Fourier transforms

Fourier transforms are mathematical tools that break down complex signals or functions into simpler components, specifically into waves of different frequencies. Imagine a musician playing multiple notes at once; a Fourier transform helps identify each individual note being played. This technique is widely used in fields like audio processing, image analysis, and telecommunications, allowing us to analyze and manipulate data. By converting a signal from the time domain (how it changes over time) to the frequency domain (how much of each frequency is present), it enables a clearer understanding of the underlying patterns and structures.