1. A method for designing a frequency-shaping equalizer to compensate for the frequency response of an existing system, said method comprising: a. providing a performance block diagram defining one or a plurality of input-output channels for performance tradeoff, said performance block diagram comprising a plurality of blocks representing the dynamics of said equalizer to be designed, the dynamics of said existing system, and the dynamics of one or a plurality of selected performance weighting filters; b. defining a set of performance tradeoff equalities relating to the frequency response of said input-output channels at a set of selected frequencies, each of said tradeoff equalities being defined at each of said set of selected frequencies; c. computing the magnitudes of the frequency response of said equalizer at said set of selected frequencies, by solving each of said tradeoff equalities independently; d. generating the phases of said equalizer at said set of selected frequencies from said magnitudes, said phases and said magnitudes corresponding to the frequency response of a stable system at said set of selected frequencies; e. providing a set of equalizer coefficients for implementation, said equalizer coefficients being derived from said magnitudes and said phases of said frequency response of said equalizer at said set of selected frequencies.