# The transfer function is applicable to which of the following?

The transfer function is applicable to which of the following?

### Right Answer is: Linear and time-invariant systemsPlease enable JavaScriptEvacuation Center Management System

#### SOLUTION

The transfer function of a linear, time-invariant system is defined as the ratio of the Laplace transform of the output to the Laplace transform of the input with all initial conditions being zero. The transfer function is applicable to linear and time-invariant systems.

The transfer function is a frequency-domain concept that is used to calculate the output of the linear system to any input.

$TF = \frac{{C\left( s \right)}}{{R\left( s \right)}}$

A transfer function may only be defined for a linear, time-invariant (constant parameter) single-input-single-output system. The transfer function is an input-output description of the behavior of a system where the information about the initial conditions is lost. Thus, the transfer function description does not include any information concerning the internal structure of the system and its behavior.

Properties of Transfer function

1. The transfer function of a system is the Laplace transform of its impulse response.
2. The transfer function concept is applicable only to linear, time-invariant systems.
3. The transfer function does not take care of the initial conditions of the system. This is the greatest disadvantage.
4. The transfer function is applicable to single-input-single-output systems, though for multivariable systems, the transfer matrix can be obtained by using the principle of superposition.
5. The degree of the denominator polynomial of the transfer function is the order of the system. The denominator polynomial gives the poles and the numerator polynomial gives the zeros.
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