A Multimode Transmultiplexer Structure

This paper introduces a multimode transmultiplexer (TMUX) structure capable of generating a large set of user-bandwidths and center frequencies. The structure utilizes fixed integer sampling rate conversion (SRC) blocks, Farrow-based variable interpolation and decimation structures, and variable frequency shifters. A main advantage of this TMUX is that it needs only one filter design beforehand. Specifically, the filters in the fixed integer SRC blocks as well as the subfilters of the Farrow structure are designed only once. Then, all possible combinations of bandwidths and center frequencies are obtained by properly adjusting the variable delay parameter of the Farrow-based filters and the variable parameters of the frequency shifters. The paper includes examples for demonstration. It also shows that, using the rational SRC equivalent of the Farrow-based filters, the TMUX can be described in terms of conventional multirate building blocks which may be useful in further analysis of the overall system.     

Linear-phase FIR interpolation, decimation, and mth-band filters utilizing the farrow structure

This paper introduces novel linear-phase finite-impulse response (FIR) interpolation, decimation, and Mth-band filters utilizing the Farrow structure. In these new overall filters, each polyphase component (except for one term) is realized using the Farrow structure with a distinct fractional delay. The corresponding interpolation/decimation structures can therefore be implemented using only one set of linear-phase FIR subfilters and one set of multipliers that correspond to the distinct fractional delays. The main advantage of the proposed structures is that they are flexible as to the conversion factors, and this also for an arbitrary set of integer factors, including prime numbers. In particular, they can simultaneously implement several converters at a low cost. The proposed filters can be used to generate both general filters and Mth-band filters for interpolation and decimation by the integer factor M. (In this paper, a general filter for interpolation and decimation by M means a filter having a bandwidth of approximately /spl pi//M without the restriction that /spl pi//M be included in the transition band. This is in contrast to an Mth-band filter whose transition band does include /spl pi//M.) In both cases, the overall filter design problem can be posed as a convex problem, the solution of which is globally optimum. Design examples are included in the paper illustrating the properties and potentials of the proposed filters.     

Design of FIR digital filters using prescribed subfilters

A method for the design of linear-phase digital filters by the tapped cascaded interconnection of identical subfilters is presented. The method is an extension of the method proposed by Saramaki (1987). An example is given to show that the number of distinct multipliers of the filter determined by the proposed method is less than that of filters determined by Saramaki's method (1987). We also consider the case in which the subfilters are determined by multiple use of a single filter. In particular, if we can make the subfilters multiplierless then the number or multiplications per sample required to implement the overall filter is less than that required by the direct-form minimax method. Methods for the design of computationally efficient filters are also developed based on the proposed transformation method. The multiplication rate of the overall filter is the same as that of the prototype filter. It is very low as compared to that designed by the equivalent direct-form minimax method. With the proposed transformation method, methods for the design of a filter having nth-order tangency at both ends (0, π) are also developed. This is an extension of Vaidynathan's method (1985) and the proposed transformation method. The advantages of the method are that the resulting filters have very flat passbands and the stopbands are computationally efficient.     

Symmetric Structures for Odd-Order Maximally Flat and Weighted-Least-Squares Variable Fractional-Delay Filters

Our previous work has shown that coefficient symmetry can be exploited for designing high-accuracy and low-complexity even-order variable fractional-delay (VFD) filters. The objectives of this paper are twofold; One is to derive a coefficient symmetry for odd-order VFD filters, and then formulate a closed-form weighted-least-squares (WLS) design. Exploiting the coefficient symmetry along with different-order subfilters reduces the number of independent VFD filter coefficients by more than 50% , and thus reduces the hardware cost and the number of multipliers by more than 50%. Another objective is to briefly derive the maximally flat (MF) VFD filters from Nth-degree polynomial interpolation, and then present two kinds of transformation matrices for transforming causal odd-order MF VFD filters into symmetric structures such that the filter complexity can be reduced. As a result, both WLS and MF VFD filters can be implemented as the Farrow structure with significantly reduced complexity, which facilitates high-speed VFD filtering. Various examples are given to illustrate the effectiveness of the symmetry-based design and implementations.     

On Low-Delay Frequency-Response Masking FIR Filters

This paper offers two main contributions to the theory of low-delay frequency-response masking (FRM) finite impulse response (FIR) filters. First, a thorough investigation of the low-delay FRM FIR filters and their subfilters or three different structures, referred to as narrow-, wide-, and middle-band filter structures, is given. The investigation includes discussions on delay distribution over the subfilters as well as estimation of the optimal periodicity of the periodic model filter. Second, systematic design procedures are given, with explicit formulas for distribution of the ripples and the delay to the subfilters. For each of the three structures, two design procedures are given that include joint optimization of the subfilters. The first proposal uses partly linear-phase FIR subfilters and partly low-delay FIR subfilters. Thus, it has a lower arithmetic complexity compared to the second proposal, which has exclusively low-delay FIR subfilters. The second proposal is instead more flexible and can handle a broader range of specifications. The design procedures result in low-delay FIR filters with a lower arithmetic complexity compared to previous results, for specifications with low delay and narrow transition band.     

Least-Squares and Minimax Design of Polynomial Impulse Response FIR Filters for Reconstruction of Two-Periodic Nonuniformly Sampled Signals

This paper proposes polynomial impulse response finite-impulse response filters for reconstruction of two-periodic nonuniformly sampled signals. The foremost advantages of using these reconstruction filters are that on-line filter design thereby is avoided and subfilters with fixed dedicated multipliers can be employed in an implementation. The overall implementation cost can in this way be reduced substantially in applications where the sampling pattern changes from time to time. The paper presents two different design techniques that yield optimum filters in the least-squares and minimax senses, respectively. Design examples are included that illustrate the benefits of the proposed filters     

Least squares approximation of perfect reconstruction filter banks

Designing good causal filters for perfect reconstruction (PR) filter banks is a challenging task due to the unusual nature of the design constraints. We present a new least squares (LS) design methodology for approximating PRFBs that avoids most of these difficult constraints. The designer first selects a set of subband analysis filters from an almost unrestricted class of rational filters. Then, given some desired reconstruction delay, this design procedure produces the causal and rational synthesis filters that result in the best least squares approximation to a PRFB. This technique is built on a multi-input multi-output (MIMO) system model for filter banks derived from the filter bank polyphase representation. Using this model, we frame the LS approximation problem for PRFBs as a causal LS equalization problem for MIMO systems. We derive the causal LS solution to this design problem and present an algorithm for computing this solution. The resulting algorithm includes a MIMO spectral factorization that accounts for most of the complexity and computational cost for this design technique. Finally, we consider some design examples and evaluate their performance     

Coefficient-Symmetries for Implementing Arbitrary-Order Lagrange-Type Variable Fractional-Delay Digital Filters

In this paper, we first derive an explicit formula for expressing the coefficients of an arbitrary-order Lagrange-type variable fractional-delay (VFD) digital filter as polynomials of the VFD parameter , and then develop some useful symmetries for both even- and odd-order Lagrange-type VFD filter coefficients. The coefficient-symmetries facilitate the evaluations of VFD filter coefficients as well as variable frequency responses with reduced computational complexity. More importantly, the coefficient-symmetries can be exploited for efficiently implementing both even- and odd-order Lagrange-type VFD filters as Farrow structure and a more efficient one called even-odd structure such that the subfilters have symmetric or anti-symmetric coefficients, which saves the storage for VFD filter coefficients and reduces the number of multiplications required in VFD filtering process by almost 50%. Therefore, exploiting the coefficient-symmetries not only speeds up the VFD filtering, but also reduces implementation cost.     

Minimax design of adjustable-bandwidth linear-phase FIR filters

This paper considers the design of digital linear-phase finite-length impulse response (FIR) filters that have adjustable bandwidth(s) whereas the phase response is fixed. For this purpose, a structure is employed in which the overall transfer function is a weighted linear combination of fixed subfilters and where the weights are directly determined by the bandwidth(s). Minimax design techniques are introduced which generate globally optimal overall filters in the minimax (Chebyshev) sense over a whole set of filter specifications. The paper also introduces a new structure for bandstop and bandpass filters with individually adjustable upper and lower band edges, and with a substantially lower arithmetic complexity compared to structures that make use of two separate adjustable-bandwidth low-pass and high-pass filters in cascade or in parallel. Design examples are included in the paper.     

Design of IIR digital filters based on eigenvalue problem

This paper presents a new method for designing IIR digital filters with optimum magnitude response in the Chebyshev sense and different order numerator and denominator. The proposed procedure is based on the formulation of a generalized eigenvalue problem by using Remez exchange algorithm. Since there exist more than one eigenvalue in the general eigenvalue problem, we introduce a very simple selection rule for the eigenvalue to be sought for where the rational interpolation is performed if and only if the positive minimum eigenvalue is chosen. Therefore, the solution of the rational interpolation problem can be obtained by computing only one eigenvector corresponding to the positive minimum eigenvalue, and the optimal filter coefficients are easily obtained through a few iterations. The design algorithm proposed in this paper not only retains the speed inherent in the Remez exchange algorithm but also simplifies the interpolation step because it has been reduced to the computation of the positive minimum eigenvalue. Some properties of the filters such as lowpass filters, bandpass filters, and so on are discussed, and several design examples are presented to demonstrate the effectiveness of this method     

Generalized WLS Method for Designing All-Pass Variable Fractional-Delay Digital Filters

This paper presents an optimal weighted least squares (WLS) method for designing low-complexity all-pass variable fractional-delay (VFD) digital filters. Instead of using a fixed range for the VFD parameter p and same-order constant-coefficient filters (subfilters), both the VFD parameter range p isin [p _Min,p _Max] and subfilter orders are optimized such that a low-complexity all-pass VFD filter can be achieved for the LS design. To suppress the peak errors of variable frequency response, weighting functions are adopted and optimized such that the boundary peak errors can be further reduced but without noticeably increasing the total error energy (integral of squared error) of variable frequency response. After optimizing the variable range of the VFD parameter, weighting functions, and subfilter orders, an all-pass VFD filter can be designed by using a generalized noniterative WLS method, which yields a closed-form solution. Design examples are given to illustrate that utilizing different-order subfilters, along with the optimal range and optimal weighting functions, can yield an all-pass VFD filter with significantly reduced complexity and design errors as compared with existing ones.     

Polynomial-Based Interpolation Filters—Part I: Filter Synthesis

This paper introduces a generalized design method for polynomial-based interpolation filters. These filters can be implemented by using a modified Farrow structure, where the fixed finite impulse response (FIR) sub-filters possess either symmetrical or anti-symmetrical impulse responses. In the proposed approach, the piecewise polynomial impulse response of the interpolation filter is optimized directly in the frequency domain using either the minimax or least mean square criterion subject to the given time domain constraints. The length of the impulse response and the degree of the approximating polynomial in polynomial intervals can be arbitrarily selected. The optimization in the frequency domain makes the proposed design scheme more suitable for various digital signal processing applications and enables one to synthesize interpolation filters for arbitrary desired and weighting functions. Most importantly, the interpolation filters can be optimized in a manner similar to that of conventional linear-phase FIR filters.     

L(p) norm design of stack filters.

Addresses the problem of designing optimal stack filters by employing an L(p) norm of the error between the desired signal and the estimated one. It is shown that the L(p) norm can be expressed as a linear function of the decision errors at the binary levels of the filter. Thus, an L(p)-optimal stack filter can be determined as the solution of a linear program. The conventional design of using the mean absolute error (MAE), therefore, becomes a special ease of the general L(p) norm-based design developed here. Other special cases of the proposed approach, of particular interest in signal processing, are the problems of optimal mean square error (p=2) and minimax (p-->infinity) stack filtering. Since an Linfinity optimization is a combinatorial problem, with its complexity increasing faster than exponentially with the filter size, the proposed L(p ) norm approach to stack filter design offers an additional benefit of a sound mathematical framework to obtain a practical engineering approximation to the solution of the minimax optimization problem. The conventional MAE design of an important subclass of stack filters, the weighted order statistic filters, is also extended to the L(p) norm-based design. By considering a typical application of restoring images corrupted with impulsive noise, several design examples are presented, to illustrate the performance of the L(p)-optimal stack filters with different values of p. Simulation results show that the L(p)-optimal stack filters with p=/>2 provide a better performance in terms of their capability in removing impulsive noise, compared to that achieved by using the conventional minimum MAE stack filters.     

The design and multiplier-less realization of software radio receivers with reduced system delay

This work studies the design and multiplier-less realization of a new software radio receiver (SRR) with reduced system delay. It employs low-delay finite-impulse response (FIR) and digital allpass filters to effectively reduce the system delay of the multistage decimators in SRRs. The optimal least-square and minimax designs of these low-delay FIR and allpass-based filters are formulated as a semi-definite programming (SDP) problem, which allows zero magnitude constraint at /spl omega/=/spl pi/ to be incorporated readily as additional linear matrix inequalities (LMIs). By implementing the sampling rate converter (SRC) using a variable digital filter (VDF) immediately after the integer decimators, the needs for an expensive programmable FIR filter in the traditional SRR is avoided. A new method for the optimal minimax design of this VDF-based SRC using SDP is also proposed and compared with traditional weight least squares method. Other implementation issues including the multiplier-less and digital signal processor (DSP) realizations of the SRR and the generation of the clock signal in the SRC are also studied. Design results show that the system delay and implementation complexities (especially in terms of high-speed variable multipliers) of the proposed architecture are considerably reduced as compared with conventional approaches.     

Use Of The Remez Algorithm For Designing FRM Based FIRr Filters

A very efficient technique for drastically reducing the number of multipliers and adders in narrow transition-band linear-phase finite impulse response (FIR) filters is to use the one-stage or multistage frequency-response masking (FRM) approach as originally introduced by Lim. In the original synthesis techniques developed by Lim and Lian, the subfilters in the overall approach were designed using time-consuming linear programming. In order to perform the overall synthesis faster, this paper shows how these subfilters can be designed with the aid of the the Remez multiple exchange algorithm, the most powerful technique for designing arbitrary-magnitude linear-phase FIR filters in the minimax sense. In addition to speeding up the overall procedure, the use of the Remez algorithm enables one to generate a very fast MATLAB program for the overall synthesis so that after being given the filter specifications as well as the number of stages, the program automatically provides the solution with the minimum number of multipliers and adders required in the overall implementation. This is possible because the MATLAB Remez routine is directly available and thus can be used for this purpose after appropriate modifications.     

Three different criteria for the design of two-dimensional zerophase FIR digital filters

An error criterion for the design of FIR filters is proposed. Filters with relatively many free filter coefficients are designed using the Chebyshev, the weighted-least-squares (WLS), and a new partitioned minimax error criterion, and the performance of the filters is compared. A general and fast technique for the WLS design is also presented     

A New Method for Designing Causal Stable IIR Variable Fractional Delay Digital Filters

This paper studies the design of causal stable Farrow-based infinite-impulse response (IIR) variable fractional delay digital filters (VFDDFs), whose subfilters have a common denominator. This structure has the advantages of reduced implementation complexity and avoiding undesirable transient response when tuning the spectral parameter in the Farrow structure. The design of such IIR VFDDFs is based on a new model reduction technique which is able to incorporate prescribed flatness and peak error constraints to the IIR VFDDF under the second order cone programming framework. Design example is given to demonstrate the effectiveness of the proposed approach.     

Design of linear combination of weighted medians

This paper introduces a novel nonlinear filtering structure: the linear combination of weighted medians (LCWM). The proposed filtering scheme is modeled on the structure and design procedure of the linear-phase FIR highpass (HP) filter in that the linear-phase FIR HP filter can be obtained by changing the sign of the filter coefficients of the FIR lowpass (LP) filter in the odd positions. The HP filter can be represented as the difference between two LP subfilters that have all positive coefficients. This representation of the FIR HP filter is analogous to the difference of estimates (DoE) such as the difference of medians (DoM). The DoM is essentially a nonlinear HP filter that is commonly used in edge detection. Based on this observation, we introduce a class of LCWM filters whose output is given by a linear combination of weighted medians of the input sequence. We propose a method of designing the 1-D and 2-D LCWM filters satisfying required frequency specifications. The proposed method adopts a transformation from the FIR filter to the LCWM filter. We show that the proposed LCWM filter can offer various frequency filtering characteristics including “LP,” “bandpass (BP),” and “HP” responses     

基于LTCC技术的椭圆函数低通滤波器设计

随着无线通信领域的快速发展,人们对微波滤波器性能的要求也越来越高。文章根据滤波器的分类和特点,研究了集总元件滤波器引入传输零点的规律和方法,分析并对比了三种不同类型低通滤波器的衰减特性。根据设计指标要求,基于LTCC技术设计了一款高性能小型化的椭圆函数七阶低通滤波器。滤波器的等效电路包括串联支路中的4个电感和并联支路中的3个LC谐振腔,共10个元件。通过对滤波器模型物理结构的优化,减小了滤波器内部元件间的寄生耦合效应,并在阻带中成功引入了传输零点,改善了滤波器的性能。     

Single Filter Frequency Masking High-Speed Recursive Digital Filters

For recursive filter the maximal sample frequency is bounded by the recursive loops in the filter. [In this paper, it is understood that recursive filters are infinite-length impulse response (IIR) filters.] In this work, a filter structure based on the use of the frequency masking approach is presented that increases the maximal sample frequency for narrowband and wideband filters by introducing more delay elements in the recursive loops. By using identical subfilters (except for the periods), the subfilters can be mapped using folding to a single pipeline/interleaved arithmetic structure yielding an area-efficient implementation. The filters are potentially suitable for low-power implementation by using power supply voltage scaling techniques. In this work, the design of the filters is discussed and estimations of the ripples are derived. Two examples show the viability of the proposed method.