| In this dissertation, we present a multi-tone signal processing paradigm that is based on the use of the warped discrete Fourier transform (WDFT). The WDFT evaluates a discrete-time signal in the context of a non-uniform frequency spectrum, a process called warping. Compared to a conventional DFT or FFT, which produces a spectrum having uniform frequency resolution across the entire baseband, the WDFT's frequency resolution is both non-uniform and programmable. This feature is exploited for use in analyzing multi-tone signals which are problematic to the DFT/FFT. This dissertation focuses on optimizing frequency discrimination by determining the best warping strategy and control by using the intelligent search algorithms and criteria of optimization, or cost functional. The system developed and tested focuses on maximizing the SDFT frequency resolution over those frequencies that exhibit a localized concentration of spectral energy and, implicitly, diminishing the importance of other frequency ranges. This dissertation demonstrates that by externally controlling the frequency resolution of the WDFT in an intelligent manner, multi-tone signals can be more readily detected and classified. Furthermore, the WDFT can be built upon an FFT enabled framework, insuring high efficiency and bandwidths. |
