Question

Correlation between time domain and frequency domain

Answer 1

In the analysis and design of linear systems, the relationship between the time domain and frequency domain characteristics plays an especially important role. In system analysis, conditions for the robust stability and robust performance are described as specifications on the frequency response in most cases. Therefore, it is indispensable to transform frequency domain conditions into equivalent time domain conditions in order to establish an effective and beautiful design theory. Parseval's theorem gives the relationship between the squared integral of a time function and that of its Fourier transform, namely, the energy in the time domain is equal to the energy in the frequency domain. As a powerful tool bridging the time domain and frequency domain properties of systems, KYP lemma plays a fundamental role in robust control. The concepts of passivity and dissipativity are the time domain characterizations of positive realness and bounded realness (frequency domain) of linear systems.



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