The recursive forms to approximate the causal linear-phase IIR digital
filters are studied. Actual causal linear-phase IIR digital filters h
ave been proposed (Clements and Pease 1989); however, the lack of rati
onal expressions of the considered systems render them unrealizable. A
s a consequence, applications for this kind of filter do not exist. In
this paper, based on the Padi approximation and the eigenfilter desig
n, the approximations of linear-phase recursive representations of the
filters are proposed for practical applications. Experimental results
show good approximation on phase linearity. Finally, the magnitude re
sponse is designed to meet the specifications in the passband of the l
ow-pass filter.