L1-impulses method as an alternative method of harmonic components in the power theory of discrete time systems

The article presents the basic mathematical theory of the operational calculus of the L1-impulses in the discrete time domain. It presents the isomorphism between the rational function set of complex variable and the exponential L1 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 L1 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.