Low-order Filters Research Articles

Statistical design of autoregressive-moving average digital filters

Procedures are presented for the systematic design of digital filters that contain poles and zeros. The procedures are simple, fast, and effective. All of the important algorithms are of the Levinson-type. The first key idea in the paper is that one may begin a design by posing a linear prediction problem for a stochastic sequence. The second is that a high-order "whitening" filter may be constructed for this sequence and "inverted" to yield a high-order all-pole filter whose spectrum approximates the spectrum of the stochastic sequence. The third key idea is that the all-pole filter may be used to generate consistent unit-pulse and covariance sequences for use in the Mullis-Roberts algorithm. This algorithm is then used to obtain a low-order digital filter, with poles and zeros, that approximates the high-order all-pole filter. The results demonstrate that the Mullis-Roberts algorithm, together with the design philosophy of this paper, may be used with profit to reduce filter or stochastic model complexity and to design spectrum-matching digital filters.

Explicit design formulae for digital tan filters with low-pass, high-pass, band-pass, and band- stop characteristics

Explicit expressions of transfer functions for digital tan filters with low-pass, high-pass, band-pass, and band-stop characteristics approximating given design specifications are advanced. The higher order transfer function satisfying the design specification is expressed as the product of first-order and second-order filter sections of identical forms but with different coefficient values. All coefficients of these low-order filter sections are expressed in explicit forms related simply to the specification values. Thus, the result developed can be easily applied for the cascade or time-sharing realization. The low-order filter section developed here can be implemented with the fewest multipliers. The design formulae for Butterworth, Chebyshev, inverse Chebyshev and elliptic approximations are included. The transfer functions for all these filters are expressed in the same form of low-order filter section with different coefficient values.

Error analysis of low-order filters and unduality between error equations of low-order filter and singular control problem

Error analysis for the two kinds of low-order filters is investigated. One low-order filter is an optimal type and the other filter is a sub-optimal Luenberger observer type. As the error analysis, algorithms representing the two actual covariances and the related moments are derived from the nominal dynamical systems and the actual low-order filters whose parameters are misidentified. It is also clarified that the duality relation does not exist between the actual-Covariance equation of an optimal low-order filter and the matrix equation of a sub-optimal performance value of the singular control problem. This investigation is motivated by the result that the duality relation exists between the actual-covariance equation of the Kalman filter and the matrix equation caused by a performance loss of the non-singular control problem.

An Algorithm for Minimizing Roundoff Noise in Cascade Realizations of Finite Impulse Response Digital Filters

Experimental results on roundoff noise in cascade realizations of Finite Impulse Response (FIR) digital filters are presented in this paper.∗ The entire roundoff noise distribution (i.e., over all possible orderings) is given for several low-order filters using both sum and peak scaling. Based on observations about this distribution, as well as intuitive arguments about the effects of ordering on roundoff noise, an algorithm for minimizing roundoff noise is presented. Experimental verification of this algorithm for a wide range of filters is given.