Real Time Approximation of a Function by a Sum of Complex Exponentials

Many problems in applied engineering and mathematical modelling require fitting a sum of complex exponentials to a given data set. This type of modeling makes it possible to go beyond the Raleigh limit introduced by Fourier techniques. This textbook shows how a set of complex data can be modeled by a sum of complex exponentials using the matrix pencil technique. The technique is computationally efficient and robust to coloured noise; and the results should be of use in many areas of data prediction and forecasting, eg, radar and sonar data analysis, including spectral estimation and extending the resolution of measured data.