Introduction to Signals and Systems

Signals and Systems are together. Because signals are process by system, such as denouncing, deblurring or heartbeat monitoring.

Input signal --> [system] --> Output

Material     --> Process -- > Finish product

This class is important for analyzing raw and messy data.

Signals
Some examples are : Traffic light, Turning light, strike signal.

The actual definition is a variable physical quantity by which a message or information can be represented.

There are 2 classes of signal. Discrete-time and continuous-time.

Most of signal are continuous time signal, which is a function of one or more independent variables like  x(t) of the real variable t. The  t can represents any continuous time and we can basically give nay unit of time that is appropriate (seconds, hours, years, etc.). That t is like an imaginary number, most of time they are actually infinite value. In REAL world though, the value is usually bounded.

Systems
A system is any thing that take signals and process it in to different kinda of signal. Engineering way we take some electrical signal from some there and go through a medium which is the system. Then the system later transfer the output electrical system other kind of signal as response. Biological approach would be digest system, which is taking food as input signal and digested by the digest system. Then the out put come out as feasts which is the finish product of the digest system.

Tools that are useful for system are:

Time domain analysis--> Convolution method.

Fourier methods--> Analyzing the frequency

Laplace transform --> The transient response and stability way.

usually its goes like x(t)--> [H] --> y(t)

The input is x(t).

The output is y(t).

The system is [H] and H can be use in 2 ways. one is Analysis or Synthesis

Analysis is to use H the system to find out the result.

Synthesis is working backward. This is to use the input and output to find the system.

Examples and Practice Problems
Time domain: Signal over time --> Think about piano chord.

Frequency analysis: taking the time domain in to next level by Fourier transform. Time domain+ Fourier transform= amplitude and frequencies.

Extra Resources
From -->Wikipedia

From --> MIT open Course. [Part 1] and [Part 2]

Credits: Wikipedia and Dr.Qi's note.