Generalized quadratic minimization and a signal processing application

This paper deals with the problem of quadratic minimization subject to linear equality constraints. Contrary to the standard formulation, we assume the most general case of a possibly singular quadratic form. As we explain, the existing formal solution to this problem has several drawbacks. Our new approach is free from most of these drawbacks. It has a simple physical interpretation and is relatively easy to implement. Practical importance of this result lies in its numerous applications : filter design, spectral analysis, direction finding and blind deconvolution of multiple FIR channels. Here we focus on the blind deconvolution application.