Comparison of Walsh and Fourier spectroscopy of geomagnetic reversals and nonsinusoidal palaeoclimatic time series

Higher resolving capabilities and theoretical appropriateness of Walsh spectral techniques as compared to Fourier spectral analyses are presented for synthetic and nonsinusoidal geotime series. Theoretical developments of Walsh transform techniques and a comparative study of Walsh and Fourier spectral estimates are presented. The Walsh spectral technique is applied specifically to two actual time series data of geomagnetic reversals in binary telegraphic wave form and nonsinusoidal palaeomagnetic and palaeoclimate time series. Walsh spectra reveal periodicities in Milankovitch frequency bands and provide exceptionally well-resolved spectral lines. The possible physical significance of these orbital periodicities is discussed. A comparative example of autocorrelation analysis in the real time domain and dyadic time domain is also presented using a telegraphic signal model of actual geomagnetic reversal time series. and the result is briefly discussed. The computational efficiency of the Walsh function could be exploited further for many other binary and nonsinusoidal geophysical/geological time series