Canonic ladder realizations of IIR digital filters

Two new canonic realizations of IIR digital filters age presented. The realizations are derived employing modified continued fraction expansion procedures. Proposed methods also provide alternate derivations to the digital lattice and ladder structures based on two-pair extractions and orthogonal polynomial expansions.     

New low roundoff noise realizations of second-order digital filtersections

New structures for second-order filter sections are proposed that yield lower output roundoff noise than many well known structures and are free of zero-input limit cycle oscillations. These new low-roundoff structures are based on these suggested by Bomar (1989) and are obtained by putting the constraint that some of the state-space coefficients be sum-of-two power-of-two terms. Numerical results are included to illustrate the performance of the proposed structures for narrow-band filters and to compare them with other structures     

Jointly optimized error-feedback and realization for roundoff noise minimization in state-space digital filters

Roundoff noise (RN) is known to exist in digital filters and systems under finite-precision operations and can become a critical factor for severe performance degradation in infinite impulse response (IIR) filters and systems. In the literature, two classes of methods are available for RN reduction or minimization-one uses state-space coordinate transformation, the other uses error feedback/feed-forward of state variables. In this paper, we propose a method for the joint optimization of error feedback/feed-forward and state-space realization. It is shown that the problem at hand can be solved in an unconstrained optimization setting. With a closed-form formula for gradient evaluation and an efficient quasi-Newton solver, the unconstrained minimization problem can be solved efficiently. With the infinite-precision solution as a reference point, we then move on to derive a semidefinite programming (SDP) relaxation method for an approximate solution of optimal error-feedback matrix with sum-of-power-of-two entries under a given state-space realization. Simulations are presented to illustrate the proposed algorithms and demonstrate the performance of optimized systems.     

Roundoff noise minimization using delta-operator realizations[digital filters]

The authors examine the advantages of using delta operator state space realizations rather than shift operator realizations of transfer functions in terms of minimizing roundoff noise gain. They give several conditions under which the optimal roundoff noise gain for delta operator realizations is smaller than the optimal gain for shift operator realizations. They then illustrate that even sparse (and hence nonoptimal) delta operator realizations can have smaller roundoff noise gain than the optimal shift operator realizations     

Efficient lattice realizations of adaptive IIR algorithms

Computationally efficient adaptive IIR-filter algorithms are presented based on lattice realizations allowing the adaptive filter stability to be easily monitored. New simplified recursive-in-order equations relating the parameters of the direct-form realization with the ones of two lattice realizations are presented. These equations lead to a simplified technique to compute the regressor vector and to a general method to implement any adaptive IIR algorithm using lattice realization. Results indicate that the proposed lattice-based algorithms converge to a set of parameters that realize the same transfer function as the corresponding direct-form algorithms     

An improved /spl rho/DFIIt structure for digital filters with minimum roundoff noise

In this brief, a new efficient digital filter structure with minimum roundoff noise is derived. This structure can be block-diagrammed as the recently proposed direct-form II transposed (DFIIt) structure in /spl rho/-operator, denoted as /spl rho/DFIIt, in which the first-order /spl rho/ operators are replaced with a set of second-order operators. The corresponding expression for the roundoff noise gain is obtained. The problem of how to choose these second-order operators is investigated in terms of minimizing the roundoff noise gain. Two design examples are given to illustrate the excellent performance of the proposed structure and to confirm the theoretical analysis.     

Efficient recursive realizations of FIR filters

A class of efficient filter structures is proposed which uses a recursive realization of an FIR filter. The structures are in some sense a generalization of the frequency sampling structure, but they are more versatile and arise from a time-domain rather than frequency-domain argument. The new structure has a tap out of every block delay, and the length of the block delay is the length of each piecewise section of the time-domain approximation. The number of taps, filter coefficients, and the amount of arithmetic are proportional to the number of piecewise sections, not to the actual filter length or order. This filter is particularly efficient when a long-length filter can be approximated by a few piecewise sections, which is the case for many practical filters.This research was supported by NSF grant ECS 81-00453.     

Quantization and roundoff noises in fixed-point FIR digital filters

The errors in a fixed-point finite impulse response (FIR) filter due to quantization (analog-to-digital conversion) and roundoff are considered. Expressions for the exact moments of the filter output noise are derived. It is well known that, when the input signal satisfies certain conditions, the popular additive white noise model can be valid in describing the quantization noise. The characteristics of multiplicative roundoff noises, however, differ from what this model predicts, even under conditions where the roundoff noises are white. Hence the additive white noise model does not provide accurate results on the characteristics of the output error in an FIR filter. Using the exact formulas for the moments, the author computes the exact power spectrum of the filter output error. These results agree well with those obtained from simulation     

Cascade lattice IIR adaptive filters

The feedback lattice filter forms, including the two-multiplier form and the normalized form, are examined with respect to their relationships to the feedback direct form filter. Specifically, the transformation matrix between the lattice forms and the direct form is derived; parameter and state relationships between the lattice forms and the direct form are therefore obtained. An IIR filter structure-the cascade lattice IIR structure-is constructed. Based on this structure, three IIR adaptive filtering algorithms in the two-multiplier form can then be developed following the gradient approach, the Steiglitz-McBride approach and the hyperstability approach. Convergence of these algorithms is theoretically analyzed using either the ODE approach or the hyperstability theorem. These algorithms are then simplified into forms computationally as efficient as their corresponding direct form algorithms. Relationships of the simplified algorithms to the direct form algorithms are also studied, which disclose a consistency in algorithm structure regardless of the filter form. Three normalized lattice algorithms can also be derived from the two-multiplier lattice algorithms. Experimental results show much improved performance of the normalized lattice algorithms over the two-multiplier lattice algorithms and the direct form algorithms     

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     

Design of IIR digital notch filters

A method is presented for the design of notch filters with specified notch frequency ₀ and 3-dB rejection bandwidthB _t, using a first-order real all-pass filter, wherein the only coefficient is used to control the notch frequency. To control the bandwidth, use is made of a new amplitude change function (ACF), and it is shown that given notch filter specifications can be exactly met thereby. Also, using the ACF, it is shown that stability of the second-order notch filter designs can be improved along with the noise gain.     

On fast FIR filters implemented as tail-canceling IIR filters

We have developed an algorithm based on synthetic division for deriving the transfer function that cancels the tail of a given arbitrary rational (IIR) transfer function after a desired number of time steps. Our method applies to transfer functions with repeated poles, whereas previous methods of tail-subtraction cannot. We use a parallel state-variable technique with periodic refreshing to induce finite memory in order to prevent accumulation of quantization error in cases where the given transfer function has unstable modes. We present two methods for designing linear-phase truncated IIR (TIIR) filters based on antiphase filters. We explore finite-register effects for unstable modes and provide bounds on the maximum TIIR filter length. In particular, we show that for unstable systems, the available dynamic range of the registers must be three times that of the data. Considerable computational savings over conventional FIR filters are attainable for a given specification of linear-phase filter. We provide examples of filter design. We show how to generate finite-length polynomial impulse responses using TIIR filters. We list some applications of TIIR filters, including uses in digital audio and an algorithm for efficiently implementing Kay's optimal high-resolution frequency estimator     

Separate/joint optimization of error feedback and coordinate transformation for roundoff noise minimization in two-dimensional state-space digital filters

This paper is concerned with the minimization of roundoff noise subject to l/sub 2/-norm dynamic-range scaling constraints in two-dimensional (2-D) state-space digital filters. Two methods are proposed, with the first one using error feedback alone and the second one using joint error feedback and coordinate transformation optimization. In the first method, several techniques for the determination of optimal full-scale, block-diagonal, diagonal, and scalar error-feedback matrices for a given 2-D state-space digital filter are proposed. In the second method, an iterative approach for minimizing the roundoff noise under l/sub 2/-norm dynamic-range scaling constraints is developed by jointly optimizing a scalar error-feedback matrix and a coordinate transformation matrix, which may be regarded as an alternative approach to the conventional method for synthesizing the optimal 2-D filter structure with minimum roundoff noise. An analytical method for the joint optimization of a general error-feedback matrix and a coordinate transformation matrix under the scaling constraints is also proposed. A numerical example is presented to illustrate the utility of the proposed techniques.     

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 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     

Digital filter roundoff noise calculation using the driving-point impedance

A method for calculating the digital-filter output roundoff noise directly from the s domain driving-point impedance is given. This method is applicable where the bilinear transformation is used for the digital-filter design.     

Design of three-dimensional adaptive IIR notch filters

This paper investigates a realization of a three-dimensional (3-D) adaptive notch filter. The procedures are mainly divided into two parts: frequency-detecting and sinusoidal interference removal. The detections are based on adaptive line enhancer on infinite impulse response (IIR) lattice structure. In the interference removal part, a non-separable version of a 3-D notch filter is effectively applied. The magnitude response of a 3-D adaptive IIR notch filter is illustrated. At the end of the paper, the implementation of an IIR notch filter on a 3-D image is also conducted in order to show how to remove a sinusoidal interference superimposed on a 3-D image.     

Novel and efficient realizations of FIR digital filters

An FIR filter can usually be realized in the direct form or in cascade form. The Chebyshev-type structures, known for the 2-D FIR filter implementation, are generalized to the realization of arbitrary 1-D causal FIR filters. The new realizations show several attractive properties and can be implemented using modular pipelineable processor arrays     

Separate/joint optimization of error feedback and realization for roundoff noise minimization in a class of 2-D state-space digital filters

Techniques for the separate/joint optimization of error-feedback and realization are developed to minimize the roundoff noise subject to l ₂-norm dynamic-range scaling constraints for a class of 2-D state-space digital filters. In the joint optimization, the problem at hand is converted into an unconstrained optimization problem by using linear-algebraic techniques. The unconstrained problem obtained is then solved by applying an efficient quasi-Newton algorithm. A numerical example is presented to illustrate the utility of the proposed techniques.