Digital Filter Transfer Research Articles

A general theorem for degree-reduction of a digital BR function

A general theorem is developed for the degree reduction of a bounded real (BR) digital filter transfer function, and is related to the extraction of a digital lossless two-pair from a BR function in such a manner that the remainder function is reduced order BR. The theorem finds applications in the synthesis of digital filter transfer functions in the form of a cascade of lossless two pairs.

Explicit formula for the coefficients of maximally flat nonrecursive digital filter transfer functions expressed in powers of cos w

An explicit formula for the coefficients of the transfer function of a maximally flat nonrecursive digital filter, expressed in powers of cos w, is derived by exploiting the properties of the Kaiser-Hamming [1] amplitude change function polynomial. Transfer functions expressed in this form are convenient for implementing variable cutoff filters [2].

Low passband sensitivity digital filters: A generalized viewpoint and synthesis procedures

The concepts of losslessness and maximum available power are basic to the low-sensitivity properties of doubly terminated lossless networks of the continuous-time domain. Based on similar concepts, we develop a new theory for low-sensitivity discrete-time filter structures. The mathematical setup for the development is the bounded-real property of transfer functions and matrices. Starting from this property, we derive procedures for the synthesis of any stable digital filter transfer function by means of a low-sensitivity structure. Most of the structures generated by this approach are interconnections of a basic building block called digital "two-pair," and each two-pair is characterized by a lossless bounded-real (LBR) transfer matrix. The theory and synthesis procedures also cover special cases such as wave digital filters, which are derived from continuous-time networks, and digital lattice structures, which are closely related to unit elements of distributed network theory.

Digital filters with fast coefficient implementation

A collection of lowpass digital-filter transfer functions is given, each of which has coefficients allowing use of a simple and very fast multiplication scheme.

Roundoff Noise Invariants in Normal Digital Filters

The unit noise gains for optimal and parallel normal realizations of digital filters can be expressed in terms of a set of noise gain parameters that are simply related to the pole locations and pole residues. These noise gain parameters are shown to be invariant under a class of frequency transformations, and for digital filter transfer functions derived by bilinear transformation of an analog transfer function, are independent of the frequency scaling parameter. As a result, the unit noise gains of normal realizations can be simply related to the performance characteristics of the filter, i.e., to filter order, passband ripple, and stopband gain. These simple relations make it easy for the filter designer to select a structure with acceptable roundbff error. Unit noise gain for normal realizations of Butterworth, Chebyshev, and elliptic filters are plotted for a range of performance characteristics, and compared with optimal state-space structures. These results show that there is no significant difference between the unit noise gains of optimal normal realizations and parallel normal realizations, and that the unit noise gains of optimal state-space structures are significantly lower than the normal forms only for high-order Butterworth filters.

Computer-aided analysis of wave digital filters

An original computer-aided analysis package of the Swamy-Thyagarajan wave digital filter structures has been developed, by the authors, on the minicomputer PDP 11/45 GT-44 Graphics System. The package utilizes the chain matrices of the digital two-ports of the Swamy-Thyagarajan wave digital filter structures which are expressed in terms of the coefficient multipliers of the digital two-ports and the Z variable. The elements and values of a doubly terminated LC ladder can be entered on a cathode ray tube display by utilizing the interactive graphics capability of a light pen. The ladder is then transformed into the Swamy-Thyagarajan wave digital filter structures. Port resistances, coefficient multipliers, chain matrices, the coefficients of the digital filter transfer function, transformed lowpass, highpass, bandstop and bandpass filters can be obtained. The package provides numerical values of the amplitude and phase responses, and plots the responses on the cathode ray tube display.

Efficient computation of mixed higher partials of digital filter transfer functions

A concise formula is derived for the computation of mixed higher partial derivatives of digital filter transfer functions with respect to any combination of multiplier coefficients. If only one multiplier coefficient is involved in the differentiation, our formula specializes to a recent result of Crochiere [1].

On pole distribution in digital filters

AbstractDue to the discrete nature of the coefficients the poles and zeros of a digital filter transfer function cannot, in general, be realized exactly. This paper introduces a new concept ‘pole sparsity factor’ as a measure of the maximum possible pole deviation after tuning, for the case of second order circuits. A new second order circuit that exhibits lower pole sparsity factor compared to presently available circuits with the same number of multipliers is presented.

Additional canonic realizations of digital filters using the continued-fraction expansion

Three new canonic realizations of a digital-filter transfer function using the continued-fraction-expansion techniques are derived.

The Design and Application of Digital Filters

The advantages of digital circuits and the frequency-response design procedures that are available for specifying the coefficients of the digital-filter transfer function are discussed. The hardware design of a digital filter is discussed, and an example is given of the application of the filter in a servo loop. Further application of the filter to generate a notch network characteristic is illustrated.

Digital filter synthesis by sampled-data transformation

The design of digital filter transfer functions is facilitated by taking advantage of well-established design techniques developed for continuous (analog) filters. Digital approximations to continuous filter functions may be found by applying an appropriate sampled-data (z) transformation to the continuous filter transfer function. Three mathematical transformations are described that find the most application: 1) the standard z-transform, 2) the bilinear z-transform, and 3) the matched z-transform. The applicability of the three transformations is discussed and examples are presented of digital filters designed using these transformations.