Transfer Function
The transfer function \(H(s)\) models a systems output for each possible input. It represents how the system acts upon the signal from end to end.
LTI System¶
For an LTI System, the effect of a system \(h(t)\) upon an input signal \(s(t)\) is given
by their [[Convolution]] \(y(t) = x(t) * h(t)\). The convolution of two signals is equivalent to the product of their spectra ([[Laplace Transform]]), so we can represent the relation as \(Y(s)=X(s){\cdot}H(s)\). Dividing the spectrum of the input \(X(s)\) on both sides gives us the typical definition of the transfer function:
For time-discrete systems, we can use the [[z-Transform]] in just the same way:
System Characteristics¶
The transfer function describes the behavior and stability of a system. Critical points in the transfer function are its zeros and poles. They describe the extrem cases of how a system reacts to an input.
Zero Points¶
Zero points come up