  Background: Windowed Fourier decompositions (WFD) are widely used in
measuring stationary and non-stationary spectral phenomena and in describing
pairwise relationships among multiple signals. Although a variety of WFDs see
frequent application in electrophysiological research, including the short-time
Fourier transform, continuous wavelets, band-pass filtering and
multitaper-based approaches, each carries certain drawbacks related to
computational efficiency and spectral leakage. This work surveys the advantages
of a WFD not previously applied in electrophysiological settings.
  New Methods: A computationally efficient form of complex demodulation, the
demodulated band transform (DBT), is described.
  Results: DBT is shown to provide an efficient approach to spectral estimation
with minimal susceptibility to spectral leakage. In addition, it lends itself
well to adaptive filtering of non-stationary narrowband noise.
  Comparison with existing methods: A detailed comparison with alternative WFDs
is offered, with an emphasis on the relationship between DBT and Thomson's
multitaper. DBT is shown to perform favorably in combining computational
efficiency with minimal introduction of spectral leakage.
  Conclusion: DBT is ideally suited to efficient estimation of both stationary
and non-stationary spectral and cross-spectral statistics with minimal
susceptibility to spectral leakage. These qualities are broadly desirable in
many settings.
