Transforms (Laplace Transform, Fourier Transform)

Transforms like the Laplace and Fourier are mathematical tools that convert complex signals or functions from their original form, often in time, into a different domain—frequency or complex frequency. This makes analyzing and understanding systems, such as electrical circuits or signals, easier by revealing underlying components like frequencies or growth rates. The Fourier Transform breaks down signals into their constituent frequencies, similar to identifying individual musical notes in a song. The Laplace Transform extends this idea, handling more complex systems, especially those involving growth or decay, and simplifying the study of system behavior and stability.