Reconstruction of Overlapping Echos with Unknown Shape in Time and Frequency Domain

In many situations one h i s to resolve an unknown number of overlapping and noisy echos of a signal. For this problem a numerical procedure 111 was developed which works as a modified version of the MUSIC algorithm [2,3]. The shape of the signal s’(t) must be known to estimate the number D and the t:ime delays fd of the echos. If K independent records are collected, all differing in the amplitudes mk,d of the echos qt fd) and the noise realization < k ( t ) , then the received and sampled waveforms can be written as