In this correspondence, we introduce a family of norms that may prove useful in system identification problems. The important property of the new norm is that for a given sequence, its value in the limit will converge to the supremum over all frequencies of the spectrum of the sequence. Using this property, a procedure is outlined to approximately minimize the weighted L(infinity) norm of the frequency response estimation error. In addition, a test for checking the Whiteness of a given sequence is proposed.