j 1 r u2062 u2211 l 1 m u2062 u03b1 j k l t u00d7 f j l t u2061 t u03b1 j k l t the smc of input channel j 39 s lth spectral band component in time aperture period t onto output channel k f j l t t the jth input channel 39 s lth spectral band signal at time t from aperture window t there are r input channels m spectral bands in the decomposition of each input signal and n output channels in the example given at any particular time t there will be contributions to the output signal from components from one or two overlapping transform windows t is the subscript indicating a particular transform window the multiply and add operations described in the invention can be carried out on one of more dsps such as a motorola 56000 series dsp in some applications particularly those in which the input digital audio signal has been digitally compressed the signal may be delivered to the playback system in a spectrally decomposed form and can be applied directly to the spectral mapping subsystem of the invention with simple grouping into appropriate bands a good spectral decomposition is one that matches the spectral masking properties of the human hearing system like the so called u201c critical band u201d or u201c bark u201d band decomposition the duration of the weighing function and hence the update rate of the smcs should accommodate the temporal masking behavior of human hearing a standard 24.