Formulas for McClellan transform parameters in designing 2-D zero-phase FIR fan filters

Abstract

New formulas for McClellan transform parameters for the design of 2-D zero-phase FIR fan filters are optimally derived under the integral squared error (ISE) criterion. By imposing the constraint that F(O,O) = cos w(c), where F(.) is the McClellan transform and w(c) is the cutoff frequency of the one-dimensional (1-D) prototype filter, the ISE is directly minimized without modifying it and, as a consequence, closed-form formulas for the McClellan transform parameters are obtained. It is shown that these formulas lead to a very efficient design for 2-D zero-phase FIR fan filters.