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.

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Abstract. The article presents the basic mathematical theory of the operational calculus of the L 1 -impulses in the discrete time domain. It presents the isomorphism between the rational function set of complex variable and the exponential L 1 impulses set of positive and negative time domain. The paper shows how for any factorization of the rational function consisting of casual and noncasual parts can be directly obtained the N -periodic version of the original signal using for the individual components of the L 1 impulses N -copy formula. It is done by the distribution of the convolution -the type admitance operator Y of electrical circuit to the two commutative convolution operators and on this basis is obtained the distribution of electrical circuit current to two components: the active current and the reactive current in the discrete time domain using the cyclic convolutions. The distribution of current in the time domain for signals significantly different from the sinusoidal is much more favorable than the distribution in the frequency domain.

Abstract. The article presents that in the circuits of electrical signals belonging to the L 1 -impulses space or periodic signals space, real distribution of electrical currents occurs which does not meet the principle of minimum energy losses. The paper presents a solution of this problem by using the control system in the form of current-dependent voltage sources entering it into a meshes set of a complex RLC network. It has been shown that the control is energy-neutral.

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