The harmonic decomposition problem considered by Pisarenko can be expressed as the solut...

The harmonic decomposition problem considered by Pisarenko can be expressed as the solution to the equation

The solution for a can be obtained by minimizing the quadratic form all subject to the constraint that . The constraint can be incorporated into the performance index by means of a Lagrange multiplier. Thus the performance index becomes

By minimizing with respect to a, show that this formulation is equivalent to the Pisarenko eigenvalue problem given in (14.5.9) with the Lagrange multiplier play-ing the role of the eigenvalue. Thus show that the minimum of is the minimum eigenvalue .