Scaling-free McClellan transform for 2-D digital filters

The original McClellan transformation used in the design of 2-dimensional digital filters having quadrantally symmetrical magnitude response, involves the substitution cos ¿ = F(cos ¿1, cos ¿2). For real frequencies, a scaling procedure was proposed by Mersereau et al. (1976) to guarantee that |F|¿1 using the two values Fmax and Fmin. In the letter, we first present extremely simple formulas for the scaling factors, then suggest a modified transform which not only is scaling-free but also contains one less coefficient than the original transform.