Fourier Transform Theorem

The Fourier Transform Theorem states that any complex signal, like a sound wave or a picture pattern, can be broken down into a combination of simple waves, each with different frequencies, amplitudes, and phases. Think of it as dissecting a musical chord into individual notes. Conversely, these simple waves can be combined to reconstruct the original signal. This process allows us to analyze and manipulate signals efficiently, revealing their underlying frequency components, and is fundamental in fields like audio processing, image analysis, and communications.