Length Three FIR Loop Filter

The simplest nondegenerate example of the loop filters of §6.8
is the three-tap FIR case (
). The symmetry constraint
leaves two degrees of freedom in the frequency response:^{10.1}

If the dc gain is normalized to unity, then , and there is only one remaining degree of freedom which can be interpreted as a

In this coefficient range, the string-loop amplitude response can be described as a ``raised cosine'' having a unit-magnitude peak at dc, and minimum gains at plus and minus half the sampling rate ( ).

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University