A least-mean-square (LMS) adaptive algorithm for calculating the discrete Hartley transform (DHT) is presented. The transform kernel of the DHT serves as the input vector and the input signal to be analysed is regarded as the ‘desired response’ for the adaptive process. For a proper choice of convergent factor, i.e. u = 1/2, the ‘LMS DHT analyser’ will provide an exact N-sample DHT. All the operations involved are real. Incorporation of one new sample requires only one adaptation.