BULLETIN
of the
POLISH ACADEMY of SCIENCES TECHNICAL SCIENCES 


Volume
57, Issue 1, March 2009
Disasters, micro and nanomechanics 

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pp 79  85 

The L^{1}impulse method as an alternative to the Fourier series in the power theory of continuous time systems 

M. SIWCZYNSKI and M. JARACZEWSKI 
The Fourier series method is frequently applied to analyze periodical phenomena in electric circuits. Besides its virtues it has
many drawbacks. Fourier series usually have slow convergence and fail for fast changing signals, especially for discontinues ones. Therefore
they are suitable to describe only quasiharmonic phenomena. For strongly nonsinusoidal signal analysis we propose the L^{1}impulse method. The L^{1}impulse method consists in an equivalent notation of a function belonging to L^{1} as a sum of exponential functions. Such exponential functions have rational counterparts with poles in both sides of imaginary axis. With the L^{1}impulse functions we can describe periodical signals, thus we get the homomorfizm between periodical signals and a rational functions sets. This approach is especially adapted to strongly deformed signals (even discontinues ones) in linear power systems, and thanks to that we can easily calculate optimal signals of such systems using the loss operator of the circuit. The loss operator is exactly the rational function with central symmetry of poles [1]. In this paper the relation between the L^{1}impulse and the Fourier series method was presented. It was also proved that in the case of strong signal deformation the L^{1}impulse method gains advantage. 
Key words: 
periodically timevarying networks, operational calculus, stability, synthesis, optimization. 

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® Bulletin of the Polish Academy of Sciences: Technical Sciences
12 March 2009 
