Theory of nonstationary linear filtering in the Fourier domain

A general linear theory is presented which describes the extension of the convolutional method to nonstationary processes. This theory can apply any linear, nonstationary filter, with arbitrary time and frequency variation, in the time, Fourier, or mixed (time-frequency) domains. The filter application equations and the expressions to move the filter between domains are all ordinary Fourier transforms or generalized convolutional integrals. Nonstationary transforms, such as the wavelet transform, are not required. There are many possible applications of this theory including: the one-way propagation of waves though complex media, time migration, normal moveout removal, time variant filtering, and forward and inverse Q filtering.