The role of biorthogonal partners in sampling theory for non bandlimited signals: a review

It is well known that a broad class of non-bandlimited signals can be reconstructed from uniformly spaced samples by relating the problem to the inversion of a digital filter. This simple idea has given rise to many applications, some of them quite sophisticated. This includes spline interpolation, fractionally spaced equalization (FSE) of noisy channels and more recently, rational FSEs. On the theoretical front, it has given rise to the idea of biorthogonal partners, which unify many aspects of wavelet theory into the same framework.