# Preface

Engineers typically like to look at everything in the real world as a system. In their fascinating systematic view, the real world problems are modeled as mathematical functions with one or multiple inputs, and one or multiple outputs. The outputs of a system whether it is a mechanical, biological, economic, chemical, or an electrical system can be represented as a function of its inputs. For example, consider the human eye as a system whose input is the visual light and its output is the signals that go to the brain. Similarly, human ear is a system where sounds are the inputs and signals that go to the brain are the outputs. As another example, a wireless channel can be considered as a communication system where the input is the electromagnetic signal and the output is the attenuated and delayed version of the input signal which might have become noisy. A building, a bridge, a wind turbine, or a car are also considered as systems. Modeling a system means to find the mathematical relationship between its inputs and output.

The beauty of a system is that it can be modeled in different levels of abstractions. For example, when considering the wireless channel between two cellphones as a system to be modeled, we can look at the signal going out of a cellphone as the input to the system and the signal going to the other cellphone as the output. In this case, we do not consider the telecommunication towers in between. We can also model the channel between a cellphone and the telecommunication tower as another system, the channel between a telecommunication tower and possibly one or more towers as another system, and finally the channel between the last telecommunication tower and the other cellphone as another system. Therefore, the channel between two cellphones can be considered as a system consisting of other sub-systems.

When modeling the system, the input-output relationship is obtained. Therefore, if we are given an input, we can find out the output. This can help us to estimate the system behaviour. If we like the system to have some specific desired outputs, we can calculate the suitable input signals using the system modeling. This can help us to design the input signals which provide us with the desired outputs. Also system modeling can help us to design a physical system that has a specific input-output relationship.

To model a system, we should find the mathematical formula that connects the inputs and outputs. This relationship can be calculated by applying the physics laws. Also, measuring the inputs and outputs of a system enables us to find a formula that fits a specific input-output relationship. In this book, we are mostly concerned about linear systems. Generally speaking, it is easier to model linear systems as compared to non-linear systems. Many physical systems can be modeled using linear systems or can be approximated as linear systems.

MATLAB is a powerful tool for system modeling. There are many books in the area of system modeling, MATLAB, and system modeling using MATLAB. In this book, we show the concept of physical system modeling using MATLAB through a lab approach. The interested readers can model several interesting physical systems in a step-by-step fashion. We ask the readers to model a physical system using various methods such as differential equations, space state, and the frequency domain. We also ask questions to help the readers think and understand the fundamentals of signals and systems in an intuitive way. The solutions are also provided in order to help the readers to verify their work and guide them to model the given systems.