Name
Abstract | ||
|---|---|---|
We present a signal processing framework for the analysis of discrete signals represented as linear combinations of orthogonal polynomials. We demonstrate that this representation implicitly changes the associated shift operation from the standard time shift to the nearest neighbor shift introduced in this paper. Using the algebraic signal processing theory, we construct signal models based on this shift and derive their corresponding signal processing concepts, including the proper notions of signal and filter spaces, $z$-transform, convolution, spectrum, and Fourier transform. The presented results extend the algebraic signal processing theory and provide a general theoretical framework for signal analysis using orthogonal polynomials. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1109/TSP.2012.2186133 | IEEE Transactions on Signal Processing |
Keywords | Field | DocType |
z transform,laguerre polynomial,spectrum,orthogonal polynomials,frequency response,convolution,legendre polynomials,z transforms,signal analysis,frequency domain analysis,shift operator,nearest neighbor,module,polynomials,fourier transform,orthogonal polynomial,signal processing,hermite polynomial,legendre polynomial,fourier transforms,filter,laguerre polynomials,visualization,algebra,hermite polynomials | Signal processing,Continuous signal,Digital signal processing,Multidimensional signal processing,Discrete-time signal,Control theory,Mathematical analysis,Algorithm,Algebraic signal processing,Mathematics,Signal transfer function,Signal reconstruction | Journal |
Volume | Issue | ISSN |
60 | 5 | 1053-587X |
Citations | PageRank | References |
7 | 1.18 | 13 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Aliaksei Sandryhaila | 1 | 603 | 28.39 |
| Jelena Kovacevic | 2 | 802 | 95.87 |
| Markus Püschel | 3 | 982 | 80.64 |