Estimating the order of a FIR filter for noise cancellation

The problem of designing a finite impulse response filter devoted to the joint process problem, and in particular to noise cancellation, is investigated. The goal is restricted to how to choose an optimal order of the FIR filter. The analysis is based on the maximization of a noise reduction criterion which is in fact perfectly matched to the desired performance, namely the minimization of residuals. The criterion includes estimation errors introduced by the substitution of the true covariance matrices for estimates. Since true covariance matrices again enter the noise reduction criterion, they must be replaced by estimates. The criterion is then modified in order to take this fact into account, but the scheme is not iterated any further. Simulations are presented for various simple cases