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.     

High strain-induced wavelength tunability in tapered fibreacousto-optic filters

A study into the effect of the strain on a tapered fibre acoustooptic filter is presented. The centre wavelengths of the resonances are dramatically affected by strain: >500 nm tunability range has been obtained for a maximum applied strain of 1.3×10^-2     

Analogue elliptical filters with digital control and memory

To control active filter characteristics a new type of integrated circuit (IC) of Xicor Inc. is used. This is an analogue potentiometer with digital control and non volatile memory. Usage of this IC is convenient when the storage of the last results is required. The control parameters are estimated for applications on elliptical low-pass and high-pass voltage-controlled voltage source filters. Practically obtained diagrams are given.     

Axial-mode elliptical helical antenna with variable pitch angle

To improve an elliptical cross-section helical antenna's radition performance, an elliptical helical antenna with a variable pitch angle is proposed. Its radiation patterns are simulated by the moment method and FEKO software. The results show that its circular polarisation as well as its directivity can be improved compared with an elliptical helical antenna of the same coil number, axial size and arm length.     

Design of 2D FIR digital filters with flatness constraints for the error function

A method will be presented for the approximation of a desired two-dimensional frequency response by the frequency response of a two-dimensional finite-impulse-response digital filter. It is possible to match the functional values and an arbitrary number of derivatives of both responses for zero frequency, thus making the error flat up to a desired degree. Remaining degrees of freedom are used for anL ₂-approximation. Closed form design formulae will be given.     

Realisation of 2D analogue filters

A modified method is presented for the realisation of 2D analogue filters used for processing television images. The proposed procedure reduces the required number of integrators considerably. For Example, for the second- and third-order cases, the reduction in the number of integrators would be seven and 21, respectively.<>     

Microstrip stepped impedance filters with variable dielectric or variable width

A stepped impedance filter has been realised on a modified substrate. The change in impedance was achieved by varying the dielectric constant in the substrate while maintaining a constant width of the microstrip. In contrast to conventional stepped impedance filters the impedance is varied by the dielectric constant instead of the microstrip line width. The manufactured filter was measured and compared with an equivalent conventional stepped impedance filter. It is shown that the modified substrate technology could offer an alternative to the standard approach for the stepped impedance filter. In combination with new materials with a high permittivity the technology could also offer a denser package since the microstrip width could be controlled as desired.     

Design of complex-coefficient variable digital filters using successive vector-array decomposition

Singular-value decomposition (SVD) can be efficiently utilized to obtain the optimal vector-array decomposition (VAD) for simplifying real-coefficient variable digital filter design problem, but the SVD-based VAD methods are not applicable to the design of complex-coefficient variable filters. This paper proposes a successive algorithm for decomposing arbitrary multidimensional complex array into the VAD form, and thus, a complex-coefficient variable digital filter with arbitrary variable frequency response can be easily obtained through constant complex-coefficient filter design and multidimensional polynomial fitting. The new VAD algorithm successively decomposes the complex array and its residual arrays into the vector-array pairs stage by stage, and each stage contains an iterative optimization that can be easily solved in a closed-form. Our computer simulations have demonstrated that the successive VAD converges very fast to the optimal solution.     

Design of arbitrary-phase variable digital filters using SVD-based vector-array decomposition

This paper proposes a straightforward method for designing variable digital filters with arbitrary variable magnitude as well as arbitrary fixed-phase or variable fractional delay (VFD) responses. The basic idea is to avoid the complicated direct design of one-dimensional (1-D) variable digital filters by decomposing the original variable filter design problem into easier subproblems that only require constant 1-D filter designs and multidimensional polynomial approximations. Through constant 1-D filter designs and multidimensional polynomial fits, we can easily obtain a variable digital filter satisfying the given variable design specifications. To decompose the original variable filter design into constant 1-D filter designs and multidimensional polynomial fits, a new multidimensional complex array decomposition called vector array decomposition (VAD) is proposed, which is based on two new theorems using the singular value decomposition (SVD). Once the VAD is obtained, the subproblems can be easily solved. Furthermore, we show that the VAD can also be generalized to the weighted least squares (WLS) case (WLS-VAD) for the WLS variable filter design. Three design examples are given to illustrate that the WLS-VAD and VAD-based techniques are considerably efficient for designing variable digital filters with arbitrary variable magnitude and arbitrary fixed-phase or VFD responses.     

On linear-phase FIR filters with variable bandwidth

Recently, a particular structure for linear-phase finite-impulse response (FIR) filters with a variable bandwidth has received attention. In this structure, the overall transfer function is a weighted linear combination of fixed subfilters, with the weights being directly determined by the bandwidth. An advantage of this structure is that there are only a few adjustable parameters (weights), which results in a simple updating routine. However, in this paper, it is demonstrated that the use of a number of fixed regular overdesigned filters, each taking care of a part of the frequency region, in fact results in a lower overall arithmetic complexity. The price to pay is an increased group and phase delay.     

Design of stable IIR filters in the complex domain by automaticdelay selection

A major problem encountered when designing infinite impulse response (IIR) filters in the complex domain is to ensure that the filter is stable. Instability occurs frequently when the IIR filter approximates the inverse of a nonminimum phase system. This is often the case for equalization filters. Addition of delay to the target frequency response can result in a stable filter. However, to date, delay selection has been a matter of trial and error. The article presents an automated method for finding the delay     

用PAC-Designer设计滤波器

近年来,数字系统的EDA技术及可编程逻辑器件的发展极大地改变了传统电子系统的设计思想和实现方法,但是模拟电路的设计手段似乎还停滞不前。现在,由美国Lattice公司推出的模拟电路在系统可编程技术ispPAC使这种情况发生了变化,为模拟电路的设计自动化翻开了新的一页。ispPAC及PAC-Designer的特点 与数字系统的在系统可编程技术类似,模拟电路的在系统可编程技术允许设计者使用开发软件在计算机中设计和修改模拟电路,并通过编程电缆将设计方案下载到可编程模拟器件中,从而加快设计进程,提高系统设计的准确性,为电子系统设计人员开发产品提供了一条崭新的途径。目前由     

Design and implementation of filters using transfer functions inthe Z domain

In this paper, a novel approach composed of digital signal-processing techniques and optimization algorithms is developed to design and implement filters at microwave frequencies. The design phase begins with the adoption of digital filter prototypes and the implementation phase is facilitated by using both parametric modeling techniques and optimization algorithms. All the zeros of digital filter prototypes are removed first; the remaining part of the prototypes is then transformed to an autoregressive (AR) process by parametric modeling techniques. The values of characteristic impedances of transmission lines synthesizing the filters are adjusted according to the AR process by optimization algorithms. Both low-pass and bandpass filters are designed and then implemented in the form of a microstrip line, and their frequency responses are measured to validate the novel approach     

N-order direct form digital filters with integer arithmetic

For direct form digital filters with integer arithmetic, a characterization of the initial condition vector and state vectorX(), for a fixed, > 1, is established without the intermediate state vectors. This is used to determine initial conditions for stability and initial conditions for convergence to a limit cycle. Also, several properties of limit cycles are proven.     

Design of 2-dimensional recursive digital filters

A method is proposed for designing 2-dimensional recursive digital filters with circular symmetry and zero phase. The method is based on transformations of the squared magnitude function of a 1-dimensional digital filter and on the stabilisation of the resulting digital filter. Design results are given.     

Fabrication of variable bandwidth filters using arrayed-waveguidegratings

Variable bandwidth filters have been fabricated using silica-based N×N arrayed-waveguide gratings. The centre wavelengths are λ₀=1.55 μm for all channels. The 3 dB bandwidths are 40, 78, 116 and 154 GHz, for the filter with a path length difference ΔL=63 μm. In the filter with ΔL=8.6 μm, the 3 dB bandwidths are 414, 769, 1198 and 1608 GHz. The on-chip losses are 2.1-2.9 dB and sidemode suppression ratios are larger than 27 dB     

Design of IIR digital filters in the complex domain by transforming the desired response

In this paper, we present a new design method of infinite impulse response (IIR) digital filters with quasi-equiripple absolute error in the complex domain. This method is based on solving a least squares solution iteratively. At each iteration, the desired response for the least squares approximation is transformed to have equiripple error. This algorithm is efficient because there is no need for any initial value or complex optimization algorithm. By this method, a quasi-equiripple solution is obtained very quickly with less computational complexity. Moreover, by multiplying an arbitrary weighting function on the desired responses of passband and stopband, respectively, the error at the passband and stopband can be controlled. Finally, we show some examples to validate the proposed method.     

A new MEMS based variable capacitor with wide tunability,high linearity and low actuation voltage

We have proposed a new RF MEMS variable capacitor to achieve high linearity, wide tunability and low actuation voltage. The idea is based on increasing the linear region in the gap between the plates of the capacitor. It is done by adding a fixed-fixed beam below the fixed-free beam. The fixed-free beam is one plate of the capacitor. The voltage is applied to the fixed-free beam. In the vicinity of the pull-in voltage, the fixed-free beam losses its equivalent stiffness. The fixed-fixed beam is located in the vicinity of pull in situation of the fixed-free beam. This condition increases the equivalent stiffness of the fixed-free beam and allows the beam to continue moving down linearly and consequently increases the maximum capacitance of the structure. Geometrical and material property effects of the second beam on the linearity, tunability and voltage are investigated. The governing nonlinear equation for static deflection of the beam based on the Euler–Bernoulli beam theory has been presented.     

Counterexample in the least-squares inverse stabilisation of 2D recursive filters

A counterexample is presented disproving the conjecture that the planar least-squares inverse of a 2-variable polynomial is devoid of zeros when both variables are inside or on the unit circle.     

Design of stable 2-dimensional discrete recursive filters

The letter presents preliminary results on the design of stable 2-dimensional (2d) discrete recursive filters. The method is based on the properties of multivariable positive real functions and multivariable passive networks, and results in an approach wherein the stability of the filter is guaranteed.