Transfer Function

In its simplest form for Continuous-time signals, the function is often written as : $H(s) = rac{Y(s)} {X(s)}$ where H(s) is the symbol for the transfer function, Y(s) is the output function, and X(s) is the input function (see Laplace Transform ). In Discrete-time systems, the function is similarly written as $H(z) = {Y(z)}/{X(z)}$ (see Z Transform ). SIGNAL PROCESSING Let $x(t)$ be the input to a general Linear Time-invariant System , and $y(t)$ be the output, and the Laplace Transform of $x(t)$ and $y(t)$ be : $X(s) = \mathcal{L}\left \{ x(t) ight \} \equiv \int_{-\infty}^{\infty} x(t) e^{-st}\, dt$ : $Y(s) = \mathcal{L}\left \{ y(t) ight \} \equiv \int_{-\infty}^{\infty} y(t) e^{-st}\, dt$ . Then the output is related to the input by the transfer function $H(s)$ as :: $Y(s) = H(s) X(s) \,$ and the transfer function itself is therefore :: $H(s) = rac{Y(s)} {X(s)}$ .
	:<math> X(t)	Xe^{j(\omega t + \arg(X))} = Xe^{j\omega t} </math>
	:where <math> X	Xe^{j\arg(X)} </math>
	:<math>y(t)	Ye^{j(\omega t + \arg(Y))} = Ye^{j\omega t} </math>
	:and <math> Y	Ye^{j\arg(Y)} </math>

	CATEGORIES ABOUT TRANSFER FUNCTION

	electrical circuits

	signal processing

	control theory

	cybernetics

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