JaJa, Joseph F.Owens, R.M.Digital convolution and the discrete Fourier transform are basic operations whose computational requirements are of great importance in many applications. In this paper, we propose new types of VLSI architectures which are shown to be quite suitable to handle these operations. These architectures will result in fully pipelined bit-serial arrays which require no control units. Some preliminary implementations indicate a substantial speed-up gain over other existing designs.en-USTechnical Report