This report describes a new filtering approach suitable for demodulating narrowband signals captured in digital wideband data. The new approach is based on generating the filtered and downconverted baseband signals using timefrequency spectral data, rather than the input wideband data. For communications electronic support measures systems, this spectral data will normally be generated to facilitate signal detection and parameter estimation i.e. frequency, bandwidth, bearing, etc.. Hence the new approach is able to take good advantage of this to reduce the overall number of computations. Through comparisons with more traditional FIR filtering techniques, it is shown that the new spectral filtering approach is computationally more efficient when multiple signals are to be simultaneously demodulated.