Chapter 6 — A Unifying View: Hilbert Spaces
Companion material for Chapter 6. Shows how MMSE estimation, the Wiener filter, and linear least squares are all instances of orthogonal projection in a Hilbert space.
§ 6.1 Inner Product Spaces
Inner Product as Similarity
The correlation coefficient \rho is the cosine of the angle between two zero-mean random variables in L^2(\Omega). This demo lets you adjust \rho and see the geometry change in real time.
Hilbert Spaces in This Course
Probability Hilbert Space L^2(\Omega)
The autocorrelation function is the inner product in L^2(\Omega). This demo makes the connection between the inner product geometry and the computed ACF values tangible.