System Identification

Many mature and existing mechanical, electrical, optical, and or chemical systems have been in place and just work without any current mathematical model. However, it is always the case that they can benefit from more efficient operation to reach peak performance, or by adding functionality; doing so requires good mathematical models for good system design outcomes. These systems can be approximated mathematically with a one to one relationship between the input and the resulting output. Electrical systems are often mathematically modeled by mapping the output frequency due to a input frequency and are called the frequency response of the system. Stimulating the input of the system with a signal composed of all frequencies results in an output of all the possibilities. Mapping the input to the output defines the frequency response of the electrical system. This technique with modification can be applied to all systems to produce a working mathematical model.