Degenerate eigenvalues — A method to design adaptive discrete time wavelets

This paper introduces a new method for designing dyadic filter banks with optimum coding gain. We conjecture that in the generic case, the optimum impulse response is the maximum eigenvector of a certain Toeplitz matrix which is maximally degenerated, which ensures that the maximum eigenvector of the Toeplitz matrix has maximum possible multiplicity. We derive analytically the optimum FIR filter of order N = 6, whereas closed form solutions have been available only up to order N = 4.