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     

Two-tap travelling-wave infinite impulse response filter with 12 dB peaking at 24 GHz

A two-tap infinite impulse response (IIR) filter using travelling-wave architecture is presented. The filter utilises poles as a means of frequency boosting, contrasting the conventional finite impulse response technique of utilising zeros and is the first ever implementation of an IIR filter using a double-loop multi-delay topology. Implemented in a 90 nm CMOS process, the filter achieves a 12.1 peak at 24 GHz when both filter taps are set to maximum peaking and consumes 55.2 mW from a 1.2 V supply.     

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.     

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     

A Fully Multiplexed First-Order Frequency-Planar Module for Fan, Beam, and Cone Plane-Wave Filters

A VLSI architecture for the on-chip realization of a first-order two-dimensional (2-D) or three-dimensional (3-D) infinte impulse response (IIR) fully multiplexed frequency-planar filter module (FMFPM) is proposed. Such filter modules may be used in 3-D video processing and 2-D/3-D plane-wave filtering using sensor arrays. The proposed FMFPM can potentially be used as a 2-D/3-D IIR building block circuit for the on-chip realization of second- (or higher) order frequency-planar filters, 3-D IIR beam filters, 2-D IIR fan filter banks and 3-D IIR cone filter banks.     

Analysis and design of periodically time-varying IIR filters, withapplications to transmultiplexing

Fundamental constraints on the form of infinite impulse response (IIR) periodically time-varying (PTV) filters are identified, and a design technique with well-defined error and stability characteristics based on those constraints is presented. The design technique is based on the selection of poles and zeros within the time-invariant filter banks of equivalent PTV filter analysis structures. A simple example is presented to illustrate the design method, which implements the IIR PTV as a time-invariant all-feedback IIR filter of the form 1/D(z^P) cascaded with an finite impulse response (FIR) PTV filter. An application of IIR PTV filters to telecommunications transmultiplexing is presented to illustrate the design method and for comparison to an existing PTV design method. The computational complexity of the resulting system compares favorably with that of existing transmultiplexers     

Pole-zero decision feedback equalization with a rapidly convergingadaptive IIR algorithm

A decision feedback equalizer (DFE) containing a feedback filter with both poles and zeros is proposed for high-speed digital communications over the subscriber loop. The feedback filter is composed of a relatively short FIR filter that cancels the initial part of the channel impulse response, which may contain rapid variations due to bridge taps, and a pole-zero, or IIR, filter that cancels the smoothly decaying tail of the impulse response. Modifications of an adaptive IIR algorithm, based on the Steiglitz-McBride (1965) identification scheme, are proposed to adapt the feedback filter. A measured subscriber loop impulse response is used to compare the performance of the adaptive pole-zero DFE, assuming a two-pole feedback filter, with a conventional DFE having the same number of coefficients. Results show that the pole-zero DFE offers a significant improvement in mean squared error relative to the conventional DFE. The speed convergence of the adaptive pole-zero DFE is comparable to that of the conventional DFE using the standard least mean square (LMS) adaptive algorithm     

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.     

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     

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     

Synthesis of grating lattice circuits

The realization of high-performance components based on optical infinite impulse response (IIR) filter design theory is desirable for next-generation global optical networks. Previously proposed IIR filter synthesis methods are matrix factorization techniques for a lattice circuit using ring resonators. The size of ring resonator limits the bandwidth of the lattice filters. In this paper, two configurations of grating lattice filters are synthesized by using a scattering matrix representation for the grating. The grating is one of the most powerful optical elements both in fiber optics and photonic integrated circuits. One configuration is a serial grating lattice filter configuration and the other is a parallel grating lattice filter configuration. The actual frequency response of the synthesized grating lattice filter is calculated to show the design limitation due to the frequency response of the element gratings     

Multidimensional orthogonal filter bank characterization and design using the Cayley transform.

We present a complete characterization and design of orthogonal infinite impulse response (IIR) and finite impulse response (FIR) filter banks in any dimension using the Cayley transform (CT). Traditional design methods for one-dimensional orthogonal filter banks cannot be extended to higher dimensions directly due to the lack of a multidimensional (MD) spectral factorization theorem. In the polyphase domain, orthogonal filter banks are equivalent to paraunitary matrices and lead to solving a set of nonlinear equations. The CT establishes a one-to-one mapping between paraunitary matrices and para-skew-Hermitian matrices. In contrast to the paraunitary condition, the para-skew-Hermitian condition amounts to linear constraints on the matrix entries which are much easier to solve. Based on this characterization, we propose efficient methods to design MD orthogonal filter banks and present new design results for both IIR and FIR cases.     

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.     

Synthesis of coherent two-port optical delay-line circuit with ringwaveguides

A method has already been reported by the author and others for synthesizing coherent two-port lattice-form optical delay-line circuits which have the same filter characteristics as finite impulse response (FIR) digital filters. This paper proposes a two-port circuit configuration with ring waveguides which can realize the same filter characteristics as infinite impulse response (IIR) digital filters. It also describes a synthesis method for realizing arbitrary IIR filter characteristics with the circuit configuration. This method is based on scattering matrix factorization. Some synthesis examples are demonstrated including an elliptic filter, a Butterworth filter, an optical filter with maximally flat group-delay characteristics, a group-delay dispersion equalizer, and a multichannel selector     

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.     

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     

IIR数字滤波器的FPGA实现

本文介绍了IIR滤波器的FPGA实现方法，给出了IIR数字滤波器的时序控制、延时、补码乘法和累加四个模块的设计方法，并用VHDL和FPGA器件实现了IIR数字滤波。结果表明，这种实现方法扩展性好，灵活性强，速度快，专用资源少，在工程实际中有较好的应用前景。     

A class of modified adaptive recursive filter algorithms

A new class or adaptive infinite impulse response ( IIR) or recursive filter algorithms is obtained by incorporating a simple modification in the correction vectors of some existing algorithms. The resulting class of algorithms explores the inherent parallelism present in their coefficient update equations, and hence the possibility of faster initial convergence. Two IIR filter algorithms are considered for discussion and simulation.     

基于FIR与相位补偿IIR滤波器的雷达回波信号处理

FIR与IIR频率选择滤波器的设计,被广泛应用于数字信号处理领域之中。文章以雷达回波信号的数字处理为例,首先分别设计FIR,IIR滤波器完成了对信号特定频率分量的滤除。进而,针对IIR滤波器的非线性相位,基于最优化设计全通系统实现了相位补偿,并对FIR,IIR滤波器进行了综合比较。     

Stable IIR notch filter design with optimal pole placement

This paper presents a two-stage approach for designing an infinite impulse response (IIR) notch filter. First, the numerator of the transfer function of the IIR notch filter is obtained by placing the zeros at the prescribed notch frequencies. Then, the denominator polynomial is determined by using an iterative scheme in which the optimal pole placements are found by solving a standard quadratic programming problem. For stability, the pole radius in the single notch filter design is specified by the designer, and in the multiple notch filter design, the pole radius is constrained by using the implications of Rouche's theorem. Examples are included to illustrate the effectiveness of the proposed techniques