The demodulated band transform

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, bandpass 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. A computationally efficient form of complex demodulation, the demodulated band transform (DBT), is described. 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. 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. 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.