Rapid method of forming spectra from regularly sampled records by rectangular wave transforms

Spectral estimation of signals sampled at equispaced time instants is discussed. Stable periodogram estimates are generally formed from the squares of Fourier coefficients summed over a large number of data blocks. An exact relationship has been shown to exist between Fourier coefficients and `rectangular wave¿ transforms, which are obtained when the sinusoidal function is replaced by the associated sign function. The coefficients so formed can be unscrambled into Fourier coefficients. A related operation can also be carried out on the powers formed from the accumulated squared-up estimates, but in this case the deconvolution is not exact. Nevertheless, in many practical situations the method provides a very good approximation to the power spectrum. The approach has the advantage that the rectangular wave coefficients can be generated only by additive operations, and these are much faster to implement on a small microprocessor. The technique is applied to digitally simulated data.