Generalized digital Butterworth filter design

This correspondence introduces a new class of infinite impulse response (IIR) digital filters that unifies the classical digital Butterworth filter and the well-known maximally flat FIR filter. New closed-form expressions are provided, and a straightforward design technique is described. The new IIR digital filters have more zeros than poles (away from the origin), and their (monotonic) square magnitude frequency responses are maximally flat at ω=0 and at ω=π. Another result of the correspondence is that for a specified cutoff frequency and a specified number of zeros, there is only one valid way in which to split the zeros between z=-1 and the passband. This technique also permits continuous variation of the cutoff frequency. IIR filters having more zeros than poles are of interest because often, to obtain a good tradeoff between performance and implementation complexity, just a few poles are best     

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.     

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。     

Maxflat Fractional Delay IIR Filter Design

Fractional delay (FD) filters are an important class of digital filters and are useful in various signal processing applications. This paper discusses a design problem of FD infinite-impulse-response (IIR) filters with the maxflat frequency response in frequency domain. First, a flatness condition of FD filters at an arbitrarily specified frequency point is described, and then a system of linear equations is derived from the flatness condition. Therefore, a set of filter coefficients can be easily obtained by solving this system of linear equations. For a special case in which the frequency response is required to be maxflat at omega = 0 or pi , a closed-form expression for its filter coefficients is derived by solving a linear system of Vandermonde equations. It is also shown that the existing maxflat FD finite-impulse-response (FIR) and IIR filters are special cases of the FD IIR filters proposed in this paper. Finally, some examples are presented to demonstrate the effectiveness of the proposed filters.     

An FIR Channel Estimation Filter with Robustness to Channel Mismatch Condition

This letter proposes a finite impulse response (FIR) channel estimation filter that has robustness against the channel mismatch due to the FIR structure. The channel impulse response is described with a complex state space model and then estimated from received data on the recent time interval. Numerical results show that the FIR channel estimation filter can provide more robust performance than conventional Kalman IIR filters when channel model parameters are not correct.     

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     

A new class of two-channel biorthogonal filter banks and waveletbases

Proposes a novel framework for a new class of two-channel biorthogonal filter banks. The framework covers two useful subclasses: i) causal stable IIR filter banks. ii) linear phase FIR filter banks. There exists a very efficient structurally perfect reconstruction implementation for such a class. Filter banks of high frequency selectivity can be achieved by using the proposed framework with low complexity. The properties of such a class are discussed in detail. The design of the analysis/synthesis systems reduces to the design of a single transfer function. Very simple design methods are given both for FIR and IIR cases. Zeros of arbitrary multiplicity at aliasing frequency can be easily imposed, for the purpose of generating wavelets with regularity property. In the IIR case, two new classes of IIR maximally flat filters different from Butterworth filters are introduced. The filter coefficients are given in closed form. The wavelet bases corresponding to the biorthogonal systems are generated. the authors also provide a novel mapping of the proposed 1-D framework into 2-D. The mapping preserves the following: i) perfect reconstruction; ii) stability in the IIR case; iii) linear phase in the FIR case; iv) zeros at aliasing frequency; v) frequency characteristic of the filters     

Least-squares design of IIR filters with prescribed magnitude andphase responses and a pole radius constraint

This paper presents a method for the frequency domain design of infinite impulse response (IIR) digital filters. The proposed method designs filters approximating prescribed magnitude and phase responses. IIR filters of this kind can have approximately linear-phase responses in their passbands, or they can equalize magnitude and phase responses of given systems. In many cases, these filters can be implemented with less memory and with fewer computations per output sample than equivalent finite impulse response (FIR) digital filters. An important feature of the proposed method is the possibility to specify a maximum radius for the poles of the designed rational transfer function. Consequently, stability can be guaranteed, and undesired effects of implementations using fixed-point arithmetic can be alleviated by restricting the poles to keep a prescribed distance from the unit circle. This is achieved by applying Rouche's theorem in the proposed design algorithm. We motivate the use of IIR filters with an unequal number of poles and zeros outside the origin of the complex plane. In order to satisfy simultaneous specifications on magnitude and phase responses, it is advantageous to use IIR filters with only a few poles outside the origin of the z-plane and an arbitrary number of zeros. Filters of this type are a compromise between IIR filters with optimum magnitude responses and phase-approximating FIR filters. We use design examples to compare filters designed by the proposed method to those obtained by other methods. In addition, we compare the proposed general IIR filters with other popular more specialized structures such as FIR filters and cascaded systems consisting of frequency-selective IIR filters and phase-equalizing allpass filters     

Multistage adaptive filters for in-phase processing ofline-frequency signals

The authors describe two adaptive multistage digital filters for 50/60-Hz line-frequency signal processing in zero-crossing detectors and synchronous power systems. These filters combine a median filter with adaptive predictors, either finite-impulse response (FIR)- or infinite-impulse response (IIR)-based, thus making it possible to extract the sinusoidal signals from noise and strong disturbances without phase shifting the primary frequency signal. The median filter is used as a prefilter because it can remove deep commutation notches from the waveform. Adaptation allows the filters to track the exact instantaneous line frequency and avoids the selectivity problem encountered with a fixed filter     

Digital integrator design using Simpson rule and fractional delay filter

The IIR digital integrator is designed by using the Simpson integration rule and fractional delay filter. To improve the design accuracy of a conventional Simpson IIR integrator at high frequency, the sampling interval is reduced from T to 0.5T. As a result, a fractional delay filter needed to be designed in the proposed Simpson integrator. However, this problem can be solved easily by applying well-documented design techniques of the FIR and all-pass fractional delay filters. Several design examples are illustrated to demonstrate the effectiveness of the proposed method.     

A digital signal processing approach to interpolation

In many digital signal precessing systems, e.g., vacoders, modulation systems, and digital waveform coding systems, it is necessary to alter the sampling rate of a digital signal Thus it is of considerable interest to examine the problem of interpolation of bandlimited signals from the viewpoint of digital signal processing. A frequency dmnain interpretation of the interpolation process, through which it is clear that interpolation is fundamentally a linear filtering process, is presented, An examination of the relative merits of finite duration impulse response (FIR) and infinite duration impulse response (IIR) digital filters as interpolation filters indicates that FIR filters are generally to be preferred for interpolation. It is shown that linear interpolation and classical polynomial interpolation correspond to the use of the FIR interpolation filter. The use of classical interpolation methods in signal processing applications is illustrated by a discussion of FIR interpolation filters derived from the Lagrange interpolation formula. The limitations of these filters lead us to a consideration of optimum FIR filters for interpolation that can be designed using linear programming techniques. Examples are presented to illustrate the significant improvements that are obtained using the optimum filters.     

Design of doubly complementary filters with approximate linearphase

A new procedure for the design of a real doubly complementary (DC) pair of digital filters obtained from an all-pass structure is presented. The filter design is based on a zero-phase FIR filter design with multi-band frequency specifications and approximate linear-phase characteristic. The resulting complex or real all-pass filter structure is guaranteed to be stable. Some examples illustrating the design method including comparisons with conventional approximately linear phase IIR filters are also shown     

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     

Frequency domain synthesis of IIR digital filters by means of associated FIR filters

This correspondence describes a synthesis technique for IIR digital filters which allows the use of approximation methods already developed for designing FIR filters. The technique is based on the definition, by means of a suitable transformation, of a FIR filter associated to the desired IIR filter. An example of application is given and the related results are briefly discussed.     

IIR Filter Adaptation Using Branch-and-Bound: A Novel Approach

Adaptive infinite impulse response (IIR) filters provide significant advantages over equivalent finite impulse response (FIR) implementations because they are able to more accurately model physical plants that have pole-zero structures. Additionally, they are typically capable of meeting performance specifications using fewer filter parameters. This savings in parameters, which can be as much as 5–10 times, leads to the use of fewer multiplier blocks and therefore, lower power consumption. Despite these advantages, adaptive IIR filters have not found widespread use because the associated mean squared error (MSE) cost function is multimodal and therefore, significantly difficult to minimize. Additionally, the filter can become unstable during adaptation. These two properties pose several problems for adaptive algorithms, causing them to be sensitive to initial conditions, produce biased solutions, unstable filter configurations or converge to local minima. These problems prevent the widespread use of adaptive IIR filters in practice and if such filter structures are to become more practical, new, innovative solutions are required. This paper proposes a new algorithm for minimizing the MSE cost function of adaptive IIR filters aimed at addressing some of the aforementioned issues. We adopt the approach of using a Branch-and-Bound algorithm, which is an exhaustive search method, and employ interval arithmetic for all computations. Simulation results show that the resulting algorithm is viable and competitive and, when compared with a number of existing state-of-the-art algorithms, outperforms them in terms of the MSE of the final point.      

Design of stable, causal, perfect reconstruction, IIR uniform DFTfilter banks

Design procedures for stable, causal and perfect reconstruction IIR parallel uniform DFT filter banks (DFT FBs) are presented. In particular a family of IIR prototype filters is a good candidate for DFT FB, where a tradeoff between frequency selectivity and numerical properties (as measured by the Weyl-Heisenberg frames theory) could be made. Some realizations exhibiting a simple and a massively parallel and modular processing structure making a VLSI implementation very suitable are shown. In addition, some multipliers in the filters (both the analysis and synthesis) could be made; powers or sum of powers of 2, in particular for feedback loops, resulting in a good sensitivity behavior. For these reasons as well as for the use of low order IIR filters (as compared with conventional FIR filters), the overall digital filter bank structure is efficient for high data rate applications. Some design examples are provided     

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     

Optical half-band filters

This paper proposes two kinds of novel 2×2 circuit configuration for finite-impulse response (FIR) half-band filters. These configurations can be transformed into each other by a symmetric transformation and their power transmittance is identical. The configurations have only about half the elements of conventional FIR lattice-form filters. We derive a design algorithm for achieving desired power transmittance spectra. We also describe 2×2 circuit configurations for infinite-impulse response (IIR) half-band filters. These configurations are designed to realize arbitrary-order IIR half-band filter characteristics by extending the conventional half-band circuit configuration used in millimeter-wave devices. We discuss their filter characteristics and confirm that they have a power half-band property. We demonstrate design examples including FIR maximally flat half-band filters, an FIR Chebyshev half-band filter, and an IIR elliptic half-band filter     

Extended-window interpolation applied to digital filter design

This paper develops a procedure for the design of frequency-selective interpolation operators that can be computed and saved once and for all. These operators are used to design real-time digital operators: interpolators, FIR differentiators, IIR filters, and composed interpolation and filtering operators. Each real-time operator is a matrix relating sets of data points to sets of interpolated values. Since these matrices are characterized by low norms, they permit reduced-word implementations, and are suitable for real-time processing with array processors and massively parallel machines. The design of the interpolation operators uses windows that, unlike traditional approaches, extend beyond the data interval up to the length permitted by the dimensionality theorem. A new form of the dimensionality theorem is used to minimize the minimax interpolation error within a predetermined frequency range, which may be either the passband of the antialiasing filter or the passband of an analog prototype filter. The main application presented in the paper is the design of combined digital filters and interpolators, which will be referred to as interpolating filters. The frequency responses of such filters, as well as the interpolated time responses, almost coincide with those of the corresponding analog prototypes