Applications of Lattice Filters to Quadrature Mirror Filter Banks

Abstract

Presented is a method for designing and implementing lattice filters to be used in Quadrature Mirror Filter (QMF) Banks. Quadrature Mirror Filter Banks find use in applications where a signal must be spilt into subbands operated on then reconstructed in the output. Because of their structure, lattice filters do this very well and allow perfect reconstruction, even when the lattice coefficients must be quantized. In this paper QMF\u27s and Lattice Filters are derived and analyzed. Application of the lattice filter is presented along with a design program and example of its use to implement a QMF. The computer aided design procedure allows the user to input the stop-band frequency, normalized to the sampling frequency, and the desired attenuation. The resulting outputs are the lattice coefficients, and the Finite Impulse Response (FIR) coefficients of an FIR filter having the same characteristics. The program selects a set of coefficients based on optimal coefficients that are within the desired tolerance. The filter design program was written in FORTRAN, with the filter coefficients stored in a data file on disk. Programs were written in MATHCAD© to show the lattice filter response and to simulate the QMF using these coefficients