| This thesis summarizes several contributions to the areas of signal processing and auditory source separation. The philosophy of Frequency-Warped Signal Processing is introduced as a means for separating the AM and FM contributions to the bandwidth of a complex-valued, frequency-varying sinusoid p (n), transforming it into a signal with slowly-varying parameters. This transformation facilitates the removal of p (n) from an additive mixture while minimizing the amount of damage done to other signal components.;The average winding rate of a complex-valued phasor is explored as an estimate of the instantaneous frequency. Theorems are provided showing the robustness of this measure.;To implement frequency tracking, a Frequency-Locked Loop algorithm is introduced which uses the complex winding error to update its frequency estimate. The input signal is dynamically demodulated and filtered to extract the envelope. This envelope may then be remodulated to reconstruct the target partial, which may be subtracted from the original signal mixture to yield a new, quickly-adapting form of notch filtering. Enhancements to the basic tracker are made which, under certain conditions, attain the Cramer-Rao bound for the instantaneous frequency estimate.;To improve tracking, the novel idea of Harmonic-Locked Loop tracking, using N harmonically constrained trackers, is introduced for tracking signals, such as voices and certain musical instruments. The estimated fundamental frequency is computed from a maximum-likelihood weighting of the N tracking estimates, making it highly robust. The result is that harmonic signals, such as voices, can be isolated from complex mixtures in the presence of other spectrally overlapping signals. Additionally, since phase information is preserved, the resynthesized harmonic signals may be removed from the original mixtures with relatively little damage to the residual signal.;Finally, a new methodology is given for designing linear-phase FIR filters which require a small fraction of the computational power of conventional FIR implementations. This design strategy is based on truncated and stabilized IIR filters.;These signal-processing methods have been applied to the problem of auditory source separation, resulting in voice separation from complex music that is significantly better than previous results at far lower computational cost. |
