This paper describes a new recursive digital algorithm for computing the response spectrum from acceleration data. The algorithm digitally implements a single degree of freedom oscillator using a covariance-invariant digital filter. It is shown that this technique will produce an accurate response spectrum from input data that have been sampled at a rate that is as low as three times the oscillator natural frequency, fn. The more common response spectrum digital filter obtained using a bilinear z transformation technique requires a sampling rate of ten times fn. The fact that the algorithm can be used for data with a low sampling rate makes it particularly well suited for real time, multi-frequency calculation of response spectra with a microprocessor system.