Discrete-time signal processing
Discrete-time signal processing
Discrete cosine transform: algorithms, advantages, applications
Discrete cosine transform: algorithms, advantages, applications
Wavelets and subband coding
A polynomial approach to linear algebra
A polynomial approach to linear algebra
SIAM Review
IEEE Transactions on Computers
Algebraic Signal Processing Theory: Cooley–Tukey Type Algorithms for DCTs and DSTs
IEEE Transactions on Signal Processing
Algebraic Signal Processing Theory: 1-D Space
IEEE Transactions on Signal Processing - Part I
Algebraic Signal Processing Theory: Foundation and 1-D Time
IEEE Transactions on Signal Processing - Part I
L/M-fold image resizing in block-DCT domain using symmetric convolution
IEEE Transactions on Image Processing
Algebraic Signal Processing Theory: 2-D Spatial Hexagonal Lattice
IEEE Transactions on Image Processing
Hi-index | 35.68 |
We derive a signal processing framework, called space signal processing, that parallels time signal processing. As such, it comes in four versions (continuous/discrete, infinite/finite),each with its own notion of convolution and Fourier transform. As in time, these versions are connected by sampling theorems that we derive. In contrast to time, however, space signal processing is based on a different notion of shift, called space shift, which operates symmetrically. Our work rigorously connects known and novel concepts into a coherent framework; most importantly, it shows that the sixteen discrete cosine and sine transforms are the space equivalent of the discrete Fourier transform, and hence can be derived by sampling. The platform for our work is the algebraic signal processing theory, an axiomatic approach and generalization of linear signal processing that we recently introduced.