Roundoff noise properties of second-order digital notch filters

Abstract

With regard to their roundoff noise properties, canonical second-order recursive digital notch filters, with zeros on the unit circle and poles near them, are shown to fall in three distinct groups depending upon the zeros of their noise transfer functions (NTF's). One of the groups, having all-pole NTF'S, shows large noise magnitudes but the noise behaviour is well defined. The second group shows low noise magnitudes that heavily depend upon the location of the zeros of their NTF's; these zeros are related to the transfer function coefficients in a particularly simple manner. When this dependence gets complicated, as for the third group, the noise properties are ill behaved.