Full spark of even discrete cosine transforms
| Autor: | Maria Elena Dominguez-Jimenez |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Signal processing
Computer science Signal reconstruction Block matrix 020206 networking & telecommunications 02 engineering and technology Compressed sensing Control and Systems Engineering Signal Processing Spark (mathematics) 0202 electrical engineering electronic engineering information engineering Discrete cosine transform 020201 artificial intelligence & image processing Computer Vision and Pattern Recognition Electrical and Electronic Engineering Algorithm Software Communication channel |
| Zdroj: | Signal Processing. 176:107632 |
| ISSN: | 0165-1684 |
| DOI: | 10.1016/j.sigpro.2020.107632 |
| Popis: | In this paper, we investigate the spark of a family of transforms that are frequently used in signal processing applications such as Multicarrier Communication systems: we consider the even Discrete Cosine Transform matrices (DCTs). On one hand, we provide several theorems that prove that the submatrices obtained from its first rows present maximum spark; on the other hand, we give counterexamples of other sets of rows that do not present this good property. Besides the mathematical interest of our contributions, we also show that our results have important novel applications in compressed sensing problems such as sparse signal reconstruction and compressed channel estimation. We also demonstrate that a channel filter can be perfectly estimated by means of a small amount of its DCT coefficients, which can be furthermore arbitrarily selected. Thus, random compressive sampling schemes are valid for solving channel estimation problems when using even DCTs. Finally, numerical simulations show the good performance of the DCT transforms for practical sparse signal recovery in both noisy and noise-free scenarios. |
| Databáze: | OpenAIRE |
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