"Fourier Transform can localize signals in frequency domain, but not in time domain." -- What does it mean in layman's terms?
In the Fourier transform, the basis functions are complex exponentials. These functions are perfectly localized in the frequency domain, i.e., they exist at one frequency, but they have no time localization because of their infinite duration. The localization of a function depends on its spread in time and frequency. A complex exponential has zero spread in frequency, but it has infinite spread in the time domain. Consequently, any signal analyzed by the Fourier transform is only localized in frequency (e.g., frequencies of sinusoidal components can be identified), but not at all in time (e.g., temporal changes of signal properties cannot be localized).