Signal processing and vector spaces

This lecture covers the importance of using vector spaces in signal processing, providing a unified framework for different classes of signals, continuous-time signals, Fourier Transform, sampling, interpolation, approximation, compression, and communication system design. It explains the general properties of vector spaces and how once these properties are satisfied, all tools for the space can be utilized. Analogies with object-oriented programming and LEGO are used to illustrate the concepts.