"time" is present in both frequency and position. The difference is how time is sampled. Fourier Transform maps between global frequency space sampling and (rep

"time" is present in both frequency and position. The difference is how time is sampled. Fourier Transform maps between global frequency space sampling and (repeating wave for all time) and local positional/point space sampling (perfect impulse). Wavelets map to an intermediate space,as you say, with smeared points/impulses and damped waves.