4 papers · 1 filter
Matched Generators for the Karhunen--Loève Transform: A Double-Commutator Eigenvalue Theory
Mitchell A. Thornton
The Karhunen--Loève transform (KLT) diagonalizes the covariance of a second-order process and is optimal for mean-square truncation. Which classical transform it reduces to is gov…
Unification of Signal Transform Theory
Mitchell A. Thornton
We unify the discrete Fourier transform (DFT), discrete cosine transform (DCT), Walsh-Hadamard, Haar wavelet, Karhunen-Loève transform (KLT), and several others along with their c…
Algebraic Diversity: Principles of a Group-Theoretic Approach to Signal Processing
Mitchell A. Thornton
We present principles of algebraic diversity (AD), a group-theoretic approach to signal processing exploiting signal symmetry to extract more information per observation, complemen…
Continuous Algebraic Diversity: Unifying Spectral, Wavelet, and Time-Frequency Analysis via Lie Group Actions
Mitchell A. Thornton
We provide a computable criterion for selecting among Fourier, wavelet, and time-frequency analysis by extending the algebraic diversity (AD) framework to Lie groups acting on $L^2…