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So far there has not been paid attention to frames that are balanced, i.e.those frames which sum is zero. In this paper we consider balanced frames, andin particular balanced unit norm tight frames, in finite dimensional Hilbertspaces.  Here we discover various advantages of balanced unit norm tight frames insignal processing. They give an exact reconstruction in the presence ofsystematic errors in the transmitted coefficients, and are optimal when thesecoefficients are corrupted with noises that can have non-zero mean. Moreover,using balanced frames we can know that the transmitted coefficients wereperturbed, and we also have an indication of the source of the error.  We analyze several properties of these types of frames. We define anequivalence relation in the set of the dual frames of a balanced frame, and useit to show that we can obtain all the duals from the balanced ones. We studythe problem of finding the nearest balanced frame to a given frame,characterizing completely its existence and giving its expression. We introduceand study a concept of complement for balanced frames. Finally, we present manyexamples and methods for constructing balanced unit norm tight frames.

Balanced frames: a useful tool in signal processing with good properties