Time Series: Linear Filtering and Spectral Estimation

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Explores cross-correlation, convolution, signal approximation, orthonormal functions, and orthogonal approximation theorem in signals and systems.

Covers the estimation of R using bivariate normal distributions and explores the marginal and conditional distributions of X₁ and X₂.

Covers the concept of power spectral density in continuous-time stochastic processes.

Covers examples of noise in optical detectors, including avalanche photodiodes and fluorescence correlation spectroscopy.

Explores filter design, boundary conditions, Fourier-domain filtering, and useful smoothing filters for image processing.

Explains the definition and properties of the Wiener process, focusing on its covariance function and continuous paths.

Explores power spectral density, Wiener-Khintchine theorem, ergodicity, and correlation estimation in random signals for signal processing.

Covers applying concepts to build linear filters and perform estimation.

Explores electrolyte diffusion in liquids and solids, emphasizing heterodiffusion mechanisms and solute interactions in crystal structures.

Covers the basics of linear regression, instrumental variables, heteroskedasticity, autocorrelation, and Maximum Likelihood Estimation.

Explores memorylessness in distributions, stationary processes, and estimation using MLE.

Covers the theory behind Maximum Likelihood Estimation, discussing properties and applications in binary choice and ordered multiresponse models.

Explores the geometric interpretation of filter responses and the challenges of achieving causal filters in real-time signal processing.

Explores phase response constraints, minimum phase systems, and digital filter design.

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