Xiaoning Nie

Edge preserving filtering by combining nonlinear mean and median filters

The authors introduce a very general class of nonlinear filters, called mapping order-statistics filters (MOSFs). A subclass of the MOSFs, called L/sub p/-mean median filters (L/sub p/-MMF), is treated in detail. Theoretical analysis and computer simulations shown that the L/sub p/-MMF removes one kind of impulse noise as well as the nonlinear mean filter and attenuates Gaussian and uniformly distributed noise efficiently. The main advantages of the L/sub p/-MMF are that it can preserve edges as well as the median filter and can remove both the positive and negative impulse noise simultaneously. Further theoretical analysis shows that a finite-length discrete signal always converges to a fixed-point signal (root signal), if the same L/sub p/-MMF is applied iteratively. A necessary condition for a signal to be a root signal is found and proved. This necessary condition is also valid for the FIR-median hybrid filter.<<ETX>>

Efficient evaluation of 1-D and 2-D polynomials at equispaced points

An extension to the two-dimensional case of a previously published fast algorithm for evaluating exponential functions and polynomials over periodically distributed points is generalized to evaluate two-dimensional polynomials efficiently over general periodic parallelograms. The problem of getting the initial values required for other fast algorithms is treated in a general manner. Fast algorithms are presented for computing initial values in both cases of one- and two-dimensional polynomials. It is observed that the two-dimensional recursion is not always advantageous compared with taking the one-dimensional recursion for each variable separately. >

McClellan transformation for two-dimensional IIR digital filter design

The McClellan transformation is extended to the design of two-dimensional zero-phase and causal IIR (infinite impulse response) digital filters. In the case of a circularly symmetric contour, explicit conditions for a certain globally type preserving property are given, where the corresponding extended McClellan transformation is consequently of the so-called scaling-free form. Examples for circularly symmetric and elliptical contours are presented. A comparison with other McClellan transformations shows the advantages of the extended transformation for the approximation of a given contour.<<ETX>>

2-D IIR filter design using the extended McClellan transformation

A straightforward technique using a 1-D to 2-D spectral transformation is proposed for designing 2-D IIR (infinite impulse response) quarter-plane digital filters. Starting with the specification on the magnitude-frequency response of the filter, an optimal extended McClellan transformation is developed. Then a 1-D equiripple IIR digital filter is designed. Introducing the transformation into the 1-D IIR filter, the 2-D IIR quarter-plane digital filter. It is shown how to design 2-D digital filters having a circularly symmetric magnitude-frequency response using this technique, and it is demonstrated that the resulting filter possesses a very good response. The specifications on the frequency response are satisfied with a small error variation, and the stability is always guaranteed without a 2-D stabilization procedure.<<ETX>>

A novel efficient algorithm for stability test by continued fraction expansion with application to 2-D digital filters

Based on a theorem on a continued fraction expansion of complex discrete reactance functions, an algorithm for the stability test of digital filters directly in the z-domain is derived. The algorithm is formulated in a table form which is similar to the Marden-Jury table but shows some more interesting numerical aspects. Finally, the application of the algorithm to the 2-D stability test is briefly discussed. >

Novel and efficient realization of arbitrary FIR digital filters

A new set of novel structures for the realization of arbitrary causal FIR (finite impulse response) filters is presented. An idea that originated in the 2-D digital filter implementation is generalized to the realization of arbitrary 1-D causal FIR filters. The key to the problem solution is the introduction of modified Chebyshev polynomials. The new realizations have the minimum number of multipliers and show attractive properties concerning the finite word length effect. The realizations can also be implemented as modular pipelineable processor arrays (systolic arrays).<<ETX>>

Result on the approximation of multivariable functions-generalization of a theorem of Walsh

In a theorem of Walsh, the approximation of a given function by a rational function has been considered. Walsh stated that the best approximate of a given function is one which interpolates the given function at several properly chosen points. Transfer functions of multidimensional digital filters with separable denominator are used for the approximation of given multivariate functions. It is shown that the result of Walsh can be generalized in a straightforward manner. By an example, it is illustrated how the new result can be applied, for example, to the order-reduction of a higher order system. The usefulness and the limitation of the result are discussed.<<ETX>>

An novel treatment of robust stability of continuous-time systems

The four-vertices concept of Kharitonovs theorem is one of the most important results in the area of robust stability of linear time-invariant continuous-time systems. If the coefficients of the characteristic polynomial of a given system are dependent, the vertex concept cannot be applied in general. If the coefficients are linearly dependent, various results can be achieved. The case where the coefficients are partly dependent is considered, and more general vertex theorems on robust stability are given where the set considered in the coefficient space does not need to be convex. The notion of the vertex polynomial is generalized. The results are based on a modified Hermite-Biehler theorem, which presents an irredundant characterization of a reactance function. A new geometrical interpretation of stability conditions is also given. Further results are presented for low-order polynomials. >

On algorithms for 2-D rational transformations

In certain applications, the independent variables of a given two-dimensional (2-D) rational function have to be transformed by substituting every variable with a specific rational function of two variables. Based on two known algorithms suited for one-dimensional (1-D) rational transformations, two useful algorithms are presented to perform general 2-D rational transformations. To compare the computational efficiency, the authors consider the number of multiplications used in both 2-D algorithms.<<ETX>>