Exact Reconstruction of Time Series with Arbitrary Bandwidths Formed by Merging Windowed DFT Spectral Bins

Overlapped and windowed fast Fourier transforms (FFT) are an efficient method of synthesizing a bank of equally spaced and equal bandwidth narrowband filters. Often there is need to recover, from these narrowband filters, the original input broadband time series or a reduced bandwidth version of that time series. This paper presents the constraints and the techniques required to recover time signals with arbitrary bandwidth from the sequence of transform outputs. In particular we address the processing technique to recover the time signal when, due to prunning of the FFT, alternate narrowband filter outputs are not available for the reconstruction.