Time-Frequency Signal Analysis and Adaptive Instantaneous Frequency Estimation

Most of the human-made and physical signals have nonstationary spectra that evolve rapidly with time. To study and characterize such signals, the classic time-domain and frequency-domain representations are inadequate, since they do not provide joint time and frequency information; meaning that, they are signal representations in which the time and frequency variables are mutually exclusive. Time-frequency (TF) signal analysis (TFSA) concerns the processing of signals with time-varying spectral content. It allows for the construction of a signal representation in which the time and frequency variables are not averaged with respect to each other, but rather present together. This doctoral thesis has two main points of focus: TFSA based on a linear TF transform with progressive frequency-dependent resolution in the TF domain, known in the literature as the S-transform (ST), and designing adaptive methods for instantaneous frequency (IF) estimation, which is a fundamental concept in TFSA with numerous practical applications. The main original contributions are: 1- Modifications in the existing discrete definitions for implementing and inverting the ST to ensure exact invertibility and eliminate artifacts in the synthesized signal. 2- Derivation of an algorithm for least-squares signal synthesis form a modified discrete ST. 3- Formulation of a computationally efficient, fully discrete, and exactly invertible ST with a controllable TF sampling scheme, providing frequency resolution that can be varied and made as high as required. 4- Accuracy analysis of IF estimation based on a family of linear TF transforms that use Gaussian observation windows to localize the Fourier oscillatory kernel with arbitrarily defined standard deviations, and derivation of closed-form easily interpreted expressions for the bias and the variance of the estimation error. 5- Design of adaptive methods for IF estimation based on linear and quadratic TF representations.