Efficient symbolic computation of approximated small-signalcharacteristics of analog integrated circuits

A symbolic analysis tool is presented that generates simplified symbolic expressions for the small-signal characteristics of large analog integrated circuits. The expressions are approximated while they are computed, so that only those terms are generated which remain in the final expression. This principle causes drastic savings in CPU time and memory, compared with previous symbolic analysis tools. In this way, the maximum size of circuits that can be analyzed, is largely increased. By taking into account a range for the value of a circuit parameter rather than one single number, the generated expressions are also more generally valid. Mismatch handling is explicitly taken into account in the algorithm. The capabilities of the new tool are illustrated with several experimental results     

Fast computation of the two-dimensional generalised Hartleytransforms

The two-dimensional generalised Hartley transforms (2-D GDHTs) are various half-sample generalised DHTs, and are used for computing the 2-D DHT and 2-D convolutions. Fast computation of 2-D GDHTs is achieved by solving (n₁+(n₀₁/2))k₁+(n₂+(n₀₂ /2))k₂=(n+(½))k mod N, n₀₁, n₀₂ =1 or 0. The kernel indexes on the left-hand side and on the right-hand side belong to the 2-D GDHTs and the 1-D H₃, respectively. This equation categorises N×N-point input into N groups which are the inputs of a 1-D N-point H₃. By decomposing to 2-D GDHTs, an N×N-point DHT requires a 3N/2ⁱ 1-D N/2ⁱ-point H₃, i=1, ..., log₂N-2. Thus, it has not only the same number of multiplications as that of the discrete Radon transform (DRT) and linear congruence, but also has fewer additions than the DRT. The distinct H ₃ transforms are independent, and hence parallel computation is feasible. The mapping is very regular, and can be extended to an n-dimensional GDHT or GDFT easily     

Efficient computation of full Lucas sequences

Recently, Yen and Laih (see IEE Poc. Comput. Digit. Tech., vol. 142, no. 2, p. 165-9, 1995) proposed an algorithm to compute LUC digital signatures quickly. This signature is based on a special type of Lucas sequence V_k. The authors generalise their method to any type of Lucas sequence, and extend it to the `sister' Lucas sequence, U_k . As an application, the order of an elliptic curve over GF(2^m) is computed quickly     

Efficient computation of local geometric moments

Local moments have attracted attention as local features in applications such as edge detection and texture segmentation. The main reason for this is that they are inherently integral-based features, so that their use reduces the effect of uncorrelated noise. The computation of local moments, when viewed as a neighborhood operation, can be interpreted as a convolution of the image with a set of masks. Nevertheless, moments computed inside overlapping windows are not independent and convolution does not take this fact into account. By introducing a matrix formulation and the concept of accumulation moments, this paper presents an algorithm which is computationally much more efficient than convolving and yet as simple.     

快速计算套筒单极子天线

利用矩量法分析计算套筒单极子天线的电性能参数。采用与实际天线较为接近的矩量法分析模型和一种新的粗圆柱线天线快速精确计算模型,大大提高了分析计算的精度;引入「Ｚ」矩阵插值法,提高了分析计算的速度。将该方法与最优化技术相结合,设计出一付工作在２００～７００ＭＨｚ频段、ＶＳＷＲ〈２．６、增益Ｇ〉５．１ｄｂ的实用套筒单极子天线,理论分析与实验测试吻合良好,从而说明了该方法的有效性和实用性。     

Efficient serial/parallel inner-product computation

A class of serial/parallel architectures for inner-product computation is described, based on carry-save accumulator arrays. In their basic form such arrays form carry-save multiply/adders. A simple modification of the coefficient feed allows flexible extension to short vector inner-product computation using distributed arithmetic. These modules may be cascaded to handle longer vectors, forming high-level VLSI digital signal processing subsystems.     

Transformations for the variable coefficient Ginzburg-Landau equation with symbolic computation

1 Introduction Of late, a research directly seeking for exact solutions of nonlinear evolution equations (NLEEs) has become increasingly attractive, because of their applications in many important scientific problems and the availability of symbolic compu…     

Efficient computation of the two-dimensional periodic Green'sfunction

An efficient scheme is introduced for computing the two-dimensional periodic Green's function. By using Kummer's method to accelerate the Hankel function series, accurate results can be rapidly obtained when the source and field points coincide in the vertical direction. Unlike with the integral acceleration form, convergence of the series is maintained when the source and field points differ horizontally by a complete period     

Efficient computation of trellis code generating functions

For trellis codes, generating function techniques provide the distance spectrum and a union bound on bit-error rate. The computation of the generating function of a trellis code may be separated into two stages. The first stage reduces the number of states as much as possible using low-complexity approaches. The second stage produces the generating function from the reduced-state diagram through some form of matrix inversion, which has a relatively high complexity. In this paper, we improve on the amount of state reduction possible during the low-complexity first stage. We also show that for a trellis code that is a linear convolutional code followed by a signal mapper, the number of states may always be reduced from N/sup 2/ to ((N/sup 2/-N)/2)+1 using low-complexity techniques. Finally, we analytically compare the complexity of various matrix inversion techniques and verify through simulation that the two-stage approach we propose has the lowest complexity. In an example, the new technique produced the union bound in about half the time required by the best algorithm already in the literature.     

Efficient computation of DFT of Zadoff-Chu sequences

An important property of a Zadoff-Chu (ZC) sequence is derived, namely that the discrete Fourier transform (DFT) of a ZC sequence is a time-scaled conjugate of the ZC sequence, multiplied by a constant factor. This result has many practical applications. For example, it can be used to generate 3GPP LTE access preambles more efficiently than the standard suggests as it allows the DFT of a ZC sequence of prime length P to be computed with P instead of PlogP arithmetic operations.     

Efficient computation of time-varying and adaptive filters

Two techniques for efficient computation of filters that support time-varying coefficients are developed. These methods are forms of distributed arithmetic that encode the data, rather than the filter coefficients. The first approach efficiently computes scalar-vector products, with which a digital filter is easily implemented in a transpose-form structure. This method, based on digital coding, supports time-varying coefficients with no additional overhead. Alternatively, distributed-arithmetic schemes that encode the data stream in sliding blocks support efficient direct-form filter computation with time-varying coefficients. A combination of both of these techniques greatly reduces the computation required to implement LMS adaptive filters     

Efficient computation of the delay-optimized finite length MMSE-DFE

We present new fast algorithms for computing the optimum settings of a finite-length minimum-mean-square-error decision feedback equalizer (MMSE-DFE) from channel and noise estimates. These algorithms are based on displacement structure theory and generalize the algorithms of Al-Dhahir and Cioffi (see ibid., vol.43, no.11, 1995) by including delay optimization. Both symbol-spaced and fractionally spaced feedforward filters are considered     

Efficient computation of scattering by inhomogeneous dielectric bodies

The computation time required for the tetrahedral method of computing scattering and absorption by dielectric bodies has been reduced by using single-point integration quadratures for most of the matrix elements. This results in a nearly Galerkin formulation and yields results that are as good as or better than the original formulation in about one-half the time.     

Efficient computation of propagation factors in ferrite-loadedrectangular waveguides

The mode matching solution of ferrite-loaded waveguide devices requires accurate knowledge of the pertinent modes. Computation of the propagating factor of such modes is essential but nontrivial. Here an efficient technique for computing these factors for an arbitrary number of modes is presented     

Efficient computation of the free-space periodic Green's function

The application of Shanks's transform is shown to improve the convergence of the series representing the doubly infinite free-space periodic Green's function. Higher order Shanks transforms are computed via Wynn's epsilon algorithm. Numerical results confirm that a dramatic improvement in the convergence rate is obtained for the on-plane case, in which the series converges extremely slowly. In certain instances, the computation time can be reduced by as much as a factor of a few thousands. A relative error measure versus the number of terms taken in the series is plotted for various values of a convergence factor as the observation point is varied within a unit cell. Computation times are also provided.<>     

Efficient calculation of multimode CPFSK spectra

The letter shows how previously developed analytic formulas for spectral calculations can be extended to handle the multi-mode CPFSK case. The results are easily programmed, and give fast run times. A numerical example of this method is included.     

Efficient computation of the time-domain TE plane-wave reflection coefficient

An efficient method for the calculation of the transient reflection coefficient for TE plane wave reflection from a conducting half space is given. The series form is shown to converge within a few terms for typical values of material parameters.     

Efficient computation of interconnect capacitances using the domaindecomposition approach

In this paper, we present a novel technique for efficient computation of capacitance matrices of complex interconnect configurations. It applies the finite difference (FD) method in conjunction with the perfectly matched layer (PML) and impedance boundary condition for mesh truncation, and combines these with the overlapping domain decomposition approach to handle complex configurations that are too large to handle in one step. Convergence and efficiency issues of the proposed algorithm are examined and numerical examples are presented to illustrate the usefulness of the proposed scheme     

Efficient computation of the Hutchinson metric between digitized images

The Hutchinson metric is a natural measure of the discrepancy between two images for use in fractal image processing. An efficient solution to the problem of computing the Hutchinson metric between two arbitrary digitized images is considered. The technique proposed here, based on the shape of the objects as projected on the digitized screen, can be used as an effective way to establish the error between the original and the, possibly compressed, decoded image. To test the performance of our method, we apply it to compare pairs of fractal objects, as well as to compare real-world images with the corresponding reconstructed ones.