Time Varying Signal Processing: Zero Crossing Based Models

This book introduces non-uniform-sample-based signal processing methods, specifically those derived based on zero-crossing measurements. Most current-day digital signal processing is based on uniform Nyquist sampling of bandlimited signals. However, most real-world signals are neither time-invariant nor bandlimited. In the past few decades, there have been significant developments in different sampling approaches: random sampling, signal-dependent sampling, and compressive sampling, which are promising both for time-varying signals as well as more compact processing in terms of the number of samples and power consumed.

Table of Contents:
Zero-crossing properties for stationary signals Zero-crossing counts Distribution and moment relations Inverse sine formula Review of Kedem’s alpha filtering technique and contraction mapping Zero-crossings of frequency-modulated signals Notion of zero-crossing instants Zero-crossing properties of angle-modulated signals Narrowband FM signals Wideband FM signals Iterative reconstruction techniques Noniterative reconstruction techniques Accuracy of reconstruction Performance comparison with other angle-demodulation schemes Optimal parameter estimation in noise Signal in noise scenario Effect of noise on angle-modulated signals Zero-crossing properties of noisy FM signals Optimal reconstruction in a minimum mean-square error framework Performance comparison with other optimal time-frequency distribution based techniques Zero-crossing based amplitude-modulation/frequency-modulation models Signals modulated in amplitude and frequency AM-FM representation problem and issues involved Zero-crossing technique Adaptation properties Nonstationary multiresolution properties Link to auditory perception criteria Comparison with state-of-the-art techniques A/D converters based on zero-crossing detection The need for A/D converters based on zero-crossings Block diagram models of ZC-A/D converters Reconstruction formulae and link with finite rate of innovation sampling Significance of ZC-based reconstruction Applications to speech signals and other real-world signals Applications to Doppler estimation in aircraft return signals Applications in radar signal parameter estimation Applications to speech and audio signal analysis Speech and audio signal compression based on AM-FM models Zero-crossing properties and short-time spectral properties of speech Time-frequency representations based on zero-crossings Applications to cricket sounds and bird songs Phase retrieval and zero-crossings