Remarks on analog approximations for constant group delay

✍ Scribed by H.M. Paynter; I.J. Busch-Vishniac

• Publisher: Elsevier Science
• Year: 1989
• Tongue: English
• Weight: 160 KB
• Volume: 326
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(89)90077-x

✦ Synopsis

In a recent paper in this journal Omprakash Sharma et al.

(1) presented a method for generating an analog approximation to a constant group delay based upon a least squares minimization.

It appears worthwhile to draw attention to an earlier definitive approach to this same problem which resulted in the now expired US Patent 3,044,703 (2) covering the so-called Paynter filter. There also exist early journal references on this filter (3,4).

The renewed interest in this long-standing problem is related to the increasing importance of ultra-high frequency pulse-compression techniques in computing and communication, where phase-distortion is at least as important as amplitudedistortion. The modern work benefits from the efforts a half-century ago in transversal filters for microwave, sonar and radar applications.

As in Omprakash Sharma et al. (l), the Paynter filter was also based on the allpole approximation of F(s) = ems = l/e" = l/Pm@). Noting that es = sinh (s) +cosh (s) and that these two hyperbolic functions, respectively odd and even, may be expanded as infinite products, then permits a finite nth order Hurwitz polynomial approximant P,(s) = O,(s) + E,(s), having respective odd and even parts, O,(s), E,,,(s), whose zeroes interleave, and where n = max (21+ 1,2m).

This alternative approach determines Q, and E,,, as the finite product expansions O,(s) = s h (1 +ar'.s*>,