On Complex Conjugate Pair Sums and Complex Conjugate Subspaces
| Autor: | Shaik Basheeruddin Shah, Vijay Kumar Chakka, Arikatla Satyanarayana Reddy |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Signal Processing (eess.SP)
Pure mathematics Complex conjugate Computer science Applied Mathematics Computation 020206 networking & telecommunications 02 engineering and technology Linear subspace Projection (linear algebra) LTI system theory Signal Processing FOS: Electrical engineering electronic engineering information engineering 0202 electrical engineering electronic engineering information engineering Electrical Engineering and Systems Science - Signal Processing Electrical and Electronic Engineering Circulant matrix Impulse response Second derivative |
| Zdroj: | IEEE Signal Processing Letters. 26:1403-1407 |
| ISSN: | 1558-2361 1070-9908 |
| DOI: | 10.1109/lsp.2019.2932717 |
| Popis: | In this letter, we study a few properties of Complex Conjugate Pair Sums (CCPSs) and Complex Conjugate Subspaces (CCSs). Initially, we consider an LTI system whose impulse response is one period data of CCPS. For a given input x(n), we prove that the output of this system is equivalent to computing the first order derivative of x(n). Further, with some constraints on the impulse response, the system output is also equivalent to the second order derivative. With this, we show that a fine edge detection in an image can be achieved using CCPSs as impulse response over Ramanujan Sums (RSs). Later computation of projection for CCS is studied. Here the projection matrix has a circulant structure, which makes the computation of projections easier. Finally, we prove that CCS is shift-invariant and closed under the operation of circular cross-correlation. 4 pages, 2 figures |
| Databáze: | OpenAIRE |
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