Signal interpolation and decimation exploiting filter symmetry

Symmetry in a filter is used to reduce the complexity of an interpolator or a decimator and to simplify derivation of resulting discrete samples. In particular, 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). In the case of interpolators, N source samples are applied to the first weight sub-filter to produce K interpolated signals and N-1 source samples are applied to the second weight sub-filter to produce M-K interpolated signals. In the case of decimators, K source samples are applied to the first weight sub-filter to produce N decimated sample components and M-K source samples are applied to the second weight sub-filter to produce N-1 decimated sample components. If the weight filter matrix is centrosymmetric, both sub-filters are also centrosymmetric. Symmetry in the weights of each sub-filter is recognized and exploited. Within each sub-filter, an inverse relationship between weights applied to two samples is recognized and exploited. An inverse relationship is recognized when a first weight is associated with a first of the samples and a second weight is associated with a second of the samples and a weight which is equivalent to the first weight is associated with the second sample and a weight which is equivalent to the second weight is associated with the first sample. The inverse relationship is exploited by forming two composite weights of the first and second weights and weighting composite sample signals with the composite weights. A first of the composite weights has a value which is one-half of the sum of the values of the first and second weights. A second of the composite weights has a value which is one-half of the difference of the values of the first and second weights. The composite weights can be used repeatedly for each subsequent interpolation or decimation and are therefore calculated only once for processing many samples according to the same filter. 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.