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B. P. Lathi & Roger Green. (2018). Chapter 7: Continuous-Time Signal Analysis. Signal Processing and Linear Systems (3nd ed., pp. 689-701). Oxford University Press.
For convenience, we now introduce a compact notation for the useful gate, triangle, and interpolation functions.
For more results, refer to Table of the Fourier Transform Pairs.
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In this section I will illustrate that, for a system specified by the differential equation \[ \begin{equation} \label{eq_2_2} Q(D) y(t)=P(D) x(t) , \end{equation} \]
its transfer function is \(H(s)\), the bilateral Laplace transform of \(h(t)\), which is the unit impulse response of the system, and that \(H(s)\) also satisfies: \[ \color{teal} {H(s)=\frac{P(s)}{Q(s)}} . \]
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This section is devoted to the determination of the zero-state response(see past post) of an LTIC system. We shall assume that the systems discussed in this section are in the zero state unless mentioned otherwise.
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Stability is an important system property. Two types of system stability are generally considered: external (BIBO) stability and internal (asymptotic) stability. Let us consider both stability types in turn.
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