A technique for realizing linear phase IIR filters

A real-time IIR filter structure is presented that possesses exact phase linearity with 10~1000 times fewer general multiplies than conventional FIR filters of similar performance and better magnitude characteristics than equiripple or maximally flat group delay IIR filters. This structure is based on a technique using local time reversal and single pass sectioned convolution methods to realized a real-time recursive implementation of the noncausal transfer function H(z^-1). The time reversed section technique used to realize exactly linear phase IIR filters is described. The effects of finite section length on the sectional convolution are analyzed. A simulation methodology is developed to address the special requirements of simulating a time reversed section filter. A design example is presented, with computer simulation to illustrate performance, in terms of overall magnitude response and phase linearity, as a function of finite section length. Nine example filter specifications are used to compare the performance and complexity of the time reversed section technique to those of a direct FIR implementation     

Equiripple phase for IIR all-pass filters

A method is presented for designing IIR all-pass filters, the phase of which approximates a given phase in the equiripple (Chebyshev) space. The method is exclusively based on the solution of the linear equation system.<>     

A new approach to the design of complex all-pass IIR digital filters

A new method is proposed for designing complex all-pass IIR filters, the all-pass IIR filters with complex coefficients, in this paper. By minimizing the integration of certain square phase error over interested frequencies, an eigenvector of an appropriate real, symmetric and positive-definite matrix is computed to get the filter coefficients. The stability is achieved by specifying properly the desired phase specifications. If an appropriate iterative process is used, equiripple complex all-pass filter design can be obtained. The method is simple and the performance is comparable to the existing methods. Several examples are presented to demonstrate the effectiveness of the approach.     

Band-pass filters with linear phase

A set of techniques has been developed which permits the simultaneous realization of flat pass band transmission (±0.15 db experimental) linear phase (to within ±5° experimental) over most (1 - 1/N) of the nominal pass band, where N is the number of "in-band" poles. Outside the pass band, the attenuation skirts are steep; experimentally, 40 db has been obtained within 1/N of the nominal filter bandwidth. Shunt L and/or stray capacitance are easily taken into account in the design; in particular, crystals as well as lumped LC have been used. The procedures can accommodate any amount of series resistance in inductors at the expense of flat loss, without any essential change in the computed values of inductors, capacitors, or resonant frequencies. The sensitivity of the network transmission to component errors is modest; discrepancies in the impedance level or tuning of a given constituent resonance in the network branches affect the characteristic mainly in the vicinity of that resonance.     

A new method for the design of IIR filters with flat magnitude response

This paper presents a new direct design of infinite-impulse response (IIR) filters with a flat magnitude response in both passband and stopband (Butterworth filters). The design specifications are passband and stopband frequencies and passband droop and stopband attenuation. The approach is based on an allpass filter with flatness at frequency points /spl omega/=0 and /spl omega/=/spl pi/. Depending on the parity of the IIR filter order, the allpass filter is either real or complex. However, in both cases, the resulting IIR filter is real.     

Sufficient stability bounds for slowly varying direct-formrecursive linear filters and their applications in adaptive IIR filters

This article derives a sufficient time-varying bound on the maximum variation of the coefficients of an exponentially stable time-varying direct-form homogeneous linear recursive filter. The stability bound is less conservative than all previously derived bounds for time-varying IIR systems. The bound is then applied to control the step size of output-error adaptive IIR filters to achieve bounded-input bounded-output (BIBO) stability of the adaptive filter. Experimental results that demonstrate the good stability characteristics of the resulting algorithms are included. This article also contains comparisons with other competing output-error adaptive IIR filters. The results indicate that the stabilized method possesses better convergence behavior than other competing techniques     

A design of linear-phased IIR Nyquist filters

This paper discusses a new method of designing linear-phased IIR Nyquist filters with zero intersymbol interference. The filters designed by this method possess linear-phase characteristics and are lower in order than other Nyquist filters designed by existing methods. Expressions are derived for zero-phased IIR Nyquist filters and efficient design methods are examined for them. The opted design method is based on an iteration process, and in each iteration step a modified version of the Remez exchange algorithm is used. In addition, the implementation of the designed zero-phased IIR filters is considered. Finally, the proposed design method is demonstrated through various design examples     

A WISE method for designing IIR filters

The problem of designing optimal digital IIR filters with frequency responses approximating arbitrarily chosen complex functions is considered. The real-valued coefficients of the filter's transfer function are obtained by numerical minimization of carefully formulated cost, which is referred here to as the weighted integral of the squared error (WISE) criterion. The WISE criterion linearly combines the WLS criterion that is used in the weighted least squares approach toward filter design and some time-domain components. The WLS part of WISE enforces the quality of the frequency response of the designed filter, while the time-domain part of the WISE criterion restricts the positions of the filter's poles to the interior of an origin-centred circle with arbitrary radius. This allows one not only to achieve stability of the filter but also to maintain some safety margins. A great advantage of the proposed approach is that it does not impose any constraints on the optimization problem and the optimal filter can be sought using off-the-shelf optimization procedures. The power of the proposed approach is illustrated with filter design examples that compare favorably with results published in research literature     

Lowpass digital filters with linear phase

A method of synthetising lowpass recursive digital filters is given in the letter. The method relies on the properties of orthogonal functions on the z plane and the impulse response of an ideal lowpass linear phase filter. Considerable saving in computation and storage appears to have been achieved by this method compared with the nonrecursive (with window functions) truncation method.     

A polynomial-operator-based DFIIt structure for IIR filters

In this paper, based on a polynomial-operator approach, a new structure is derived. This structure is a generalization of the transposed direct-form II structures in the conventional shift operator and the prevailing delta operator. The use of polynomial operators provides more degrees of freedom to minimize the roundoff noise gain of the filter without increasing the implementation complexity. Numerical examples are presented to illustrate the design procedure.     

The gamma-filter-a new class of adaptive IIR filters withrestricted feedback

Generalized feedforward filters, a class of adaptive filters that combines attractive properties of finite impulse response (FIR) filters with some of the power of infinite impulse response (IIR) filters, are described. A particular case, the gamma filter, generalizes Widrow's adaptive transversal filter (adaline) to an infinite impulse response filter. Yet, the stability condition for the gamma filter is trivial, and LMS adaptation is of the same computational complexity as the conventional transversal filter structure. Preliminary results indicate that the gamma filter is more efficient than the adaptive transversal filter. The authors extend the Wiener-Kopf equation to the gamma filter and develop some analysis tools     

A comparison of LTE channelizers implemented with linear phase m-path recursive filters and FIR filters

Cell sites repeaters may receive a composite signal containing a mix of long term evolution channels with bandwidths of 5, 10, 15, and 20 MHz and be required to rearrange the frequency plan of the channels or to drop and insert specific channels prior to transmitting the altered composite signal. The straight forward approach to this task is to down-convert, and down-sample each channel in the mix and then up-sample and up-convert and merge the new traffic mix. The filters applied to the up and down conversion task as well as the up and down sampling task would likely be linear phase finite impulse response (FIR) filters because of the ease with which the resampling task can be embedded in the filtering task. We present an alternate filter structure formed from linear phase recursive filters and compare their performance and computational complexity with their FIR filter counterparts. We show that the recursive filter version of the channel extractor requires significantly few arithmetic operations and actually outperforms the non-recursive version as demonstrated by the error vector magnitude of the two options.     

Reduced order IIR approximation to FIR digital filters

An algorithm for designing an infinite-impulse-response (IIR) stable filter using a finite-impulse-response (FIR) given filter, with the objective of reducing the delay and order, is described. The design is in the time domain using the least-squares-inverse algorithm, which is briefly described. In this method, the numerator of the approximated filter is part of the FIR filter itself and no calculations and minimization are needed to find the numerator coefficients (except finding the FIR roots). An error analysis between the given FIR and approximated IIR filters is provided. This error analysis enables the designer to fix a design parameter, often unnoted, keeping the energies of the approximated and original filters equal. Results and two illustrative examples are presented     

On the approximation of the magnitude response of two-dimensional IIR digital filters using linear programming

The design of two-dimensional IIR digital filters is approached using linear-programming techniques. The problem is formulated as an approximation problem and filter frequency response characteristics are represented via the square of the magnitude of the filter transfer function. An appropriate approximation error is minimized leading to a linear problem formulation. The latter problem does not require differential correction methods for its solution, thus resulting in a computationally efficient algorithm. Stability conditions and symmetry considerations are easily accounted for. The linear programming approach assures convergence of the solution to a global minimum, among other advantages over nonlinear methods. Several examples illustrate the strength and effectiveness of the methodology.     

Multidimensional IIR filters and robust rational interpolation

It is well-known that IIR filters can have a much lower order than FIR filters with the same performance. On the downside is that the implementation of an IIR filter is an iterative procedure while that of an FIR filter is a one-shot computation. But in higher dimensions IIR filters are definitely more attractive. We offer a technique where the filter’s performance specifications, stability constraints, its convergence speed and a protection against possible adverse effects of perturbations are all included in the design from the start. The technique only needs an off-the-shelf LP solver because the filter is obtained as a Chebyshev center of a convex polytope. The method deals with general non-causal non-separable filters.     

A CONFIGURATION FOR REALIZATION OF THE MULTICHANNEL AND HIGH-ORDER IIR ADAPTIVE FILTERS

This paper develops a new hyperstable adaptive algorithm which can be used inthe multichannel ⅡR conflguration and/or the high-order ⅡR or zero-pole configuration for jointprocess estimation.     

Chebyshev approximation for linear phase nonrecursive digital filters

A procedure has been developed for the design of nonrecursive digital filters with prescribed passband and stopband amplitude characteristics. The proposed procedure is based on an efficient algorithm utilizing the simplex method of linear programming. The design algorithm yields equiripple approximation and it is an alternative to the one which is based on the Remz exchange algorithm. The design procedure allows exact specifications for arbitrary passband and stopband edges. Furthermore, no prior knowledge of the degree of the filter is required. To demonstrate the potential of the design algorithm, several examples with different requirements are worked out and a sample is presented. The obtained results show that the design procedure performed very well where the various parameters of the filter were taken into consideration.     

Design of nonrecursive digital filters with linear phase

A new class of selective nonrecursive digital filters with independently prescribed equiripple passband and stopband attenuation and linear phase is obtained by numerical solution of a set of nonlinear equations. Some examples are given, and a comparison is made of the new solutions and those previously known.     

A note on block implementation of IIR digital filters

A matrix formulation of the IIR digital filter implementation technique via direct convolution or FFT methods originally proposed by Gold and Jordan is described and is shown to be a particular case of the block implementation of IIR filters developed by Burrus.