On the optimum design of symmetric two-dimensional IIR digital filters with coefficients of finite word length

A method is described for the design of octagonally symmetric, non-symmetric half plane, two-dimensional IIR digital filters with integer coefficients. The design problem is formulated as an integer non-linear problem and the solution is achieved via an integer non-linear optimization algorithm. An example illustrates the features of the proposed approach.     

On the design of 2D IIR digital filters using penalty optimization techniques

In this paper an efficient technique is developed for the design of two-dimensional recursive digital filters in the frequency domain. the formulation of the design problem is based upon a rational approximation method in parallel with a suitable interior penalty technique. the structure of the proposed approach permits one to include in the design optimization problem additional constraints related to the stability, linear phase and symmetries properties of the resultant filter. In contrast with previous design methods, the coefficients of the filters are determined directly and it is not required to apply any ‘inverse’ or stabilization technique. Analytical examples illustrate the features and effectiveness of the proposed approach.     

A fast linear programming approach to the design of 1D IIR digital filters

A general method is proposed for the design of optimal 1D IIR digital filters via linear programming. the method is based upon the formulation of an appropriate linear problem which assures satisfactory approximation error for the filter's magnitude frequency response. the linear problem does not require differential correction methods or other iterative techniques for its solution, thus resulting in a computationally efficient algorithm. Analytical examples are presented to illustrate the efficiency of the method for the design of stable 1D recursive digital filters.     

Comparative study of finite word length effects in digital filter design via the shift and delta transforms

This paper deals with the influence of the rounding of parameters represented in floating-point number systems in high-speed digital signal processing and control. It is shown that in high-performance applications, that may involve high sampling rates and/or shorter word lengths, the usual shift operator formulation is inferior to an alternative formulation based on the delta operator. The analysis is illustrated by an example.     

On hilbert space design of least-weighted-squares digital filters

Numerical convolution operations, executed on noise contaminated signals, are approximated by FIR digital filters in such a way that the effect of random coloured noise is minimized. Using elementary Hilbert space techniques, the filter functions of certain least-weighted-squares digital filters are derived explicitly by the use of discrete orthogonal functions (e.g. Hahn polynomials). the approach is suitable especially for narrowband operations such as smoothing, narrowband differentiation, and narrowband deconvolution (resolution enhancement). Examples of linear-phase lowpasses with monotone passband, obtained with the aid of Hahn polynomials, are discussed in detail. Also the well-known maximally flat digital lowpasses which can be derived with the aid of Krawtchouk polynomials, and narrowband differentiators are considered. In the case of least-weighted-squares approximation by Hahn polynomials, powerful recursive realizations can be developed to reduce computational requirements.     

Iterative design of two-channel IIR perfect construction QMG filters

A simple rapidly convergent method is described for the design of two-channel IIR perfect reconstruction quadrature mirror filters. For any prescribed characteristic, it has been shown how one can construct a stable two-channel IIR banks, starting from any random transmission zero locations. A simple rapidly convergent search algorithm is also described for the determination of the exact locations of these transmission zeros, such that the filter has equiripple pass and stop responses as well as almost constant group delay. Illustrative examples are also given to show that the proposed design method competes very well with the existing design methods. © 1998 John Wiley & Sons, Ltd.     

On the sensitivity analysis of digital filters

A very quick and simple algorithm for the overall evaluation of the sensitivity performance of a digital filter is introduced. To this end, it is shown that the sensitivity of the system function with respect to a given coefficient comes out equal to the output of a special digital network with unitary input. Having defined, then, an ‘overall sensitivity index’ as the sum of the various network sensitivities, it is shown that such an index can still be considered as the output of a digital network with unitary input. This network is composed of two subnetworks, identical to the original circuit, connected by a special set of branches.     

Synthesis of IIR digital filters exhibiting simultaneous amplitude and phase responses for VLSI implementations

A method is described for the design and implementation, in a double-lattice form, of selective linear phase digital filters. It is shown that these filters are optimum in the sense that all available degrees of freedom are used in adjusting the filter parameters to meet the specified characteristics. The designed filters, apart from satisfying the linear phase requirement, exhibit equiripple loss response over both the pass- and stopbands. A novel computationally efficient method based on computing the complex cepstrum is proposed for the construction of orthogonal double-lattice structures that realize the designed filters. It is based on the important property of cepstrum functions, namely decomposing mixed sequences into both minimum and maximum phase sequences. Illustrative examples are given to support the theoretical analysis. © 1997 John Wiley & Sons, Ltd.     

The design of low noise digital filters with controlled dynamic range

A novel digital filter structure, that allows proper positioning of the zeros of the noise transfer functions to reduce the output roundoff noise, is introduced. Relations between zero locations, roundoff noise and dynamic range are derived and are then utilized in an heuristic optimization method for synthesizing a low noise scaled digital filter structure. Illustrative examples supporting the proposed approach are included.     

On the design of multi notch filters

A methodology for designing FIR multi notch filters (NFs) derived from second‐order prototype IIR NFs is suggested. Rejection bandwidth for the designed filter can be controlled by suitable choice of ‘r’, the pole radius of the IIR prototype NFs. The suggested multi NF can also be adapted to eliminate second‐, third‐ and fourth‐order harmonics of periodic noise besides the fundamental noise frequency component. A special case when two notch frequencies ω₁ and ω₂ are such that [(cosω₁)(cosω₂) = ? 1/2] has also been discussed. The IIR multi NF design for this special case results in reduction of the number of multipliers without affecting the response of the desired NF. For the aforereferred condition, the required coefficients of impulse response of FIR multi notch filter get reduced to almost half in number resulting in reduced computations. The number of zero coefficients further reduces with increase in ‘r’ value. In addition, the frequency response becomes better, with reduced ripples in the pass bands, when ‘r’ is increased and length ‘L’ of the FIR NF is chosen appropriately. Copyright © 2010 John Wiley & Sons, Ltd.     

On the design of adaptive notch filters

In instrumentation and other applications, the on‐line estimation of the frequency and amplitude of a noise‐corrupted sinewave is of great practical interest. Recently an adaptive notch filter (ANF) with global convergence properties has been developed, and is a candidate approach to our problem. This paper analyses the transient and noise properties of this ANF and equips the method with design equations. Using frequency ranges greater than (up to 2 decades) and signal/noise ratios less than (down to ?16 dB) those commonly found in the ANF literature, it is verified by extensive simulations that the new frequency estimator has excellent tracking and noise‐rejection properties, provided that the signal/noise ratio is not too small. A comparison is made of its behaviour with that of a phase‐locked loop, a method commonly used in practice. Copyright © 2001 John Wiley & Sons, Ltd.     

扫频型接地电阻测量中IIR数字滤波器的设计

为克服传统单一异频法测量精度低的缺点,本文将扫频测量法应用到接地电阻测量中.信号源采用异频扫频电源,测量系统采用IIR数字滤波器进行选频滤波以减弱干扰信号.文中着重介绍了测量系统中IIR数字滤波器的设计,利用Matlab的可视化工具FDATool(Filter Design and Analysis Tool)进行滤波器设计并结合Simulink进行模拟仿真.根据信号源的一系列频率对应设计得到一系列数字滤波器,然后在DSP上编程运算.其特点是可根据设计要求实现可变中心频率的滤波器,进而在高速DsP中实时处理,而且方便调整滤波器参数,直观简便,有利于滤波器的最优化设计.     

Time domain analysis and design of multirate wave digital filters

A generalized time domain approach is described for the analysis and design of wave digital filters capable of performing sampling rate alterations whether integer or non-integer. It is based on sequential computation of the filter's system response; then this discrete response is reduced to a rational function form. the proposed approach is characterized by its simplicity as well as its ability to analyse and design multistage, multirate wave digital structures. Illustrative examples are also given.     

Computer-aided design of stable recursive digital filters from magnitude specifications

This paper presents a method of designing one- and two-dimensional recursive digital filters making use of the properties of bilinear transformation of strictly Hurwitz polynomials. The result is a stable digital filter in both one- and two-dimensional cases, which requires no further testing for stability. The well known unconstrained minimization technique of Fletcher—Powell is used, making use of a transformation of optimization parameters to satisfy the mild constraints of stability. This method is considered to be more efficient on an overall basis than the existing l_p design technique of Maria and Fahmy. Nor does it rely on Deczky's theorem to ensure a stable filter which may sometimes lead to unstable solutions in the two-dimensional case. An example is provided illustrating the method.     

A simple derivation of the spectral transformations for IIR filters

A simple method is given for deriving the spectral transformations for infinite-impulse response (IIR) filters, which can be used to transform a prototype low-pass (LP) digital filter to another LP, high-pass (HP), bandpass (BP), or band-stop (BS) digital filter with prescribed passband edge(s) and the same tolerances as those of the prototype. The method is based on a combination of bilinear transformation with the analog frequency transformation and is simpler-conceptually, as well as from the calculation point of view-than the conventional method based on all-pass transformation functions.     

On the design of RC-active follow-the-leader. Feedback filters

For RC-active filters of the ‘follow-the-leader’ feedback type, a synthesis procedure is presented that is suitable for application also to the general case in which differently tuned biquadratic functional blocks are used. Their losses can either be concentrated in one of the blocks, or given by a prescribed distribution.     

Letter to the editor design of low-sensitivity quarter-plane recursive 2d digital filters

A new technique is given for designing two-dimensional quarter-plane recursive digital filters. These filters have low sensitivity in the passband. an implementation scheme using complex multipliers is also given for these filters.