The letter deals with the special class of digital filters that possess a prescribed notch frequency. The present techniques for synthetising such filters rest on the bilinear-transformation method, where the designer is required to synthetise a continuous splane notch filter, prewarp it, and then apply the transformation. It is shown here that notch filters can be synthetised directly into the z-1 plane. © 1969, The Institution of Electrical Engineers. All rights reserved.