Frames, as a generalization of bases, allow redundant representations, that still allow perfect reconstruction. We will shortly review the basic notions of frame theory, and, in particular explain, why they are especially interesting for signal-processing applications. As a particular useful case, we will briefly review the basic notions of non-stationary Gabor frames.

Certain kind of operators appear in a lot of scientific fields, like mathematics, physics, signal processing and acoustics. Those operators consist in analysis, multiplication and re-synthesis. In the frame theory context, we will review these operators as frame multipliers, and their applications as time-variant filters. We will show recent (mathematical) results about the invertibility of multipliers. As possible application we will introduce the notion of irrelevance filters, as well as a denoising approach in the time-frequency plane.