Dynamic spectral transforms: properties of the canted spectral transform

A generalized spectral transform is defined by extending the kernel of the conventional sectionalized Fourier transform (SFT). The generalized transform accumulates signal energy along narrow dynamic spectral channels that may be made to conform to the instantaneous-frequency dynamics of a given signal. This property may be used to achieve optimum detection of a deterministically known signal or to estimate the spectral dynamics of an unknown signal over the temporal limits of the transform. As an initial step toward achieving the spectral transform, the canted spectral transform (CST) is defined by using a quadratic phase kernel. The statistical properties of the CST are derived and compared with those of the conventional SFT. In general, the use of shaded windows in the CST does not appear to be advantageous and can degrade the selectivity of the transform in estimating the signal frequency dynamics. Statistical distributions of the peak cant variable for an idealized signal in Gaussian noise provide a basis for determining the performance of the CST in practical applications.