Signal Identification Using a Least L1 Norm Algorithm

In many important applications a signal consists of a sum of exponential terms. The signal is measured at a discrete set of points in time, with possible errors in the measurements. The Signal Identification (SI) problem is to recover the correct exponents and amplitudes from the noisy data. An algorithm (SNTLN) has been developed which can be used to solve the SI problem by minimizing the residual error in the L1 norm. In this paper the convergence of the SNTLN algorithm is shown, and computational results for two different types of signal are presented, one of which is the sum of complex exponentials with complex amplitudes. For comparison, the test problems were also solved by VarPro, which is based on minimizing the L2 norm of the residual error. It is shown that the SNTLN algorithm is very robust in recovering correct values, in spite of some large errors in the measured data and the initial estimates of the exponents. For the test problems solved, the errors in the exponents and amplitudes obtained by SNTLN1 were essentially independent of the largest errors in the measured data, while the corresponding errors in the VarPro solutions were proportional to these largest data errors.