New linear systolic arrays for digital filters and convolution

Abstract

The algorithm transformation techniques described in [1] and the data broadcast elimination method from [2] are used to represent the algorithm as a system of uniform recurrence equations. Usually the algorithms are given in iterative form, i.e. as a repetitive operation on data. The procedure A transforms these algorithms into a recursive form. The algorithm is then transformed to a single assignment code presentation by procedure B. The problem of recurrences defined in the iteration is solved by procedure C. Then the full index form of the algorithms are obtained by applying procedure D. By applying these algorithm transformation techniques a system of affine recurrence equations with the data broadcast property is obtained. The data broadcast elimination method is used to transform the algorithm into a system of uniform recurrence equations. The reader is referred to [3–9] for a description of the data dependence method and linear transformations. In this paper we will use the notation proposed in [1,9]. The folding transformations, described in [10], are used to obtain more efficient processor array implementations for both the MA and AR filters. The ARMA filter is a composition of these two implementations that have an interlocking property. However the systolic array designed by H.T. Kung in [11] is rather straight forward solution resulting in cells with double complexity according to the inner product step processors. A much better solution is obtained by using a translation and the interlocking property of the partial implementations in the composition.