Some Exchange Algorithms Complementing the
	Parks-McClellan Program for Filter Design

	Ivan W. Selesnick and C. Sidney Burrus
	Electrical and Computer Engineering Department - MS 366 
	Rice University, Houston, TX 77251-1892, USA 
	selesi@rice.edu, csb@rice.edu

        International Conference on Digital Signal Processing.
        pages 804-809, Limassol, Cyprus, June 26-28, 1995.

In this paper, several modifications of the Parks-McClellan (PM) program 
are described that treat the band edges differently than does the PM program.  
The first exchange algorithm we describe allows (1) the explicit specification 
of $\del_p$ and $\del_s$ and (2) the specification of the half-magnitude 
frequency, $\om_o$.  The set of lowpass filters obtained with this algorithm
is the same as the set of lowpass filters produced by the PM algorithm.  We 
also find that if passband monotonicity is desired in the design of filters 
having very flat passbands it is also desirable to modify the usual way of 
treating the band edges.  The second multiple exchange algorithm we describe
produces filters having a specified $ \del_p $ and $ \del_s $ but also 
includes a measure of the integral square error.