Stochastic operator norms for two-parameter adaptive lattice filters

Expressions are derived for bounds on average output power in lattice filters with unequal forward and backward reflection coefficients, such as arise in the adaptive least-squares lattice algorithms [3]. It is shown that under stationary, noisy conditions, these bounds will in general be larger than in the case of equal forward and backward reflection coefficients, as in the adaptive gradient lattice filters. Expressions obtained here can be used to derive the average output power for several (adaptive) lattice filters. They suggest that misadjustment may be higher under noisy conditions for the ALSL than for the AGL.