Consider a CTLTI system described by the following ordinary differential equation with constant coefficients: N M dky(t) 2 ak ak dtk , dkx(t) Ok atk bk – 2 k=0 k=0 The system function H(s) is defined as the Laplace transform of the impulse response h(t) of the system. Write and prove the expression of H(s) as a function of the coefficients of the differential equation. Justify each single step of the proof from first principles (hypothesis, thesis, proof).
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