator and denominator of the filter transfer function are designed iteratively by recourse to the Remez algorithm and to appropriate design parameters and criteria at each iteration. This makes it possible for the algorithm to be implemented by means of a short main program which uses (at each iteration) the finite impulse response (FIR) filter design algorithm of McClellan et al. as a subroutine. As a consequence, the entire design procedure proves to be very efficient. The approach taken also permits the filter to be designed with a desired (passband-to-stopband) ripple ratio. Typically, the design algorithm converges to the optimal solution within a few iterations. Several examples are given to illustrate the procedure. The filter design computer program is provided in the Appendix.

Design of circularly symmetric two-dimensional FIR digital filters employing transformations with variable parameters

A modification of the trasformation method used for the design of two-dimensional (2-D) circularly symmetric finite impulse response (FIR) digital filters from one-dimensional (1-D) filters is described. This modification entails the embedding of variable parameters in the different transformations applied to the different factors of the 1-D reference function. This new method results in the design of 2-D FIR filters whose frequency response characteristics meet the cutoff boundary specifications more closely than the transformations without the modification. This method is quite useful for the design of 2-D FIR filters with multiple cutoff boundaries such as bandpass filters.

Performance Analysis of FIR ADM Digital Filters

Performance and realization of finite impulse response (FIR) digital filters that use an adaptive delta modulator as an analog/ digital converter have been studied. These filters require no multiplication and offer many advantages over conventional PCM filters including low power consumption, small size, and cost effectiveness. Analytical formulas have been derived for the expected mean-squared errors and also for the word length necessary to achieve the desired performance. Computer simulation has been done to optimize the parameter values and to verify the results of performance analysis. In addition, design of FIR ADM digital filters for processing single and multichannel signals has been considered.

Application of digital filters in the processing of eye movement data

Digital filter techniques have been applied to the analysis of eye movement data. Methods were developed to calculate eye velocity and eye acceleration in real-time from an electronystag-mogram (ENG) signal that was recorded using a one-pole RC high-pass filter in the preamplifier. Nonrecursive, finite impulse-response digital filters were designed to remove the effects of the RC high-pass filter and calculate the first and second time derivatives of the ENG signal, as well as remove high-frequency noise. Applying these new techniques to the analysis of vestibular nystagmus enables estimation of the transfer characteristics of the vestibuloocular system.

SHARF convergence properties

A class of stable algorithms for adapting infinite impulse response (IIR) digital filters based on the concepts of nonlinear stability theory prominent in the control literature is emerging. While this class of adaptive filters offers much promise in practical applications, little has been done toward providing a characterization that would guide selection of design parameters such as adaptation constants and error smoothing coefficients. This paper focuses on the simplest well-behaved member of this class of adaptive recursive filters, SHARF. Progression from a local linearization of the nonlinear parameter estimate convergence behavior, through an idealized eigenvalue/eigenvector analysis of the parameter estimate time-varying recursion, to Lyapunov function establishment for the full output and parameter error system reveals the exponential, local, nongradient descent convergence character of SHARF and provides initial insight into the effects of adaptation constants and error smoothing coefficients on these characteristics.

SHARF convergence properties

A class of stable algorithms for adapting infinite impulse response (IIR) digital filters based on the concepts of nonlinear stability theory prominent in the control literature is emerging. While this class of adaptive filters offers much promise in practical applications, little has been done toward providing a characterization that would guide selection of design parameters such as adaptation constants and error smoothing coefficients. This paper focuses on the simplest well-behaved member of this class of adaptive recursive filters, SHARF. Progression from a local linearization of the nonlinear parameter estimate convergence behavior, through an idealized eigenvalue/eigenvector analysis of the parameter estimate time-varying recursion, to Lyapunov function establishment for the full output and parameter error system reveals the exponential, local, nongradient descent convergence character of SHARF and provides initial insight into the effects of adaptation constants and error smoothing coefficients on these characteristics.

New methods for the design of recursive digital filters in the time domain

This paper presents new methods for the design of optimal and suboptimal recursive digital filters in the time domain. The proposed methods are based on the approximation of the desired impulse response of a digital filter. Since the duration of impulse response of a recursive digital filter is not finite, it is desirable to use an infinite interval performance index from the point of stability. First, a method for the design of an optimal recursive digital filter is presented. The optimal solution is obtained by minimizing the given infinite interval performance index. Multivariable optimization techniques such as the Fletcher-Powell method can be applied to obtain the optimal solution. However, when the order of a filter becomes high, it is difficult to obtain the optimal solution. Next, suboptimal recursive digital filters with parallel and cascade structures are proposed. When these methods are used, it becomes easy to design a high-order suboptimal filter. Various numerical examples are shown to illustrate the results in detail.

I.I.R. digital filter design using constrained optimisation techniques

A new design method for all-pole infinite impulse response (i.i.r.) digital filters is introduced. The method involves minimising the area between the ideal lowpass filter response in the passhand and the actual passband response, subject to a quadratic constraint which ensures filter realisability. A unique solution is obtained to the minimisation which relates the filter weights to the eigenvector of a Toeplitz matrix. The filters are seen to have a small ripple in the passhand and a sharp cutoff in the stopband.

A Gait Analysis Subsystem for Smoothing and Differentiation of Human Motion Data

A computer-based subsystem has been implemented for the smoothing and differentiation of human motion data. Nonrecursive finite impulse response digital filtering has been employed for this purpose. Filter cutoff frequency was determined using a statistical error analysis. The method of data differentiation used here is compared to other methods presented in the literature.