Frequency-Response Masking Filters Based on Serial Masking Schemes

In this paper, computationally efficient filter structures based on the frequency-response masking (FRM) technique are proposed for the synthesis of arbitrary bandwidth sharp finite impulse response (FIR) filters. A serial masking scheme is introduced in the new structures to perform the masking task in two stages, which reduces the complexity of the masking filters. Compared to the original FRM and interpolated FIR-FRM (IFIR-FRM) structures, the proposed structures achieve additional savings in terms of numbers of arithmetic operations.     

Two-Channel FIR Filter Banks Utilizing the FRM Approach

The frequency-response masking (FRM) approach has been introduced as a means of generating narrow transition band linear-phase finite impulse response (FIR) filters with a low arithmetic complexity. This paper proposes an approach for synthesizing two-channel maximally decimated FIR filter banks utilizing the FRM technique. For this purpose, a new class of FRM filters is introduced. Filters belonging to this class are used for synthesizing nonlinear-phase analysis and synthesis filters for two types of two-channel filter banks. For the first type, there exist no phase distortion and aliasing errors, but this type suffers from a small amplitude distortion as for the well-known quadrature mirror filter (QMF) banks. Compared to conventional QMF filter banks, the proposed banks lower significantly the overall arithmetic complexity at the expense of a somewhat increased overall filter bank delay in applications demanding narrow transition bands. For the second type, there are also small aliasing errors, allowing one to reduce the arithmetic complexity even further. Efficient structures are introduced for implementing the proposed filter banks, and algorithms are described for maximizing the stopband attenuations of the analysis and synthesis filters in the minimax sense subject to the given allowable amplitude and/or aliasing errors. Examples are included illustrating the benefits provided by the proposed filter banks.     

Two Classes of Frequency-Response Masking Linear-Phase FIR Filters for Interpolation and Decimation

This paper introduces two classes of frequency-response masking (FRM) linear-phase finite (length) impulse response (FIR) filters for interpolation and decimation by arbitrary integer factors M. As they are based on the FRM approach, the proposed filters are low-complexity (efficient) sharp-transition linear-phase FIR interpolation and decimation filters. Compared to previously existing FRM linear-phase FIR filter classes for interpolation and decimation, the new ones offer lower complexity and more freedom in selecting the locations of the passband and stopband edges. Furthermore, the proposed classes of FRM filters can, as special cases, realize efficient Mth-band FRM linear-phase FIR interpolation and decimation filters for all values of M. Previously, only half-band (M = 2) FRM linear-phase FIR filters have appeared in the literature. The paper includes design techniques suitable for the new filters and design examples illustrating their efficiency.     

On the Applications of the Frequency-Response Masking Technique in Array Beamforming

The frequency-response masking (FRM) technique is well known to be very efficient in the implementation of finite impulse response (FIR) filters with sharp transition bands. As sensor array beamforming is closely related to FIR filtering, the feasibility of the applications of the FRM technique in array beamforming is investigated in detail in this paper. On one hand, it is shown that there is a limitation in applying the FRM technique in passive array beamforming. On the other hand, for active array beamforming, a novel combination of the concept of effective aperture and the FRM technique does lead to the synthesis of desirable beamformers. These beamformers have effective beampatterns with sharp transition bands and low sidelobes, and can be implemented with fewer sensors than other design techniques.     

一种可变带宽FRM滤波新结构

设计窄过渡带FIR滤波器的一种非常有效的方法是采用频率响应屏蔽技术(FRM).但是如果过渡带要求过窄,经典FRM滤波器各子滤波器的阶数会变得很高.据此,本文提出一种可变带宽镜像半带滤波FRM滤波新结构,通过增加两个镜像半带滤波器,将原型滤波器及其互补滤波器的镜像分别分成奇偶两部分,使得原型滤波器和屏蔽滤波器的设计更加灵活,并降低了滤波器的计算复杂度,达到了设计高效窄过渡带滤波器的目的.理论分析和实例均验证了该结构的有效性.     

Complexity Reduction For FRM-based FIR Filters Using The Prefilter-Equalizer Technique

A new method to reduce the number of arithmetic operations in a sharp FIR filter synthesized by the frequency-response masking (FRM) technique is presented. The success of the proposed method is based on a modified FRM approach where the subfilters in the FRM approach are implemented by using recently introduced prefilter-equalizer based filters. It is shown, by means of examples, that the proposed method yields considerable savings in the numbers of multipliers and adders compared to the original single-stage FRM approach.     

Synthesis of Wideband Linear-Phase FIR Filters with a Piecewise-Polynomial-Sinusoidal Impulse Response

A method is presented to synthesize wideband linear-phase finite-impulse-response (FIR) filters with a piecewise-polynomial-sinusoidal impulse response. The method is based on merging the earlier synthesis scheme proposed by the authors to design piecewise-polynomial filters with the method proposed by Chu and Burrus. The method uses an arbitrary number of separately generated center coefficients instead of only one or none as used in the method by Chu–Burrus. The desired impulse response is created by using a parallel connection of several filter branches and by adding an arbitrary number of center coefficients to form it. This method is especially effective for designing Hilbert transformers by using Type 4 linear-phase FIR filters, where only real-valued multipliers are needed in the implementation. The arithmetic complexity is proportional to the number of branches, the common polynomial order for each branch, and the number of separate center coefficients. For other linear-phase FIR filter types the arithmetic complexity depends additionally on the number of complex multipliers. Examples are given to illustrate the benefits of this method compared to the frequency-response masking (FRM) technique with regard to reducing the number of coefficients as well as arithmetic complexity.     

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.     

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.     

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.     

A Novel Diversity-Controlled Genetic Algorithm for Rapid Optimization of Bandpass FRM FIR Digital Filters Over CSD Multiplier Coefficient Space

The conventional frequency response masking (FRM) approach is one of the most well-known techniques for the design of sharp transition band finite impulse response (FIR) digital filters. The resulting FRM digital filters permit efficient hardware implementations due to an inherently large number of zero-valued multiplier coefficients. The hardware complexity of these digital filters can further be reduced by representing the remaining (non-zero) multiplier coefficient values by using their canonical signed-digit (CSD) representations. This paper presents a novel diversity-controlled (DC) genetic algorithm (GA) for the discrete optimization of bandpass FRM FIR digital filters over the CSD multiplier coefficient space. The resulting bandpass FIR digital filters are permitted to have equal or unequal lower and upper transition bandwidths. The proposed DCGA is based on an indexed look-up table of permissible CSD multiplier coefficients such that their indices form a closed set under the genetic operations of crossover and mutation. The salient advantage of DCGA over the conventional GA lies in the external control over population diversity and parent selection, giving rise to a rapid convergence to an optimal solution. The external control is achieved through the judicious choice of a pair of DCGA optimization parameters. An empirical investigation is undertaken for choosing appropriate values for these control parameters. The convergence speed advantages of the DCGA are demonstrated through its application to the design and optimization of a pair of bandpass FRM FIR digital filters with equal or arbitrary lower and upper transition bandwidths. In both cases, an increase of about an order of magnitude in the speed of convergence is achieved as compared to the conventional GAs.     

基于频率响应屏蔽技术的采样率变换新结构

介绍了频率响应屏蔽(FRM)技术在采样率变换技术中的应用,分析了FRM的简化结构——内插滤波器的设计方法。将此滤波器应用于采样率变换中,并结合多相滤波思想提出了一种高效的FRM采样率变换结构,此结构能极大降低采样率变换实现复杂度。最后通过设计实例,验证了此结构的高效性。     

Complexity Reduction By Decoupling The Masking Filters From The Bandedge Shaping Filter In The FRM Technique

In the frequency-response masking (FRM) approach, the complexity of two masking filters is heavily dependent on the interpolation factor and the cutoff frequencies of the bandedge shaping filter. In this paper, we propose a novel structure that decouples the masking filters from the bandedge shaping filter. The design equations together with the design procedures are presented. With the introduction of an additional decoupling stage, the complexity of the overall filter can be greatly reduced. Our example shows that more than 40% savings in the numbers of multipliers and adders can be achieved compared with the original FRM approach.     

On the synthesis of very sharp decimators and interpolators using the frequency-response masking technique

Decimation and interpolation are very common multirate signal processing operations. Conventional decimation or interpolation technique using polyphase filters has the advantage that for a given transition-band sharpness, the filter's computational complexity decreases with increasing interpolation or decimation factor. Nevertheless, if the transition band of the decimation or interpolation filter is very sharp, the complexity of the filter may still be very high. The complexity of a very sharp filter may be reduced using the frequency-response masking (FRM) technique. However, as shown in this paper, for a given transition-band sharpness, the computational complexity of the classical FRM method does not reduce as rapidly as the increase in decimation or interpolation factor. In this paper, we present a novel variant of the FRM technique for interpolation or decimation application. In this new variant, the computational complexity reduces as rapidly as the interpolation or decimation factor increases. The reduction in computational complexity increases with decreasing transition width. Over an order of magnitude reduction in computational complexity is achieved when compared with conventional polyphase approach in a particular example presented in this paper.     

A Low Complexity Reconfigurable Multi-stage Channel Filter Architecture for Resource-Constrained Software Radio Handsets

Software defined radio (SDR) is emerging as a powerful platform for future generation cellular systems, due to its capability to operate conforming to multiple mobile radio standards. Channelizer in an SDR operates at the highest sampling rate and hence a low complexity design is needed for the most computationally intensive part of the SDR receiver. The channel filters in the channelizer extracts radio channels of varying bandwidths, corresponding to various communication standards from the wideband input signal. An architecture for implementing low complexity, low power and reconfigurable channel filter for the SDR mobile handsets, based on multi-stage frequency response masking (FRM) is proposed in this paper. The proposed architecture is unique in a way that it is able to effectively exploit the redundancy in multi-stage realization by utilizing the common masking filters and also capable of extracting varying bandwidth channels. Design examples show that the proposed architecture offers 47.5% complexity reduction and 18.1% power reduction over single-stage FRM approach.     

An Efficient Algorithm for the Optimization of FIR Filters Synthesized Using the Multistage Frequency-Response Masking Approach

A very efficient technique to drastically reduce the number of multipliers and adders in narrow transition-band linear-phase finite-impulse response digital filters is to use the one-stage or multistage frequency-response masking (FRM) approach, which has been originally introduced by Lim and further improved by Lim and Lian. In these original synthesis techniques, the subfilters in the overall implementation are separately designed. As shown earlier by the authors of this contribution together with Johansson, the arithmetic complexity in one-stage FRM filter designs can be considerably reduced by using the following two-step technique for simultaneously optimizing all the subfilters. First, a suboptimal solution is found by using a simple design scheme. Second, this solution is used as a start-up solution for further optimization, which is carried out with the aid of an efficient nonlinear optimization algorithm. This paper exploits this approach to synthesizing multistage FRM filters. An example taken from the literature illustrates that both the number of multipliers and the number of adders for the resulting optimized multistage FRM filters are approximately 70 percent compared with those of the filters synthesized using the original multistage FRM filter design schemes. Additional examples are included in order to show the benefits provided by the proposed synthesis scheme over other recently published design techniques, in terms of an improved performance of the resulting solution, a higher accuracy of the solution, and a faster speed required to arrive at the best solution.     

Reconfigurable Frequency Response Masking Filters for Software Radio Channelization

Low complexity and reconfigurability are two key requirements of channel filters in a software defined radio receiver. A new reconfigurable architecture based on frequency response masking (FRM) technique for the implementation of channel filters is proposed in this paper. Our architecture offers reconfigurability at filter and architecture levels, in addition to the inherent low complexity offered by the FRM technique. The proposed reconfigurable filter has been synthesized on 0.18- CMOS technology and implemented and tested on Virtex-II 2v3000ff1152-4 field-programmable gate array. Synthesis results show that the proposed channel filter offers average area and power reductions of 53.6% and 57.6%, respectively ,with average improvement in speed of 47.6% compared to other reconfigurable filters in literature.     

基于FRM结构的FIR滤波器的采样率变换方法

该文在分析滤波器传递函数的对称性与其冲激响应的关系的基础上,提出了一类具有稀疏冲激响应系数的特殊滤波器,以这类滤波器作为原型滤波器可以进一步降低FRM结构FIR滤波器的计算复杂度。并研究了基于此类FRM结构FIR滤波器的采样率变换算法、实现结构、计算复杂度及其设计问题等。最后,通过实际例子验证这种采样率变换方法的有效性。     

Modified Metaheuristic Algorithms for the Optimal Design of Multiplier-Less Non-uniform Channel Filters

Reconfigurable non-uniform channel filters are now being widely used in software define radio (SDR). The hardware implementation of these filters requires low complexity, low chip area and low power consumption. The frequency response masking (FRM) approach is proved to be a good candidate for the realization of a sharp digital finite impulse response (FIR) filter with low complexity. To reduce the complexity further, this paper gives an optimal design method which makes the channel filters totally multiplier-less. This is done in two steps. The channel filters are designed using the FRM approach with continuous filter coefficients. To obtain multiplier-less design, these filter coefficients are converted to finite-precision coefficients using signed power of two (SPT) space and the filter coefficients are synthesized in the canonic signed-digit (CSD) format. But this may lead to degradation of the filter performance. Hence the filter coefficients synthesis in the CSD format is formulated as an optimization problem. Several meta-heuristic algorithms like Differential Evolution (DE), Artificial Bee Colony (ABC), Harmony Search Algorithm (HSA) and Gravitational Search Algorithm (GSA) are modified and deployed and the best one is selected.     

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