Synthesis of Narrowband Linear-Phase FIR Filters With a Piecewise-Polynomial Impulse Response

Classes of linear-phase finite-impulse response (FIR) filters with a piecewise-polynomial impulse response are proposed for the four types of linear-phase FIR filters. In addition, very efficient recursive structures to implement these filters in a straightforward and consistent manner are proposed. The desired impulse response is created by using a parallel connection of several filter branches. Only one branch has an impulse response of the full filter length, whereas the impulse responses are shorter for the remaining branches but the center is at the same location. The arithmetic complexity of these filters is proportional to the number of branches and the common polynomial order for each branch, rather than the actual filter order. In order to generate the overall piecewise-polynomial impulse response the polynomial coefficients are found, with the aid of linear programming, by optimizing the responses in the minimax sense, for both narrowband conventional filters and narrowband differentiators. The generation of these structures is based on the use of accumulators so that after using an accumulator, the resulting impulse response is divided into two parts. The first part follows the desired polynomial form, and the second part is what is left after the division, i.e., the nonpolynomial part. This same procedure can be used for all the following accumulators. Several examples are included, illustrating the benefits of the proposed filters, in terms of a reduced number of unknowns used in the optimization and the reduced number of multipliers required in the actual implementation.     

Applications of Directional Filters for Multiplexing Systems

The design of microwave multiplexing systems for frequency channelization of a broad-band microwave spectrum is complicated by problems such as off-resonance mismatch and mutual interaction between adjacent filters. By employing directional filters as basic building blocks, it is possible to construct multiplexing filters with a perfect input match since the input VSWR of a directional filter is theoretically unity both at resonance and off-resonance. Less insertion loss of a manifold may be obtained by the use of directional filters than with conventional band-pass filters. Curves giving the predicted response of a manifold containing n elements are presented for single-tuned and double-tuned directional filters. An asymmetrical response shape is obtained which has a midband insertion loss related to the separation of adjacent channels. An experimental model consisting of a five-channel multiplexer has been constructed utilizing double-tuned-circular-waveguide directional filters.     

Fixed-point design of generalised comb filters: a statistical approach

This study is concerned with the problem of designing computationally efficient generalised comb (GC) filters. Basically, GC filters are anti-aliasing filters that guarantee superior performance in terms of selectivity and quantisation noise rejection compared to classical comb filters, when used as decimation filters in multistage architectures. Upon employing a partial polyphase (PP) architecture proposed in a companion study, the authors develop a sensitivity analysis in order to investigate the effects of the coefficients' quantisation on the frequency response of the designed filters. The authors show that the sensitivity of the filter response to errors in the coefficients is dependent on the particular split of the decimation factor between the two sub-filters constituting the PP architecture. The sensitivity analysis is then used for developing a fixed-point implementation of a sample filter from the class of GC filters, used as reference filter throughout the study. Finally, the authors present computer simulations in order to evaluate the performance of the designed fixed-point filters.     

Implementation of Digital Unbiased FIR Filters with Polynomial Impulse Responses

This paper addresses the design and implementation of digital unbiased finite impulse response (FIR) filters with polynomial impulse response functions. The transfer function, its fundamental properties, and a general block-diagram are discussed for the impulse response represented with the l-degree Taylor series expansion. As a particular results, we show a fundamental identity uniquely featured to such filters in the transform domain. For low-degree impulse responses, the transfer functions are found in simple closed forms and represented in compact block-diagrams. The magnitude and phase responses are also analyzed along with the group delays. A comparison with predictive FIR filters is given. As examples of applications, filtering of time errors of local clocks is discussed along with the low-pass filter design employing a cascade of the unbiased FIR filters.     

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.     

Optimum masking levels and coefficient sparseness for Hilbert transformers and half-band filters designed using the frequency-response masking technique

Hilbert transformers and half-band filters are two very important special classes of finite-impulse response filters often used in signal processing applications. Furthermore, there exists a very close relationship between these two special classes of filters in such a way that a half-band filter can be derived from a Hilbert transformer in a straightforward manner and vice versa. It has been shown that these two classes of filters may be synthesized using the frequency-response masking (FRM) technique resulting in very efficient implementation when the filters are very sharp. While filters synthesized using the FRM technique has been characterized for the general low-pass case, Hilbert transformers and half-band filters synthesized using the FRM technique have not been characterized. The characterization of the two classes of filter is a focus of this paper. In this paper, we re-develop the FRM structure for the synthesis of Hilbert transformer from a new perspective. This new approach uses a frequency response correction term produced by masking the frequency response of a sparse coefficient filter, whose frequency response is periodic, to sharpen the bandedge of a low-order Hilbert transformer. Optimum masking levels and coefficient sparseness for the Hilbert transformers are derived; corresponding quantities for the half-band filters are obtained via the close relationship between these two classes of filters.     

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     

Monotonic lowpass filters with maximum selectivity

Lowpass filters with no finite zeros and a monotonic magnitude response are discussed. A characteristic function is derived by maximising the mean-square error in the stopband. Analytically, it has been proved that H filters are the most selective of all other filters with monotonic magnitude response.     

Filters involving derivatives with application to reconstructionfrom scanned halftone images

This paper presents a method for designing finite impulse response (FIR) filters for samples of a 2-D signal, e.g., an image, and its gradient. The filters, which are called blended filters, are decomposable in three filters, each separable in 1-D filters on subsets of the data set. Optimality in the minimum mean square error sense (MMSE) of blended filtering is shown for signals with separable autocorrelation function. Relations between correlation functions for signals and their gradients are derived. Blended filters may be composed from FIR Wiener filters using these relations. Simple blended filters are developed and applied to the problem of gray value image reconstruction from bilevel (scanned) clustered-dot halftone images, which is an application useful in the graphic arts. Reconstruction results are given, showing that reconstruction with higher resolution than the halftone grid is achievable with blended filters.     

Digital linear filters with finite pulse response. Brief collected results

It is represented brief review investigations, related to development and enhancement of digital linear filters with finite pulse response (FPR-filters). It is proposed high-quality low-pass filters and filters, approximating definite digital filters with infinite pulse response (IPR-filters). The basis of all proposed filters is Fourier transformation of polynomial trigonometrical kernels of Jackson type.     

Dispersive properties of optical filters for WDM systems

Wavelength division multiplexing (WDM) communication systems invariably require good optical filters meeting stringent requirements on their amplitude response, the ideal being a perfectly rectangular filter. To achieve high bandwidth utilization, the phase response of these filters is of equal importance, with the ideal filter having perfectly linear phase and therefore constant time delay and no dispersion. This aspect of optical filters for WDM systems has not received much attention until very recently. It is the objective of this paper to consider the phase response and resulting dispersion of optical filters in general and their impact on WDM system performance. To this end we use general concepts from linear systems, in particular, minimum and nonminimum phase response and the applicability of Hilbert transforms (also known as Kramers-Kronig relations). We analyze three different classes of optical filters, which are currently being used in WDM systems and compare their performance in terms of their phase response. Finally, we consider possible ways of linearizing the phase response without affecting the amplitude response, in an attempt to approximate the ideal filter and achieve the highest bandwidth utilization     

Calculation of narrowband lowpass filters with finite impulse response

This study provides a review of digital filters known under the name “interpolated finite impulse response filters” (IFIR filters) that make it possible to create narrowband lowpass filters (LPF) with substantially reduced computational load and, consequently, a simpler design as compared with the conventional finite impulse response filters (FIR filters).     

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     

Low-power digital filtering using approximate processing

We present an algorithmic approach to the design of low-power frequency-selective digital filters based on the concepts of adaptive filtering and approximate processing. The proposed approach uses a feedback mechanism in conjunction with well-known implementation structures for finite impulse response (FIR) and infinite impulse response (IIR) digital filters. Our algorithm is designed to reduce the total switched capacitance by dynamically varying the filter order based on signal statistics. A factor of 10 reduction in power consumption over fixed-order filters is demonstrated for the filtering of speech signals     

Universal maximally flat lowpass FIR systems

The family of FIR digital filters with maximally flat magnitude and group delay response is considered. The filters were proposed by Baher (1982), who furnished them with an analytic procedure for derivation of their transfer function. The contributions of this paper are the following. A simplified formula is presented for the transfer function of the filters. The equivalence of the novel formula with a formula that is derived from Baher's analytical procedure is proved using a modern method for automatic proof of identities involving binomial coefficients. The universality of Baher's filters is then established by proving that they include linear-phase filters, generalized half-band filters, and fractional delay systems. In this way, several classes of maximally flat filters are unified under a single formula. The generating function of the filters is also derived. This enables us to develop multiplierless cellular array structures for exact realization of a subset of the filters. The subset that enjoys such multiplierless realizations includes linear-phase filters, some nonsymmetric filters, and generalized halfband filters. A procedure for designing the cellular array structures is also presented     

带DGS结构的宽带微带线准椭圆函数滤波器设计

准椭圆滤波器体积小，重量轻，结构紧凑，比契比雪夫滤波器有更好的过渡特性，更高的带外抑制，在卫星通信和移动通信中有广泛的应用前景。但在用准椭圆滤波器实现宽带滤波器时，有时会遇到耦合间隙过小难以加工的问题。在准椭圆滤波器的谐振器底板加入缺陷接地结构（DGS），可以增强谐振器之间的耦合。应用DGS结构，用较宽的耦合间隙实现较强的耦合，从而使宽带滤波器物理上更容易实现。应用三维电磁场仿真软件，设计了一种带DGS结构的宽带微带线准椭圆函数滤波器。     

Interpolated LIR Mth-band filter design with allpass subfilters

We propose a new allpass-based structure for the IIR Mth-and 2Mth-band filters. These filters consist of M allpass filters and an interpolation filter (sum of two allpasses). Consequently, the proposed structure is very efficient in implementation. By choosing the allpass phase appropriately, the resulting phase response of the IIR Mth-band filter becomes approximately linear. An example is designed and compared with FIR Mth-band filters     

A new method for adaptive IIR filter design based on tabu search algorithm

Adaptive digital filters have proven their worth in a wide range of applications such as channel equalisation, noise reduction, echo cancelling, and system identification. These filters can be broadly classified into two groups: finite impulse–response (FIR) and infinite impulse–response (IIR) filters. IIR filters have become the target of increasing interest because these filters can reduce the filter order significantly as compared to FIR filters. Tabu search is a heuristic optimisation algorithm which has been originally developed for combinatorial optimisation problems. It simulates the general rules of intelligent problem solving and has the ability of discovering the global minima in a multi-modal search space. In this work, a novel method based on tabu search is described for the design of adaptive IIR filters.     

Closed-Form Design of Generalized Maxflat$R$-Regular FIR$M$th-Band Filters Using Waveform Moments

$M$th-band filters have found numerous applications in multirate signal processing systems, filter banks, and wavelets. In this paper, the design problem of generalized maxflat$R$-regular finite impulse response (FIR)$M$th-band filters with a specified integer group delay at$ omega =0 $is considered, and the closed-form expression for its impulse response is presented. The filter coefficients are directly derived by solving a linear system of Vandermonde equations that are obtained from the regularity condition of the maxflat$R$-regular FIR$M$th-band filters via the blockwise waveform moments. Differing from the conventional FIR$M$th-band filters with exactly linear phase responses, the generalized FIR$M$th-band filters proposed in this paper have an arbitrarily specified integer group delay at$ omega =0 $. Moreover, a new efficient implementation of the generalized maxflat$R$-regular FIR$M$th-band filters is proposed by making use of the relationship between the filter coefficients in the closed-form solution. Finally, several design examples are presented to demonstrate the effectiveness of the proposed FIR$M$th-band filters.