## What is The System Function?

The system function which is also called as the transfer functionand the network functions is the mathematical representation of the system which shows the relation between the input and the output of the linear time-invariant systems. This is the frequency domain system representation of the Signal & system’s system function by H(jw)

The system functions are normally used to the analysis of the systems which has a single-input and also a single output filters. This term is widely used in the signal system engineering. The term is refers to as the linear, time-invariant systems (LTI). In the most simple form for the continuous-time the  input signal x(t) and the output y(t), the system function is the linear mapping of theLaplace transform of the input, X(s), to the output Y(s):

Y (s) = H ( s ) X ( s )

Or

H ( s) =

The system function is defined as the ratio of the output of the system to the input of the system. In the Laplace transform domain while considering the initial conditions to be zero. If the input function of X(s), and the output function Y(s), So the system function H(s) can be defined as:

In the time domain the variables are generally written with lower-case letters. So in the time domain, the input to a system is denoted as x(t), and the output of the system as the y(t). The relationship between the input and the output is denoted as the impulse response, h(t).We define the impulse response as being the relationship between the system output to its input. We can use the following equation to define the impulse response:

h ( t ) =

## Interconnection of Systems

SERIES INTERCONNECTION OF SYSTEMS

Fig:Systems connected in series

The systems of the system connected in the series format. If all the systems are single input

and single output. So that the total system transfer function can be expressed as

T (s ) =

Here, T(s) is define the total transfer function of the system, and  are define the individual system transfer function of the system.The SISO system functions. However, if two MIMO systems are interconnected as shown in the multiplication of the system functions is not anymore applicable.

Fig: Systems Connected into parallel

When the two systems are interconnected into parallel manner so that the system function is defined as the

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