Design of two-dimensional directional filters

A directional filter has a passband extending fully along a straight line passing through the origin. In its original form the transformation technique, a powerful tool for designing two-dimensional FIR filters, is not useful to design such a filter. In this communication we suggest a few analytical and optimisation-based methods to design directional filters using the transformation technique. The superiority of the proposed methods over existing techniques is demonstrated.     

Quasi-elliptic compact high-power notch filters using a mixedlumped and distributed circuit

A quasi-elliptic notch filter response is defined as one in which the ultimate stopband depth is sacrificed in favor of a faster transition from the passband to a specified minimum equiripple stopband attenuation level (i.e., steeper attenuation slope) with no increase in filter order (as compared to a Chebyshev or similar transfer function design). Such notch-filter responses can be achieved if the topology synthesized includes arbitrary frequency invariant impedances and line lengths in the main series line of filters. Using lumped approximations to the series coaxial sections but with the series sections not at 50 Ω (for a 50-Ω filter), it is possible to improve upon the Chebyshev-based results. The resulting network provides lower passband insertion loss, with no reduction in minimum notch depth or power handling, improved temperature performance and additional harmonic reduction. The improvements are due to the implementation of the quasi-elliptic response defined above, and are made possible by the larger range of main line impedances and line lengths available using inductors and capacitors rather than lengths of transmission line. In principle, the technique can be extended to achieve full-elliptic responses     

Design of 2-D FIR Filters by a Feedback Neural Network

A Hopfield-type neural network for the design of 2-D FIR filters is proposed. The network is contrived to have an energy function that coincides with the sum-squared error of the approximation problem at hand and by ensuring that the energy is a monotonic decreasing function of time, the approximation problem can be solved. Two solutions are obtained. In the first the 2-D FIR filter is designed on the basis of a specified amplitude response and in the second a filter that has specified maximum passband and stopband errors is designed. The network has been simulated with HSPICE and design examples are included to show that this is an efficient way of solving the approximation problem for 2-D FIR filters. The neural network has high potential for implementation in analog VLSI and can, as a consequence, be used in real-time applications.     

A filter bank for the directional decomposition of images: theoryand design

The authors introduce a directionally oriented 2-D filter bank with the property that the individual channels may be critically sampled without loss of information. The passband regions of the component filters are wedge-shaped and thus provide directional information. It is shown that these filter bank outputs may be maximally decimated to achieve a minimum sample representation in a way that permits the original signal to be exactly reconstructed. The authors discuss the theory for directional decomposition and reconstruction. In addition, implementation issues are addressed where realizations based on both recursive and nonrecursive filters are considered     

A new method for the design of IIR filters with flat magnitude response

This paper presents a new direct design of infinite-impulse response (IIR) filters with a flat magnitude response in both passband and stopband (Butterworth filters). The design specifications are passband and stopband frequencies and passband droop and stopband attenuation. The approach is based on an allpass filter with flatness at frequency points /spl omega/=0 and /spl omega/=/spl pi/. Depending on the parity of the IIR filter order, the allpass filter is either real or complex. However, in both cases, the resulting IIR filter is real.     

Design of nonseparable 3-D filter banks/wavelet bases usingtransformations of variables

The authors present a technique to design two-channel filter banks in three dimensions where the sampling is on the FCO (face centred orthorhombic) lattice, The ideal 3-D sub-band is of the truncated octahedron shape. The design technique is based transformation of variable method equivalent to the generalised McClellan transformation. The filters are FIR, have linear phase and achieve perfect reconstruction. Although the sub-band shape is quite complicated, the ideal frequency characteristics are well approximated. This is illustrated with an example. The technique provides the flexibility of controlling the frequency characteristics of the filters with ease. The filters can be implemented quite efficiently due to the highly symmetrical nature of the coefficients of the transformation. The authors also modify and extend the basic design technique to impose the zero property (the number of zeros of the filter transfer function at the aliasing frequency) on the sub-band filters. This property is important when the filter bank is used iteratively in a tree-structured manner as a discrete wavelet transform system and the issue of regularity arises. Several design examples are presented to illustrate the design technique     

Selective filters using least-mean-square approximation technique

A new clan of all-pole lowpass filters having a flat magnitude characteristic at the origin and at a frequency ?0 in the pass-band is presented. The remaining degree of freedom is used to minimise the characteristic function over the passband using least-mean-square norm. It is shown that the magnitude characteristic of new filters is superior to those for the Butterworth and transitional Butterworth-Cheby?shev filters, both in the passband and in the stopband.     

Optimisation of SIW bandpass filter with wide and sharp stopband using space mapping

This work presents a substrate integrated waveguide (SIW) bandpass filter with wide and precipitous stopband, which is different from filters with a direct input/output coupling structure. Higher modes in the SIW cavities are used to generate the finite transmission zeros for improved stopband performance. The design of SIW filters requires full wave electromagnetic simulation and extensive optimisation. If a full wave solver is used for optimisation, the design process is very time consuming. The space mapping (SM) approach has been called upon to alleviate this problem. In this case, the coarse model is optimised using an equivalent circuit model-based representation of the structure for fast computations. On the other hand, the verification of the design is completed with an accurate fine model full wave simulation. A fourth-order filter with a passband of 12.0–12.5 GHz is fabricated on a single layer Rogers RT/Duroid 5880 substrate. The return loss is better than 17.4 dB in the passband and the rejection is more than 40 dB in the stopband. The stopband is from 2 to 11 GHz and 13.5 to 17.3 GHz, demonstrating a wide bandwidth performance.     

Analytical design of 3-D wavelet filter banks using themultivariate Bernstein polynomial

The design of 3-D multirate filter banks where the downsampling/upsampling is on the FCO (face centred orthorhombic) lattice is addressed. With such a sampling lattice, the ideal 3-D sub-band of the low-pass filter is of the TRO (truncated octahedron) shape. The transformation of variables has been shown previously to be an effective technique for designing M-D (multidimensional) filter banks. A design technique is presented for the transformation function using the multivariate Bernstein polynomial which provides a good approximation to the TRO sub-band shape. The method is analytically based and does not require any optimisation procedure. Closed form expressions are obtained for the filters of any order. Another advantage of this technique is that it yields filters with a flat frequency response at the aliasing frequency (ω₁, ω₂ , ω₃)=(π, π, π). This flatness is important for giving regular discrete wavelet transform systems     

二维线性相位FIR数字滤波器的优化设计

该文提出了一种用神经网络算法来设计二维线性相位数字滤波器的新方法。通过分析二维FIR线性相位滤波器的幅频响应特性,建立了神经网络算法。根据给定的幅频响应指标,按该算法可获得滤波器系数。为保证该算法的稳定性,提出并证明了该算法的收敛定理。文中给出了圆对称和矩形对称二维低通线性相位FIR数字滤波器优化设计实例。计算机仿真结果表明由该方法设计的二维数字滤波器,通带和阻带范围波动小,所需计算量非常少,稳定性强,因而是一种优异的设计方法。     

Chebyshev approximation for linear phase nonrecursive digital filters

A procedure has been developed for the design of nonrecursive digital filters with prescribed passband and stopband amplitude characteristics. The proposed procedure is based on an efficient algorithm utilizing the simplex method of linear programming. The design algorithm yields equiripple approximation and it is an alternative to the one which is based on the Remz exchange algorithm. The design procedure allows exact specifications for arbitrary passband and stopband edges. Furthermore, no prior knowledge of the degree of the filter is required. To demonstrate the potential of the design algorithm, several examples with different requirements are worked out and a sample is presented. The obtained results show that the design procedure performed very well where the various parameters of the filter were taken into consideration.     

Method for designing recursive digital filters with short wordlength

With specified passband ripple, stopband ripple and cutoff frequencies, this method employs Crochiere's 2-parameter optimisation to equalise the passband and stopband statistical wordlengths before optimising coefficients in a multi-dimensional discrete space. Better design can be obtained by investing more computational time. This method is applicable to any recursive digital filters.     

Synthesis and Realization of Multisection Tandem Stripline Bandpass Filters

A bandpass filter is described which is made up of two identical multi-element coupled symmetrical striplines in tandem connection. For the filter, a precise synthesis procedure is presented reducing the design to the synthesis of a directional coupler. The required equal-ripple polynomials are calculated by an iterative method. Relations for the polynomial extreme values are provided, derived from the attenuation requirements in passband and stopband. On the basis of this procedure the coupling factors of two 21-element filters are calculated and realized three-layer polyolefin. Measurements show good agreement with theoretical results.     

几种图像缩放算法的研究

时域内常用的几种图像缩放算法有：最近邻插值、线性插值、二次插值、三次插值、拉格朗日插值、高斯插值等,对这些算法的性能进行分析比较,综合通带、阻带及截止频率,最近邻插值和线性插值应该避免,高斯基函数（N较大者）具有较好性能;并且在频域内研究了二维可分离插值滤波器和不可分离插值滤波器,这两种方法以对通带和阻带的要求作为优化目标,以滤波器的结构为约束条件,将滤波器的设计转化为一个约束优化问题进行解决;实验结果表明二维不可分离插值滤波器的方法图像缩放后的效果最好。     

Parallel-coupled line filters with enhanced stopband performances

A new class of parallel-coupled line filters with broad stopband response is introduced. The design is based on the synthesis of bandpass prototypes with pre-defined upper stopband characteristics. The new filters have uniform- and stepped-impedance resonators, some of which are loaded by open-circuited stubs at their open-circuited ends. A seventh-order filter implementation is presented with a fundamental passband centered at 1 GHz. The measured wide-band transmission characteristic of the filter demonstrated a broad upper stopband and was in agreement with simulations. The performance of the new filter is also compared with the characteristic of a conventionally designed filter to highlight the advantages of the proposed design method.     

B-spline design of maximally flat and prolate spheroidal-type FIRfilters

A digital FIR filter is described that offers excellent passband and stopband characteristics for general applications. Design formulae include parameters that adjust the magnitude response from one having characteristics like the maximally flat designs of Hermann (1971) and Kaiser (1975, 1979) to one having characteristics like the minimum-sidelobe energy approximations of Kaiser and Saramaki (1989). The impulse response coefficients are more straightforward to obtain than these filter designs while offering preferable response characteristics in many instances. Unlike FIR filters designed by window- or frequency-sampling methods, the filter coefficients are determined from the inverse Fourier transform in closed form once B-splines have been used to replace sharp transition edges of the magnitude response. Although the filters are developed in the frequency domain, a convergence window is identified in the convolution series and compared with windows of popular FIR filters. By means of example, adjustment of the transitional parameter is shown to produce a filter response that rivals the stopband attenuation and transition width of prolate spheroidal designs. The design technique is extended to create additional transitional filters from prototype window functions, such as the transitional Hann window filter. The filters are particularly suitable for precision filtering and reconstruction of sampled physiologic and acoustic signals common to the health sciences but will also be useful in other applications requiring low passband and stopband errors     

Design of generalized Chebyshev filters with asymmetrically located transmission zeros

A simple design technique is introduced for generalized Chebyshev filters with asymmetrically located transmission zeros. The efficient and exact procedure is given for the calculation of transmission zeros for a class of generalized Chebyshev low-pass prototype filters with a maximum of four asymmetrically located transmission zeros of any multiplicity. This technique is based on obtaining the frequencies of magnitude characteristic extreme values in closed form, and after this, transmission zeros can be calculated by solving a system of nonlinear equations. Novel formulas for orders of zeros of maximally selective filters with equiripple characteristics in the passband and stopband are deduced. The obtained results are verified and illustrated by given examples.     

E-Plane Integrated Circuit Filters with Improved Stopband Attenuation (Short Papers)

Improved stopband attenuation is achieved by thick strips, by reduced waveguide sidewall dimensions, and by double planar integrated circuits. In contrast to thick strips which may cause high passband insertion losses and filters with reduced waveguide dimensions which require additional tapers, double planar E-plane integrated circuit filters combine the advantages of low costs, high stopband, and low passband insertion losses. Computer-aided design of a four-resonator Ka -band double metal insert filter achieves a calculated stopband attenuation between 40 and 60 GHz of more than 50 dB, the calculated minimum passband insertion loss is 0.43 dB (measured 1.8 dB). Higher order mode excitation and finite thicknesses of the inserts are included in the calculations.     

Theory and design of two-parallelogram filter banks

It is well known that the analysis and synthesis filters of orthonormal DFT filter banks can not have good frequency selectivity. The reason for this is that each of the analysis and synthesis filters have only one passband. Such frequency stacking (or configuration) in general does not allow alias cancellation when the individual filters have good stopband attenuation. A frequency stacking of this nature is called nonpermissible and should be avoided if good filters are desired. In a usual M-channel filter bank with real-coefficient filters, the analysis and synthesis filters have two passbands. It can be shown that the configuration is permissible in this case. Many designs proposed in the past demonstrate that filter banks with such configurations can have perfect reconstruction and be good filters at the same time. We develop the two-parallelogram filter banks, which is the class of 2-D filter banks in which the supports of the analysis and synthesis filters consist of two parallelograms. The two-parallelogram filter banks are analyzed from a pictorial viewpoint by exploiting the concept of permissibility. Based on this analysis, we construct and design a special type of two-parallelogram filter banks, namely, cosine-modulated filter banks (CMFB). In two-parallelogram CMFB, the analysis and synthesis filters are cosine-modulated versions of a prototype that has a parallelogram support. Necessary and sufficient conditions for perfect reconstruction of two-parallelogram CMFB are derived     

Pseudo-elliptic microstrip line filters with zero-shifting properties

The paper presents a new design of pseudo-elliptic microstrip line filters. These filters employ a coupling scheme which allows shifting of transmission zeros from one side of the passband to the other by only changing the resonant frequencies of the resonators. To demonstrate the performance of these filters, a fourth-order bandpass filter with one transmission zero in the upper stopband is first designed. A second filter with a transmission zero in the lower stopband is then designed by simply adjusting the lengths of the resonators followed by minor optimization to account for the fact that the resonant frequencies can not be changed without slightly affecting the coupling coefficients in the used layout. Measured and simulated results are presented.