A Class of Finite Memory Interpolation Filters
John E. Hopcroft, Ken Steiglitz · IEEE Transactions on Circuit Theory · 1968
Sufficient conditions are given for an interpolation filter to have an impulse response that vanishes outside a finite interval of the time axis, that is to have a finite memory. These conditions are that the transfer function be of the formG(s)/G(z), whereG(s)is proper, rational, and has poles limited to the strip|Im s| < \pi; and where1/G(z)is a polynomial. The filtersR_{mp}are included in this class, and these are characterized by the fact that their effect is to interpolate an(m + p - 1)-order polynomial in each interval throughppast andmfuture points. The interpolation filters described can be used to derive digital filters that approximate an arbitrary linear timeinvariant continuous-time operator. It is shown that in the case of integration, theR_{mp}filters lead to well-known Lagrangian integration formulas.