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     

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     

Design of stable IIR digital filter based on least P-power error criterion

In this paper, the least p-power error criterion is presented to design digital infinite impulse response (IIR) filters to have an arbitrarily prescribed frequency response. First, an iterative quadratic programming (QP) method is used to design a stable unconstrained one-dimensional IIR filter whose optimal filter coefficients are obtained by solving the QP problem in each iteration. Then, the proposed method is extended to design constrained IIR filters and two-dimensional IIR filters with a separable denominator polynomial. Finally, design examples of the low-pass filter are demonstrated to illustrate the effectiveness of the proposed iterative QP method.     

Low roundoff noise augmented realizations of IIR filters

The scaling factor in a direct form II infinite impulse response (IIR) digital filter depends on only the system poles, not its zeros. Adding pole-zero cancellation pairs changes the scaling factor and the associated roundoff noise without affecting the transfer function. It is shown that with l₂ scaling, the upper bound of the noise reduction for direct form II IIR digital filters using K pole-zero cancellation pairs is about 6K dB. The authors consider parallel form 3P to be the basic structure, in which each subfilter is augmented with one or two pole-zero cancellation pairs and realized in direct form II. They seek an iterative optimization process for each subfilter to find the optimal pole-zero cancellation pairs that minimize the roundoff noise. Experimental results indicate the global optimal solution for these augmented subfilters can be obtained by using simple criteria to determine the starting points of the iterative processes. Alternative structures, illustrative examples, and overflow limit cycles are examined     

Minimax design of two-channel IIR QMF banks with arbitrary groupdelay

The paper deals with the minimax design of two-channel infinite impulse response (IIR) QMF banks with arbitrary group delay, for which the IIR analysis filters and the resulting filter bank possess the frequency response optimal in the minimax (L_∞) sense. Utilising a lattice structure for the denominators of the IIR analysis filters, a design technique is presented based on an approximation scheme and a weighted least-squares (WLS) algorithm, previously developed by one of the authors for solving the resulting design problem that is basically a nonlinear optimisation problem. During the design process, this technique finds the tap coefficients for the numerator and the reflection coefficients for the denominator of the prototype IIR analysis filter simultaneously. The stability of the designed prototype IIR analysis filter is ensured by incorporating an efficient stabilisation procedure to make all of the reflection coefficient values fall between -1 and +1. Computer simulations show the effectiveness of the proposed design technique     

A direct approach to H2 optimal deconvolution ofperiodic digital channels

This paper studies the H₂ optimal deconvolution problem for periodic finite impulse response (FIR) and infinite impulse response (IIR) channels. It shows that the H₂ norm of a periodic filter can be directly quantified in terms of periodic system matrices and linear matrix inequalities (LMIs) without resorting to the commonly used lifting technique. The optimal signal reconstruction problem is then formulated as an optimization problem subject to a set of matrix inequality constraints. Under this framework, the optimization of both the FIR and IIR periodic deconvolution filters can be made convex, solved using the interior point method, and computed by using the Matlab LMI Toolbox. The robust deconvolution problem for periodic FIR and IIR channels with polytopic uncertainties are further formulated and solved, also by convex optimization and the LMIs. Compared with the lifting approach to the design of periodic filters, the proposed approach is simpler yet more powerful in dealing with multiobjective deconvolution problems and channel uncertainties, especially for IIR deconvolution filter design. The obtained solutions are applied to the design of an optimal filterbank yielding satisfactory performance     

General IIR optical filter design for WDM applications usingall-pass filters

A general design algorithm is presented for infinite impulse response (IIR) bandpass and arbitrary magnitude response filters that use optical all-pass filters as building blocks. Examples are given for an IIR multichannel frequency selector, an amplifier gain equalizer, a linear square-magnitude response, and a multi-level response. Major advantages are the efficiency of the IIR filter compared to finite impulse response (FIR) filters, the simplicity of the optical architecture, and its tolerance for loss. A reduced set of unique operating states is discussed for implementing a reconfigurable multichannel selection filter     

Optimization-based design and implementation of multidimensional zero-phase IIR filters

This paper considers multidimensional infinite-impulse response (IIR) filters that are iteratively implemented. The focus is on zero-phase filters with symmetric polynomials in the numerator and denominator of the multivariable transfer function. A rigorous optimization-based design of the filter is considered. Transfer function magnitude specifications, convergence speed requirements for the iterative implementation, and spatial decay of the filter impulse response (which defines the boundary condition influence in the spatial domain of the filtered signal) are all formulated as optimization constraints. When the denominator of the zero-phase IIR filter is strictly positive, these frequency domain specifications can be cast as a linear program and then efficiently solved. The method is illustrated with two two-dimensional IIR filter design examples.     

An improved systolic architecture for 2-D digital filters

An improved systolic architecture for two-dimensional infinite-impulse response (IIR) and finite-impulse-response (FIR) digital filters is presented. Comparisons with recently published work are made. When compared with the architecture of M.A. Sid-Ahmed (1989), a substantial reduction in the number of delay elements is observed. This reduction is of the order of 10² for a 2-D IIR filter and equals N+1 for an Nth-order 2-D FIR filter. The clock period has been made independent of the order of the filter. The speed-up factor is the maximum achievable and is independent of the filter order. Comparison with the work of S. Sunder et al. (1990) shows an improvement in the latency of the systolic array, which has been reduced from 1 to 0. A reduction of N+1 delay elements has been achieved for the FIR filter. An error analysis for the architecture is made     

Multidimensional multirate filters and filter banks derived fromone-dimensional filters

A method by which every multidimensional (M-D) filter with an arbitrary parallelepiped-shaped passband support can be designed and implemented efficiently is presented. It is shown that all such filters can be designed starting from an appropriate one-dimensional prototype filter and performing a simple transformation. With D denoting the number of dimensions, the complexity of design and implementation of the M-D filter are reduced from O(N^D) to O(N). Using the polyphase technique, an implementation with complexity of only 2N is obtained in the two-dimensional. Even though the filters designed are in general nonseparable, they have separable polyphase components. One special application of this method is in M-D multirate signal processing, where filters with parallelepiped-shaped passbands are used in decimation, interpolation, and filter banks. Some generalizations and other applications of this approach, including M-D uniform discrete Fourier transform (DFT) quadrature mirror filter banks that achieve perfect reconstruction, are studied. Several design example are given     

In the optimum design of the block adaptive FIR digital filter

A general optimum block adaptive (GOBA) algorithm for adaptive FIR (finite impulse response) filtering is presented. In this algorithm, the correction terms for the filter coefficients in each block, instead of the convergence factors, are optimized in a least squares sense. There are no constraints on the block length L and the filter tap number N. It is shown that the GOBA algorithm is reduced to the normalized LMS algorithm when L⩾N. The convergence of the GOBA algorithm can be assured if the correlation matrix of the input signal is positive definite. Computer simulations based on an efficient computing procedure confirm that the GOBA algorithm achieves faster convergence with slightly degraded convergence accuracy in stationary environments and better weight tracking capability in nonstationary environments as compared to existing block adaptive algorithms with no constraints on L and N     

Design of 3-D Noncausal Filters with Small Roundoff Noise and No Overflow Oscillations

The contribution of this paper consists of two individual parts. First, an invertible mapping technique is presented for 3-D digital system design, and it is applied to approximate 3-D noncausal filters in the spatial domain. Secondly, an algorithm is proposed for obtaining a structure for 3-D IIR filters with small roundoff noise and no overflow oscillations. The design of noncausal filters can be carried out by three steps: 1), a given noncausal impulse response is transformed into the first octant using the proposed 3-D invertible mapping technique; 2), the transformed impulse response in the first octant is approximated by balanced model reduction of 3-D separable denominator systems;3), the resultant 3-D IIR filter is transformed back to the original coordinates.     

Design of two-channel linear-phase QMF banks based on real IIR all-pass filters

The design of two-channel linear-phase quadrature mirror filter (QMF) banks constructed by real infinite impulse response (IIR) digital all-pass filters is considered. The design problem is appropriately formulated to result in a simple optimisation problem. Using a variant of Karmarkar's algorithm, the optimisation problem can be efficiently solved through a frequency sampling and iterative approximation method to find the real coefficients for the IIR digital all-pass filters. The resulting two-channel QMF banks possess an approximately linear phase response without magnitude distortion. The effectiveness of the proposed technique is achieved by forming an appropriate Chebyshev approximation of the desired phase response and then finding its solution from a linear subspace in a few iterations. Finally, several simulation examples are presented for illustration and comparison     

A stable and distortion-free IIR echo and howling canceler

The authors propose a configuration for an infinite impulse response (IIR) adaptive echo and howling canceller, which consists of a two-channel maximum entropy lattice filter and its inverse filter. The echo is canceled by the adaptive lattice filter, while the signal distortion is eliminated by the inverse lattice. With stability guaranteed without the necessity of testing, the structure costs O (N) multiplications per sampling period. The algorithm can also be greatly simplified for white input cases     

Recursive weighted median filters admitting negative weights andtheir optimization

A recursive weighted median (RWM) filter structure admitting negative weights is introduced. Much like the sample median is analogous to the sample mean, the proposed class of RWM filters is analogous to the class of infinite impulse response (IIR) linear filters. RWM filters provide advantages over linear IIR filters, offering near perfect “stopband” characteristics and robustness against noise. Unlike linear IIR filters, RWM filters are always stable under the bounded-input bounded-output criterion, regardless of the values taken by the feedback filter weights. RWM filters also offer a number of advantages over their nonrecursive counterparts, including a significant reduction in computational complexity, increased robustness to noise, and the ability to model “resonant” or vibratory behavior. A novel “recursive decoupling” adaptive optimization algorithm for the design of this class of recursive WM filters is also introduced. Several properties of RWM filters are presented, and a number of simulations are included to illustrate the advantages of RWM filters over their nonrecursive counterparts and IIR linear filters     

Minimax design of two-channel nonuniform-division filterbanks using IIR allpass filters

The design of two-channel linear-phase nonuniform-division filter (NDF) banks constructed by infinite impulse response (IIR) digital allpass filters (DAFs) in the sense of L/sub /spl infin// error criteria is considered. First, the theory of two-channel NDF bank structures using two IIR DAFs is developed. Then, the design problem is appropriately formulated to result in a simple optimization problem. Utilizing a variant of Karmarkar's algorithm, we can efficiently solve the optimization problem through a frequency sampling and iterative approximation method to find the coefficients for the IIR DAFs. The resulting two-channel NDF banks can possess approximately linear-phase response without magnitude distortion. The effectiveness of the proposed technique is achieved by forming an appropriate Chebyshev approximation of a desired phase response and then to find its solution from a linear subspace in a few iterations. Several simulation examples are presented for illustration and comparison.     

Polyspectrum modeling using linear or quadratic filters

The polyspectrum modeling problem using linear or quadratic filters is investigated. In the linear case, it is shown that, if the output pth-order cumulant function of a filter, driven by a white noise, is of finite extent, then the filter necessarily has a finite-extent impulse response. It is proved that every factorable polyspectrum with a non-Gaussian white noise can also be modeled with a quadratic filter driven by a Gaussian white noise. It is shown that, if the quadratic filter has a finite-extent impulse response, then the output pth-order cumulant function is of finite extent; and if the output pth-order cumulant function of a quadratic filter is of finite extent, then the impulse response may or may not be of finite extent. It is shown that there exist finite and infinite extent p th-order cumulant functions that are not factorable but can be modeled with quadratic filters     

Design of linear-phase IIR filters via impulse-response gramians

A new method for the design of a linear-phase infinite-impulse-response (IIR) filter is presented. It involves designing a finite-impulse-response (FIR) filter satisfying the given frequency response specifications and subsequently obtaining a significantly lower order IIR filter using model reduction based on impulse-response gramians. The general outline of the method and a brief overview of the existing linear-phase FIR filter design and model-reduction techniques are presented. The impulse-response gramian and the model-reduction algorithm used are presented. The method is illustrated by design examples and is compared with other methods for the design of linear-phase IIR filters using equalizers     

Two-channel IIR QMF banks with approximately linear-phase analysisand synthesis filters

Perfect linear-phase two-channel QMF banks require the use of finite impulse response (FIR) analysis and synthesis filters. Although they are less expensive and yield superior stopband characteristics, perfect linear phase cannot be achieved with stable infinite impulse response (IIR) filters. Thus, IIR designs usually incorporate a postprocessing equalizer that is optimized to reduce the phase distortion of the entire filter bank. However, the analysis and synthesis filters of such an IIR filter bank are not linear phase. In this paper, a computationally simple method to obtain IIR analysis and synthesis filters that possess negligible phase distortion is presented. The method is based on first applying the balanced reduction procedure to obtain nearly allpass IIR polyphase components and then approximating these with perfect allpass IIR polyphase components. The resulting IIR designs already have only negligible phase distortion. However, if required, further improvement may be achieved through optimization of the filter parameters. For this purpose, a suitable objective function is presented. Bounds for the magnitude and phase errors of the designs are also derived. Design examples indicate that the derived IIR filter banks are more efficient in terms of computational complexity than the FIR prototypes and perfect reconstruction FIR filter banks. Although the PR FIR filter banks when implemented with the one-multiplier lattice structure and IIR filter banks are comparable in terms of computational complexity, the former is very sensitive to coefficient quantization effects     

Q value analysis of microwave photonic filters

This paper first presents the fundamental principles of the microwave photonic filters.As an example to explain how to implement a microwave photonic filter, a specific finite impulse response (FIR) filter is illustrated.Next, the Q value of the microwave photonic filters is analyzed theoretically, and methods around how to gain high Q value are discussed.Then,divided into FIR filter, first-order infinite impulse response (IIR) filter, and multi-order IIR filter, several novel microwave photonic filters with high Q value are listed and compared.The technical difficulties to get high Q value in first-order IIR filter and multi-order IIR filter are analyzed concretely.Finally, in order to gain higher Q value, a multi-order IIR microwave photonic filter that easily extends its order is presented and discussed.