An economical approach is described for estimating power spectra from sampled data through the application of Z -transform theory. The method consists of computing a weighting sequence whose frequency characteristics approximate a one-third octave bandwidth filter, and applying these coefficients recursively to the digitized data record. Filtering is followed by a variance calculation and a division by the appropriate filter bandwidth. A specific example of power spectra computed in the usual manner (Fourier transformation of the autocorrelation function) and power spectra computed by the method in this paper demonstrates the practicability of the technique. The most significant advantage is the economical aspect. It is shown that owing to the variable bandwidth and the small number of filtering coefficients, the savings that may be realized by the employment of this technique, in lieu of the autocorrelation transformation approach, may be quite considerable, depending on the record length and the number of lag products.