Fourier Transform and Schwartz Space

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Covers the properties of signal/data representations using Fourier transformations and matrices.

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Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Determinantal Point Processes and Extrapolation

Covers determinantal point processes, sine-process, and their extrapolation in different spaces.

Signal Representation: Fourier Transforms

Covers the representation of signals using Fourier transforms and the properties of signal vectors.

Fourier Analysis: Applications and Inversion Formula

Explores Fourier analysis applications and the inversion formula in the context of periodicity and continuous functions.

Fourier Analysis: Fourier Series and Transform

Explores Fourier series, DFT, FFT, and their applications in signal processing and spectroscopy.

Fourier Series: Understanding Coefficients and Periodicity

Explores Fourier series coefficients, periodicity, and series relations.

Fourier Transform: Concepts and Applications

Covers the Fourier transform, its properties, applications in signal processing, and differential equations, emphasizing the concept of derivatives becoming multiplications in the frequency domain.

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Explores the general solutions for wave propagation and Fourier transforms in periodic functions.