The first condition provides stability for (or continuous-time) linear systems, and the second case relates to stability of discrete-time linear systems.
All wavelet transforms may be considered forms of time-frequency representation for continuous-time (analog) signals and so are related to harmonic analysis.
However, because of the limited frequency spectrum allowed for modulated digital video signal, the digital video signal must become a continuous-time digital video signal.
Conventional sampled-data control uses a zero-order hold, which produces a piecewise-constant control signal and can be used to give a sampled-data implementation which approximates previously-designed continuous-time controller.
