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We introduce frames, tight frames, Gabor frames and OFDM (orthogonal frequency-division multiplexing) systems. We discuss the problem of intersymbol and interchannel interference for OFDM systems and are thus led to consider Lowdin orthogonalization, which, of all orthogonalizations of a linearly independent set, does the best job of preserving that set in the sense of least squares. Some properties of Lowdin orthogonalization are introduced and proved. Our current research, the study of pulse shape optimization with respect to time-frequency localization, is discussed briefly.