Fourier transform pairs

Fourier transform pairs describe the relationship between two types of representations of a signal: the time (or spatial) domain and the frequency domain. A signal's time-domain form shows how it varies over time, while its frequency domain form reveals the different frequencies that make up the signal and their intensities. The Fourier transform converts a time-based signal into its frequency components, and the inverse Fourier transform reconstructs the original signal from these components. Think of it as breaking down a complex sound into individual notes or combining those notes back into the full sound, providing a powerful way to analyze and process signals.