From Cauer synthesis to Legendre polynomials — The case of the lossless transmission line
Résumé
In this article, we study a simple Time Delay System (tds), the short-circuited lossless transmission line. By realizing the Cauer synthesis of the input impedance, we can put in evidence a special expression of the impulse response of this system. Furthermore, we illustrate on this example a particular link between the Cauer synthesis of infinite order systems and the Legendre polynomials.
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