Device for real time processing of digital signals by convolution

A device for real time processing of digital signals by convolution, comprising:

• (a) multiplier means having a plurality of inputs and an output;
• (b) a plurality of circuits for performing a Numerical Theoretic Transform (NTT) with a modulus M of the form
• 2.sup.p -2.sup.q +1,
• where "P" and "q" are integers, each of said NTT circuits being connected to one of said multiplier inputs for delivering said NTT to the associated one of said inputs;
• (c) a reverse transformation circuit for performing an inverse Numerical Theoretic Transform (NTT.sup.-1), said reverse transformation circuit connected to said output of said multiplier means for providing the NTT.sup.-1 transform of said output;
• (d) a first unit consisting of (d1) means connected to each of said NTT circuits for performing an arithmetic base change and (d2) means for encoding, said first unit connected to receive an input digital signal and deliver an encoded signal to the respective one of said NTT circuit;
• (e) a second unit consisting of (e1) means for decoding and (e2) means for return to the original arithmetic base of the output of said circuit for performing NTT.sup.-1, said means being so arranged that to a number X modulo M representing one of said input signals in the original (powers of 2) base, there corresponds, in the new base, a number x.sub.p-1 . . . x.sub.p-2 . . . x.sub.1 x.sub.0 such that ##EQU7## where f.sub.o is an integer of from 1 to N-1 and f.sub.i and e.sub.j are numbers that fulfill the following conditions:
• 2f.sub.p-q-1 =e.sub.o +f.sub.o (mod M) and 2e.sub.q-1 =-f.sub.o (mod M)
• 2f.sub.i =f.sub.i+1, 2e.sub.i =e.sub.i+1 for the other values of index i
• where "p", "q", and P are integers;
• and where "i" and "j" are integer indicies.