Autoconvolution and panorama: Augmenting second-order signal analysis

Abstract

The autocorrelation does not differentiate between deterministic and stochastic signals, as phase information is not maintained. This paper introduces the autoconvolution for both deterministic and stochastic signals. The autoconvolution with the autocorrelation provides a second-order description that discriminates between deterministic and stochastic signals - even those with identical power spectra. We also introduce the panorama as the Fourier transform of the autoconvolution. The power spectrum and panorama admit a two-dimensional spectral representation that has unique and powerful properties, such as detecting deterministic sinusoidal components in correlated stochastic noise without knowledge of the sinusoidal frequencies or amplitudes. Additional extensions are indicated.