Image Processing I: Filter Design and Boundary Conditions

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Linear Phase Filters: Step Response and Characteristics

Explores linear phase filters, rise time, Gaussian filters, and rational transfer functions.

Poisson Problem: Fourier Transform Approach

Explores solving the Poisson problem using Fourier transform, discussing source terms, boundary conditions, and solution uniqueness.

Boundary Conditions and Basis Decomposition

Explores boundary conditions, basis functions, and PDE solutions using Fourier and Bessel series.

Rayleigh Taylor: Normal Mode Expansion

Explores normal mode expansion, Laplace equation solution, and dispersion relation analysis in Rayleigh Taylor instability.

Green Functions: Dynamics

Covers the solution of Maxwell equations using advanced and retarded Green functions, focusing on electrostatics with general boundary conditions.

Unbounded and Bounded Systems: Fourier Methods

Explores the spectral properties of unbounded and bounded systems using Fourier methods and emphasizes the importance of choosing the correct representation for different boundary conditions.

Signals, Instruments, and Systems: System Properties and Transforms

Introduces system properties, Laplace Transform, and analog filters for signal analysis.

Analog Filters: General Synthesis and Transfer Functions

Explores analog filters, rational transfer functions, and stability analysis of causal systems.

Signals & Systems I: Filter Equations and Poles

Explores rational transfer functions, filter equations, poles, zeros, and impulse response in signal processing.

Signals & Systems II: Filter Implementations

Explores IIR filter implementations, canonical vs. non-canonical forms, stability, DTFT properties, and eigenvectors in LID systems.