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, 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. The number of required adders is further reduced in accordance with the present invention by using a single adder to produce two intermediate signals corresponding to respective sums of two pairs of source samples. The adder is used during one time interval to produce the first of the intermediate signals and during a subsequent time interval to produce the second of the intermediate signals. The two intermediate signals are combined in the production of a resulting sample by producing a signal corresponding to the first intermediate signal, delaying for a time interval, producing a signal corresponding to the second intermediate signal, and applying the signals corresponding to the intermediate signals to an adder which produces a signal representing the sum of the values of the two signals.