The digital function filters – algorithms and applications

Abstract

The simple digital filters are not sufficient for digital modeling of systems with distributed parameters. It is necessary to apply more complex digital filters. In this work, a set of filters, called the digital function filters, is proposed. It consists of digital filters, which are obtained from causal and stable filters through some function transformation. In this paper, for several basic functions: exponential, logarithm, square root and the real power of input filter, the recursive algorithms of the digital function filters have been determined The digital function filters of exponential type can be obtained from direct recursive formulas. Whereas, the other function filters, such as the logarithm, the square root and the real power, require using the implicit recursive formulas. Some applications of the digital function filters for the analysis and synthesis of systems with lumped and distributed parameters (a long line, phase shifters, infinite ladder circuits) are given as well.

Calculus of the fractional order operators in a discrete time domain

“…This publication presents the mathematical convolution method as well as digital filter impulse response method with the application for distributed parameters system analysis in the theory of electrical circuits. The authors' previous studies in this field can be found in publications [14][15][16][17][18][19][20][21][22][23].…”

Digital filters: hermitian, antihermitian, unitary and their applications

“…Often it is better to use a recursive method, which is more effective for some function f(A). More about the functional filters can be found in [6]. In this paper two important functional filters are used: f A A ( )= …”

Biometric speech signal processing in a system with digital signal processor

“…Such a multistage speech processing for the speaker recognition is composed of: a parameterization of the input signal (preprocessing e.g. with the use of digital function filters [11], signal division into blocks, multiplication by a window function, determining the linear prediction coefficients or mel-cepstral coefficients with the use of the FFT), a modeling phase (such as the vector quantization and the creation of mixtures of Gaussians) and then comparing with the base pattern [2].…”