Lectures related to Signal Representations

Covers the representation of signals in vector spaces and inner product spaces, including the Projection Theorem.

Explores the postulates of Quantum Mechanics, focusing on states, time evolution, and measurement.

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

Covers fundamental concepts in quantum mechanics, including vector spaces, superposition, observables, and inner product.

Covers the quantization of topological operators and Ising models on square lattices.

Introduces Hilbert space as a big place where quantum systems evolve with unitaries.

Covers signal representation and manipulation techniques in different domains.

Discusses signal representation, focusing on mathematical expressions and inequalities in signal processing.

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

Explores the space of bandlimited functions, focusing on 1-bandlimited functions as a basis and their representation through sequences.

Introduces function spaces and Hilbert spaces, discussing inner product spaces and the importance of completeness in Hilbert spaces.

Covers the definition and properties of Hilbert spaces, including the Cauchy-Schwarz inequality and norm definition.

Explores thought experiments with polarisation qubits of photons and the concept of superposition in Hilbert space.

Explores the incompleteness of Cc(RN, K) and the challenges of Riemann integrability.

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

Covers the weak formulation of elliptic partial differential equations and the uniqueness of solutions in Hilbert space.

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

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

Explores linear estimation and prediction in AR parametric models, focusing on Yule Walker equations and Wiener filter.

Explores Sobolev spaces in higher dimensions, discussing derivatives, properties, and challenges with continuity.