A Unified Transform for LTI Systems—Presented as a (Generalized) Frame

Heuberger PSC, de Hoog TJ, Van den Hof PMJ, Wahlberg B: Orthonormal basis functions in time and frequency domain: Hambo transform theory. SIAM Journal on Control and Optimization 2003, 42(4):1347-1373. 10.1137/S0363012902405340

Oppenheim AV, Willsky AS, Young IT: Signals and Systems. Prentice-Hall, Englewood Cliffs, NJ, USA; 1983.

Vetterli M, Kovacevic J: Wavelets and Subband Coding. Prentice-Hall, Englewood Cliffs, NJ, USA; 1995.

Mallat S: A Wavelet Tour of Signal Processing. 2nd edition. Academic Press, San Diego, Calif, USA; 1999.

Daubechies I: Ten Lectures on Wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics. SIAM, Philadelphia, Pa, USA; 1992.

Chui CK: An Introduction to Wavelets, Wavelet Analysis and Its Applications. Academic Press, Boston, Mass, USA; 1992.

Christensen O: An Introduction to Frames and Riesz Bases. Birkhäuser, Boston, Mass, USA; 2003.

Kaiser G: A Friendly Guide to Wavelets. Birkhäuser, Boston, Mass, USA; 1994.

Ali ST, Antoine JP, Gazeau JP: Continuous frames in Hilbert space. Annals of Physics 1993, 222(1):1-37. 10.1006/aphy.1993.1016

Viscito E, Allebach JP: The analysis and design of multidimensional FIR perfect reconstruction filter banks for arbitrary sampling lattices. IEEE Transactions on Circuits And Systems—Part I : Fundamental Theory and Applications 1991, 38(1):29-41.

Apostol TM: Mathematical Analysis. 2nd edition. Addison-Wesley, Sydney, Australia; 1974.

Paley REAC, Wiener N: Fourier Transforms in the Complex Domain. American Mathematical Society, New York, NY, USA; 1934.

de Hoog TJ: Rational orthonormal bases and related transforms in linear system modeling, M.S. thesis. Delft University of Technology, Delft, The Netherlands; 2001.

Donoho DL, Stark PB: Uncertainty principles and signal recovery. SIAM Journal on Applied Mathematics 1989, 49(3):906-931. 10.1137/0149053

Donoho DL, Elad M:Optimally sparse representation in general (nonorthogonal) dictionaries via minimization. Proceedings of the National Academy of Sciences of the United States of America 2003, 100(5):2197-2202. 10.1073/pnas.0437847100