A consideration for the interpolation problem with first‐and second‐order information

Abstract

AbstractA wave digital filter (WDF) is a low‐sensitivity digital filter which simulates lossless analog circuits. A lattice‐type digital filter (AR lattice filter), which is used in digital signal processing, is a WDF equivalent to a cascade of unit elements (u.e.). As the generalization of this relation, a WDF realizing a modeling filter for an ARMA process has been obtained and the network theory with WDF's has been applied to the digital signal processing. The conventional WDF's, except for the AR lattice filter, are constructed by using the transfer functions to be realized. In this paper, unlike the conventional network synthesis, we propose a synthesis method. In this method, a network approximating a modeling filter for a stationary stochastic process is synthesized recursively using a finite number of data of the autocorrelation coefficients (second‐order information) and the impulse response of the modeling filter (first‐order information). A lattice‐type digital filter is derived realizing an approximation of the transfer function. The approximation is one in which first‐ and second‐order information matches the forementioned data. Also, modified least square approximations due to Kalman and Mullis can be realized by this lattice‐type digital filter. This lattice‐type digital filter is a kind of WDF and the relationship between the global stability and the local stability is clear.