Miroslav Vlcek

Fast analytical design algorithms for FIR notch filters

Fast analytical design procedures for finite impulse response (FIR) maximally flat (MF) and optimal equiripple (ER) notch filters are introduced. The closed form solution provides recursive computation of the impulse response coefficients of the filter. The ER FIR filters are optimal in the Chebyshev sense. The relation between the MF and ER notch filter is presented in order to emphasize the superior performance of the ER narrow-band filters over their MF counterparts. The discrete nature of the notch frequency in both filter types is emphasized. Four design examples are included to demonstrate the efficiency of the presented approach.

Induction Motor Diagnosis by Advanced Notch FIR Filters and the Wigner–Ville Distribution

During the last years, several time-frequency decomposition tools have been applied for the diagnosis of induction motors, for those cases in which the traditional procedures, such as motor current signature analysis, cannot yield the necessary response. Among them, the Cohen distributions have been widely selected to study transient and even stationary operation due to their high-resolution and detailed information provided at all frequencies. Their main drawback, the cross-terms, has been tackled either modifying the distribution, or carrying out a pretreatment of the signal before computing its time-frequency decomposition. In this paper, a filtering process is proposed that uses advanced notch filters in order to remove constant frequency components present in the current of an induction motor, prior to the computation of its distribution, to study rotor asymmetries and mixed eccentricities. In transient operation of machines directly connected to the grid, this procedure effectively eliminates most of the artifacts that have prevented the use of these tools, allowing a wideband analysis and the definition of a precise quantification parameter able to follow the evolution of their state.

Zolotarev polynomials and optimal FIR filters

The algebraic form of Zolotarev polynomials refraining from their parametric representation is introduced. A recursive algorithm providing the coefficients for a Zolotarev polynomial of an arbitrary order is obtained from a linear differential equation developed for this purpose. The corresponding narrowband, notch, and complementary pair FIR filters are optimal in the Chebyshev sense. A recursion giving an explicit access to the impulse response coefficients is also presented. Some design examples are included to demonstrate the efficiency of the presented approach.

Analytical design method for optimal equiripple comb FIR filters

A novel analytical design method for highly selective digital optimal equiripple comb finite-impulse response (FIR) filters is presented. The equiripple comb FIR filters are optimal in the Chebyshev sense. The number of notch bands, the width of the notch bands and the attenuation in the passbands can be independently specified. The degree formula and the differential equation for the generating polynomial of the filter is presented. Based on the differential equation, a fast simple algebraic recursive procedure for the evaluation of the impulse response of the filter is described. Its arithmetic robustness outperforms, by far, the known analytical design method. Highly selective equiripple comb FIR filters with thousands of coefficients can be designed. One example demonstrates the efficiency of the filter design.

Fast design algorithms for FIR notch filters

Based on symmetry of the maximally flat frequency response of a FIR notch filter the new design procedure is developed. The closed form solution provides direct computation of the frequency response, recursive computation of the impulse response coefficients, simple windowing technique, and an access to new implementation. Several examples are included.<<ETX>>

An analytical procedure for critical frequency tuning of FIR filters

A novel analytical procedure for the tuning of finite-impulse response (FIR) filters is introduced. The tuning procedure adjusts a single frequency of the frequency response to the desired value while preserving the nature of the filter. The impulse responses of the original and of the final filter are related by the transformation matrix. Two examples in the analytical design of notch FIR filters demonstrate the usefulness of the proposed tuning procedure

Analytical solutions for design of IIR equiripple filters

A purely analytical technique for the design of recursive digital filters with equiripple magnitude behavior is presented. The design is accomplished in a transformed variable denoted by w and defined as w=(z+1/z)/2. The method can be attributed to the class of rational Chebyshev approximations. It uses design steps corresponding to those for elliptical filters in the analog domain. Using Jacobian elliptic functions, a conformal mapping of the w-plane is introduced which describes the solutions of equiripple symmetric specifications. These are not halfband specifications, since the attenuation and the bandripple in the passband are chosen independently of those in the stopband. Examples are given to demonstrate the efficiency of the approach. It is suggested that this sort of algorithm can be used advantageously in adaptive filtering because of the simplicity of the analytical solutions. The algorithms are well behaved, since the infinite series expansion of elliptic functions and the consecutive manipulation with abridged forms of these series have been avoided. >

Almost equiripple FIR half-band filters

Based on Chebyshev polynomials a novel analytical design procedure of almost equiripple FIR half-hand filters is developed. The closed form solution provides a direct computation of the frequency response. A formula for the impulse response coefficients is also derived. Several examples are included.

Design of Optimal Comb FIR Filters-Speed and Robustness

An extension to the analytical design of digital equiripple comb FIR filters is presented here. The filters are optimal in Chebyshev sense. The design runs from the filter specification through the degree formula to the impulse response coefficients, which are evaluated by an extremely efficient recursive algorithm. The proposed design method outperforms the standard procedures in terms of speed and robustness.

Note on the Design of an Equiripple DC-Notch FIR Filter

An extremely robust analytical procedure for the effective evaluation of the impulse response of a highly selective optimal equiripple DC-notch finite-impulse response (FIR) filter is presented. The DC-notch filter is optimal in the Chebyshev sense. The computational superiority of the presented procedure over the standard approach is emphasized