AbstractThis paper presents the theory and a time domain synthesis procedure for a class of orthogonal digital filters. These filters are derived from discrete Laguerre polynomials and in the case of exact representation possess an infinitely long structure whilst exhibiting an infinite impulse response.In practice the desired impulse response of a filter to be synthesized is truncated in time whilst speed and economic considerations impose a constraint on its length. By the nature of these filters, very few stages usually suffice to yield excellent fidelity in most practical cases. The filters, whose cascaded stages are eminently suited to multiplexing, are inherently stable.A computer‐aided design algorithm using a Fibonacci search algorithm is presented for optimizing the practical case having finite length and span. Two examples illustrate the procedur