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, 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. Symmetry in weights applied to a single sample is recognized and exploited. For example, if two or more equivalent weights of a filter are applied to the same sample, one of the equivalent weights is applied to the sample once and the resulting weighted signal is used repeated rather than weighting the sample by each of the equivalent weights. Symmetry of weights applied to samples in producing a single resulting sample is recognized and exploited. For example, if equivalent weights are applied to two samples and the weighted samples are combined in producing a resulting sample, one of the equivalent weights is applied to the sum of the two samples. As a result, only one of the equivalent weights is applied to reduce the multiplication complexity of the interpolator or decimator.
