Importance

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Abstract

Symmetry in a filter is used to reduce the complexity of an interpolator or a decimator. A weight filter matrix which includes L=(N-1)M+K weights is divided into two sub-filters, the first having L1=NK weights and the second having L2=(N-1)(M-K). For interpolators, N source samples are applied to the first sub-filter to produce K signals and N--1 source samples are applied to the second sub-filter to produce M-K signals. For decimators, K source samples are applied to the first sub-filter to produce N samples and M-K source samples are applied to the second sub-filter to produce N-1 samples. An inverse relationship is recognized when a first weight is associated with a first of the samples and a second weight with a second of the samples and a weight equivalent to the first weight is associated with the second sample and a weight equivalent to the second weight is associated with the first sample. Two composite weights of the first and second weights and composite sample signals weighted therewith are formed. The composite weights can be used repeatedly for each subsequent interpolation or decimation and are calculated only once. The two composite samples have values which are, respectively, (i) the sum of the values of the first and second samples and (ii) the difference of the values of the first and second samples.

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