双模方形带通滤波器的分析、建模及设计

本文报道一种利用谐振器中缺口位置设计双模带通滤波器的新方法.用这种方法既可以实现具有一对传输零点的双模带通滤波器,也可以实现无传输零点的双模带通滤波器.通过分析缺口位置对谐振器内电场模式分布的影响,建立了双模滤波器的拓扑结构图.利用全波仿真软件,基于不同的缺口位置设计了中心频率为2.05GHz,带宽为100MHz的两种...     

Design of separable-denominator 2-D digital filters using the reduced-dimensional decomposition model

A separable-denominator 2-D digital filter (SD-2DDF) can be decomposed into the cascade form of a pair of 1-D digital filters (1DDFs) with different delay elements. Based on this reduced-dimensional decomposition, in this paper, we propose a new technique for designing SD-2DDFs in the spatial domain. The technique determines the coefficient matrices of 1DDFs by nonlinear optimization techniques first, and then a SD-2DDF can be easily synthesized. In addition, since the existent 1-D linear system realization techniques can be used to choose a good starting point for the optimization, extremely accurate design results can be easily achieved.     

Efficient design of digital filters for 2-D and 3-D depth migration

Two- and three-dimensional (2-D and 3-D) depth migration can be performed using 1-D and 2-D extrapolation digital filters, respectively. The depth extrapolation is done, one frequency at a time, by convolving the seismic wavefield with a complex-valued, frequency- and velocity-dependent, digital filter. This process requires the design of a complete set of extrapolation filters: one filter for each possible frequency-velocity pair. Instead of independently designing the frequency- and velocity-dependent filters, an efficient procedure is introduced for designing a complete set of 1-D and 2-D extrapolation filters using transformations. The problem of designing a desired set of migration filters is thus reduced to the design of a single 1-D filter, which is then mapped to produce all the desired 1-D or 2-D migration filters. The new design procedure has the additional advantage that both the 1-D and 2-D migration filters can be realized efficiently and need not have their coefficients precomputed or tabulated     

A Very Efficient Approach for the Synthesis of 2-D Recursive Fan Filters

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基于扩频通信的抗干扰陷波技术研究

通过分析直接序列扩频通信系统所面临的阻塞式窄带干扰问题,提出了一种抗干扰窄带陷波技术;对集总参数、分布式参数滤波器进行了分析和变换,建立了同轴腔可调谐窄带陷波器电路模型,给出了一种适于宽频段抗干扰陷波的工程设计和实现方法,并对所设计电路进行了制作和实验;测试结果表明,该方法不但能提高滤波器的通带调谐范围,而且还可以对阻带的凹口深度和宽度进行叠加控制.试验结果证实了该方法的有效性和正确性.     

Design of some 2-D filters through the transformation technique

The transformation technique is a powerful tool for designing 2-D FIR filters. However, it is not useful for the design of specially shaped filters with passband/stopband regions not centred around the origin. The authors extend this technique to design two types of filters. A notch filter has a stopband centred about a small region in the 2-D frequency plane. The authors propose an extension to the transformation technique with the windowing concept to achieve the design of notch filters. A directional filter has a passband extending fully along a straight line passing through the origin. The transformation technique is further extended to yield such directional filters. Design and application examples for both these filters are also presented     

Design of zero-phase recursive 2-D variable filters with quadrantal symmetries

The digital filters with adjustable frequency-domain characteristics are called variable filters. Variable filters are useful in the applications where the filter characteristics are needed to be changeable during the course of signal processing. In such cases, if the existing traditional constant filter design techniques are applied to the design of new filters to satisfy the new desired characteristics when necessary, it will take a huge amount of design time. So it is desirable to have an efficient method which can fast obtain the new desired frequency-domain characteristics. Generally speaking, the frequency-domain characteristics of variable filters are determined by a set of spectral parameters such as cutoff frequency, transition bandwidth and passband width. Therefore, the characteristics of variable filters are the multi-dimensional (M-D) functions of such spectral parameters. This paper proposes an efficient technique which simplifies the difficult problem of designing a 2-D variable filter with quadrantally symmetric magnitude characteristics as the simple one that only needs the normal one-dimensional (1-D) constant digital filter designs and 1-D polynomial approximations. In applying such 2-D variable filters, only varying the part of 1-D polynomials can easily obtain new desired frequency-domain characteristics.     

基于巴特沃斯逼近的二维IIR数字滤波器的设计

本文给出了一种基于巴特沃斯逼近的二维ＩＩＲ数字滤波器的设计方法，得到了由基本的全通节级联，并联实现的各种二维滤波器函数，包括，镜象对称互补滤波器，扇形滤波器和具有任意矩形通、阻带的滤波器，结果表明，这种实现结构具有通有灵敏度低、滤波器系数少的优点，并且由于巴特沃斯逼近的最大平坦性，得到的滤波器具有良好的相位特性。     

Flexible design of multidimensional perfect reconstruction FIR2-band filters using transformations of variables

An approach to designing multidimensional linear-phase FIR diamond subband filters having the perfect reconstruction property is presented. It is based on a transformation of variables technique and is equivalent to the generalized McClellan transformation. Methods for designing a whole class of transformation are given. The approach consists of two parts; design of the transformation and design of the 1-D filters. The use of Lagrange halfband filters to design the 1-D filters is discussed. The modification of a particular Lagrange halfband filter which gives a pair of simple 1-D filters that are almost similar to each other in their frequency characteristics but still form a perfect reconstruction pair is presented. The design technique is extended to other types of two-channel sampling lattice and subband shapes, in particular, the parallelogram and the diagonally quadrant subband cases. Several numerical design examples are presented to illustrate the flexibility of the design method.     

使用差分方法消除微机电滤波器的穿通以及对由此引入的陷波现象的分析

This paper presents and analyzes a notch observed in MEMS(micro electric mechanical system) filter characterization using the difference method.The difference method takes advantage of the cancellation of parasitic feed-through,which could potentially obscure the relatively small motional signal and lead to failure in characterization of the MEMS components.In this paper,typical clamped-clamped beam MEMS filters are fabricated and characterized with the difference method.Using the difference method a better performance is obtained but a notch is induced as a potential problem.Analysis is performed and reveals the mismatch of the two differential excitation signals in measurement circuit contributes to the notch.The relevant circuit design rule is also proposed to avoid the notch in the difference method.     

巴特沃斯数字陷波滤波器的设计

随着数字技术的发展,数字滤波器在许多领域得到广泛的应用。研究一种在Matlab语言环境下设计IIR数字陷波滤波器的方法,在数字陷波滤波器设计过程中,先进行模拟低通滤波器的设计,然后进行模拟低通/模拟带阻滤波器转换,最后采用双线性变化法将模拟陷波滤波器转化成数字陷波滤波器。提出一种用所有零点和极点来表达数字陷波器传递函数的方法,同时给出以巴特沃斯模拟低通为原型设计数字陷波滤波器的程序。     

A novel nonnegative decomposition method and its application to 2-D digital filter design

In designing two-dimensional (2-D) digital filters in the frequency domain, an efficient technique is to first decompose the given 2-D frequency domain design specifications into one-dimensional (1-D) ones, and then approximate the resulting 1-D magnitude specifications using the well-developed 1-D filter design techniques. Finally, by interconnecting the designed 1-D filters one can obtain a 2-D digital filter. However, since the magnitude responses of digital filters must be nonnegative, it is required that the decomposition of 2-D magnitude specifications result in nonnegative 1-D magnitude specifications. We call such a decomposition the nonnegative decomposition. This paper proposes a nonnegative decomposition method for decomposing the given 2-D magnitude specifications into 1-D ones, and then transforms the problem of designing a 2-D digital filter into that of designing 1-D filters. Consequently, the original problem of designing a 2-D filter is significantly simplified.     

Design of two-dimensional digital filters using singular-valuedecomposition and balanced approximation method

It is shown that the singular-value decomposition (SVD) of the sampled amplitude response of a two-dimensional (2-D) digital filter possesses a special structure: every singular vector is either mirror-image symmetric or antisymmetric with respect to its midpoint. Consequently, the SVD can be applied along with 1-D finite impulse response (FIR) techniques for the design of linear-phase 2-D filters with arbitrary prescribed amplitude responses which are symmetrical with respect to the origin of the (ωΨω₂) plane. The balanced approximation method is applied to linear-phase 2-D FIR filters of the type that may be obtained by using the SVD method. The method leads to economical and computationally efficient filters, usually infinite impulse response filters, which have prescribed amplitude responses and whose phase responses are approximately linear     

On the use of continued fraction filter structures for the design of 2-D digital filters

In this paper a method for the realization of 2-D recursive digital filters of second order by means of continued fraction filter structures is presented. The proposed method is based on the interconnection of basic filter structures of first order and gives also the set of all 2-D transfer functions that are realizable by these structures. The general rule for interconnecting these basic structures is described. It is proved that, on the set of second order fraction filter structures, some classes of structures and ordering relations can be defined, so that the set of all the classes form a partially ordered set (poset). Those structures which least constrain the coefficients of the transfer function are defined maximum elements of the poset. It is shown that among all possible continued fraction structures of second order only six are suitable for realization of two dimensional filters. Some results following from the use of spectral transformations are discussed.     

Generating 2-D FIR filter functions by Christoffel–Darboux formula for Chebyshev polynomials of the second kind

Global Christoffel–Darboux formula for different polynomials has already been used for the filter design. Here, this formula for orthonormal Chebyshev polynomials of the second kind and for two independent variables is applied in generating novel class linear-phase two-dimensional (2-D) finite impulse response (FIR) digital filter functions. In this way, 2-D filters with some specific features including economy, phase linearity, symmetry and selectivity are designed. Representative examples of the 2-D FIR digital filters of a new class obtained by the proposed approximation technique are given. A filter generated by the proposed approach is compared with the corresponding one generated by the procedure from literature.     

Digital notch filters

The letter deals with the special class of digital filters that possess a prescribed notch frequency. The present techniques for synthetising such filters rest on the bilinear-transformation method, where the designer is required to synthetise a continuous s plane notch filter, prewarp it, and then apply the transformation. It is shown here that notch filters can be synthetised directly into the z?1 plane.     

Duality of log-polar image representations in the space andspatial-frequency domains

In this paper, we study the result of applying a lowpass variant filtering using scaling-rotating kernels to both the spatial and spatial-frequency representations of a two-dimensional (2-D) signal (image). It is shown that if we apply this transformation to a Fourier pair, the two resulting signals can also form a Fourier pair when the filters used in each domain maintain a dual relationship. For a large class of “self-dual” filters, a perfect symmetry exists, so that the lowpass scaling-rotating variant filtering (SRVF) is the same in both domains, thus commuting with the Fourier transform operator. The lowpass SRVF of an image is often referred to as a “foveated” image, whereas its Fourier pair (the lowpass SRVF of its spectrum) can be realized as a local spectrum estimation around the point of attention. This lowpass SRVF is equivalent to a log-polar warping of the image representation followed by a lowpass invariant filtering and the corresponding inverse warping. The use of the log-polar warped representation allows us to extend the one-dimensional (1-D) scale transform to higher dimensions, in particular to images, for which we have defined a scale-rotation invariant representation. We also present an efficient implementation using steerable filters to compute both the foveated image and the local spectrum     

An iterative approach for minimax design of multidimensional quadrature mirror filters

In this paper, a nest of iterative techniques is proposed for the minimax design of quadrature mirror filter (QMF) banks. The method can be generalized such that multidimensional QMF banks can be designed by the proposed algorithm. For a given weighting function, an iterative method is used to minimize the objective error function in the inner iterations. To further reduce the peak error of overall magnitude response, an iterative weighting-updated technique is adopted in the outer iterations. Comparing with the existing works concern the design of perfect-reconstruction QMF banks, only one of the filters is needed to be designed under the cost of magnitude distortion, but the system complexity can be reduced drastically. Several examples, including design of 2-D and 3-D QMF banks, will be presented to demonstrate the effectiveness of the proposed method.     

Time-varying AR modeling and adaptive IIR notch filter for anti-jamming DSSS receiver

Using Time-Varying AR (TVAR) model and adaptive notch filter is a new method for the non-stationary jammer suppression in Direct Sequence Spread Spectrum (DSSS). The performance of TVAR model for Instantaneous Frequency (IF) estimation will be affected by some factors such as basis functions. Focusing on this problem, the optimal basis function of TVAR model for the IF estimation of the LFM signal is obtained in this paper. Besides the depth and width of notching, the phase properties of notch filter affect the Signal-to-Interference plus-Noise Ratio (SINR) of correlation output to the narrowband jammer suppression in DSSS, in response to the problem the closed solution of correlation output SINR improvement has been derived when a single frequency jammer passes through direct IIR notch filter, and its performance has been compared with those of five coefficient FIR filters. Later, a novel method for LFM jammer suppression based on Fourier basis TVAR model and direct IIR notch filter is proposed. The simulation results show the effectiveness of the proposed method.     

Realization of 2-D Variable IIR Digital Filter Structures with a Small Amount of Calculations for Coefficient Update

This paper proposes 2-D variable IIR digital filter structures with a small amount of calculations for coefficient update. The proposed realization method uses the 2-D parallel allpass structure derived from the separable denominator 2-D filter as the prototype structure for 2-D variable digital filters. In order to reduce the amount of calculations, all the redundant first-order complex allpass sections are combined by modularization of the variable structure. Furthermore, we can realize a very compact variable structure with a minimal number of first-order complex allpass sections by combining complex allpass sections with their complex conjugate allpass sections. Comparison of the calculation loads of the variable structures is presented to demonstrate that the amount of calculations for coefficient update of the proposed variable structure is far less than that of the original and the modular variable structure.