The connection between continuous and discrete lattice filters

The importance of lattice structures in connection with filtering and prediction has been known for decades. The demand for faster processing has led to steadily increasing sampling rates, and as a result the behavior of the discrete filters as the sampling period tends to zero has become an important theoretical and practical issue. One way of solving the numerical problems that arise in the usual filter structures when the sampling period becomes small compared with the dynamics of the underlying physical processes is to resort to Æ operators instead of delay operators. Although the interrelations between the continuous and discrete lattice structures have been rarely studied, it is known that the Æ lattice naturally leads to a continuous form as the sampling rate increases. This paper addresses this point and establishes the rate of convergence of the discrete lattice filter to the continuous filter as a function of the sampling period or of the filter order.