Signal Representations

This lecture focuses on signal representations, discussing the importance of base functions with certain widths in time, space, and frequency. The instructor explains the Fourier transform, time-frequency representations, and the short-term Fourier transform using window functions like Gaussians. The lecture delves into the concept of multi-resolution analysis, where a single base function is dilated and scaled to create a family of base functions, allowing for the representation of all L2 functions. The instructor demonstrates how to decompose signals using base functions and highlights the completeness of the system. Through examples and visual aids, the lecture illustrates how signals can be efficiently represented using a set of base functions with different scales and shifts.