This chapter presents a review on auditory processing and the how it motivates an alternate non-stationary signal processing approach contrasting with traditional stationary methods.
It serves as a tutorial illustrating some of the lucunae of traditional time-frequency analysis approaches.
Speech signals have a time-varying spectral content. This implies presence of time-varying redundancy in the signal, and opens up a possibility for adapting the sampling rate in continuous-time to discrete-time conversion. In this chapter, event-synchronized sampling using higher- order zero-crossings (HoZCs) is explored to facilitate such adaptation.
HoZCs refer to ZCs associated with higher-order derivatives of the signal. Signal reconstruction from the captured samples is pursued within a convex optimization framework.
A variety of non-stationary signals can be modeled as time-varying sinusoids, that is,
Of interest in this signal model is estimating the instantaneous amplitude (IA,\(a(t)\)) and the instantaneous frequency (IF, \(f(t)\)). In this chapter, we evaluate the effectiveness of samples drawn from ESS in estimating the IA and IF. The proposed approach shows similar accuracy as widely used analytic signal, energy separation (which are based on uniform Nyquist-rate sampling and processing) and ZC based approaches, and some improvement in case of measurement noise. For the same dataset size, performance for extrema versus uniform sampling dataset, the former gives much better IA and IF estimation. An analysis for robustness of extrema instants to Gaussian additive in-band noise and jitter in sampling time instants is also pursued.
Here, we generalize the application of ESS from mono-component time-varying sinusoids to multi-component signals. We propose higher-order ZCs (HoZCs), or ZCs of signal derivatives, as informative samples for precise IA and IF estimation of each sinusoid in multi-component signals. It is shown that, over a wide range of modulation parameters, namely, bandwidth and modulation indices, the IA and IF signals associated with each sinusoid are preserved over successive signal derivatives. Further, successive differentiation induces a highest IF sinusoid amplitude dominance into the signal.
Accurate analysis of this time-evolving speech spectrum is an open challenge in signal processing. Towards this, we designed an approach which overcomes some of the challenges using foundational concepts in signal processing. This is a suprisingly simple approach based on fundamental signal processing tricks to play with modulations in the signal. Here, we demonstrate the application to speech representation-modification-synthesis, with improved perceptual quality.
Here, I present some future directions which build on the topics explored in this thesis.