ABSTRACT
Choosing a basis in which to decompose a signal means selecting a certain compromise between time and frequency. This choice can be represented in terms of Heisenberg boxes. Each box corresponds to one element of the basis and roughly represents the time-frequency information it encodes. A Heisenberg box (also called a "cell") is a rectangle in the plane whose sides are respectively the range of values and the range of frequencies represented by the basis element. The Heisenberg uncertainty principle sets a lower bound to the size of these boxes: the product &AT must be at least 1/27r. One can think of the elements of an orthogonal basisfor example, all the translates and dilates of a given mother waveletas paving the time-frequency plane with Heisenberg boxes: the boxes covering the plane without overlapping.
