Signals & Systems I: Cross-Correlation and Convolution

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Signals & Systems I: Cross-Correlation and Convolution

Explores cross-correlation, signal detection, Hilbert spaces, orthogonal approximation, and image compression using DCT.

Signal Approximation and Orthogonal Bases

Explores signal approximation, orthogonal bases, Fourier series, correlation, and vector geometry.

Signal Processing Fundamentals

Explores signal processing fundamentals, including discrete time signals, spectral factorization, and stochastic processes.

Signals & Systems I: Vector Approximation and Signal Comparison

Explores vector approximation, signal detection, correlation, Fourier series, and signal comparison in signals and systems.

Causal Systems & Transforms: Delay Operator Interpretation

Covers z Variable as a Delay Operator, realizable systems, probability theory, stochastic processes, and Hilbert Spaces.

Fourier Series: Complex Case

Covers the calculation of Fourier coefficients for periodic complex signals and the concept of a complete orthonormal system.

Dirac's Notation, Tensor Product

Covers Dirac's notation in linear algebra and the tensor product concept in Hilbert spaces.

Stochastic Processes and Spectral Densities

Covers spectral densities, signal correlations, and white noise processes in stochastic systems.

Air Pollution: Correlation Analysis

Covers correlation and cross-correlations in air pollution data analysis, including time series, autocorrelations, Fourier analysis, and power spectrum.

Hilbert Space: Geometry, Bases

Explores Hilbert space, scalar product, geometry, bases, complex functions, and quantum mechanics applications.