A generalized correlation function for magnified/reduced signals

A generalization of the correlation function is explored which, besides a relative time shift between the signals to be correlated, also takes into account different scalings on the time axis (i.e., magnification/reduction). It is shown how the generalized correlation function for continous signals can be sampled and computed without loss of information and thus can be described by discrete-time signals. Envisaged applications comprise coded aperture imaging, measurement, radar, and digital communications. Special attention is paid to tomo-graphic imaging using coded apertures. It is demonstrated how individual slices of an object can be reconstructed by correlating the recorded image with suitably designed decoding filters using the generalized correlation function.