Interpolator/decimator filter structure and a notch filter therefor

DETAILED DESCRIPTION The present invention is intended as a solution to the problem of providing in excess of 3 dB attenuation at one half of the lower sampling frequency.
Interpolator and Decimator filter structures are provided wherein this problem is overcome by introducing a notch filter.
This filter, which operates at the lower of the two sampling frequencies, introduces a transmission zero at some frequency slightly less than half of the lower sampling frequency and considerably more than 3 dB attenuation at half the lower sampling frequency.
In accordance with the invention there is provided an interpolator-or-decimator filter structure, operable between a lower and a higher sampling rate, comprising: an interpolating or decimating switched branched network, including one or more all-pass-network filters; and, connected in series therewith, a notch filter, this filter having a transmission zero at a frequency displaced from a frequency of one half of the lower sampling rate, and being comprised of a plurality of all-pass-network filters; each all pass network filter including a delay element and at least one coefficient multiplier and having as characteristic a transform function X(Z) of the form: X(Z)=[Z.
sup.
-1 -K]/[1-KZ.
sup.
-1 ] where Z.
sup.
-1 is the unit delay operator and K the multiplier coefficient.
In accord with the invention there is also provided a notch filter for use in the interpolator/decimator filter structure as set forth above, the notch filter comprising: A pair of all-pass-network filters connected in-line between an input node and an output node, the input to the first one of the pair of filters being connected to the output node, and a tapped output of the second one of these filters being connected to the input node, and wherein each all-pass-network filter is defined by a throughput transform function X(Z): X(Z)=[Z.
sup.
-1 -K]/ [1-KZ.
sup.
-1 ], and wherein the second of these filters has an intermediate transform function Y(Z): Y(Z)=.
alpha.
Z.
sup.
-1 /[1-KZ.
sup