Device generating a digital filter and a discrete convolution function therefor

A circular convolution function generator comprising:

• means for determining the primitive root transforms of a sequence of terms of a series {a.sub.n } and including:
• accumulating means for building at least some of the 1 to p-1 multiples of the terms of said series where p is a prime number;
• a first memory for storing partial terms of said transforms as said terms are formed;
• an adder having its output connected as an input of said first memory;
• and
• means for connecting an output of said memory and the output of said accumulating means to inputs of said adder to selectively combine partial transform terms from said memory with said multiples to form more complete partial terms of said transforms;
• a second memory for storing the negatives of the transforms of the terms of series {b.sub.n };
• a multiplying means fed corresponding terms of said transforms of said {a.sub.n } series and said negatives of the transforms of said {b.sub.n } series by said first and second memories, to generate terms of a transform of a function of said {a.sub.n } and said {b.sub.n } terms;
• and
• means for determining the inverse transforms of the transform terms generated by the multiplying means, said means for determining including:
• a second accumulating means for building, at least some of the 1 to p-1 multiples of the terms issued by said multiplying means;
• another adder having an input receiving said multiples from said second accumulating means;
• a third memory connected to the output of said other adder for storing partial terms of said inverse transforms as said partial terms are formed in said other adder;
• and
• gating means for reading out selected ones of said stored partial terms from said third memory to another input of said other adder for addition to selected ones of said multiples from said second accumulator to generate more complete partial terms for storage in said third memory.