On Complex Conjugate Pair Sums and Complex Conjugate Subspaces

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...

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Bibliographic Details
Published in:IEEE signal processing letters 2019-09, Vol.26 (9), p.1403-1407
Main Authors: Shah, Shaik Basheeruddin, Chakka, Vijay Kumar, Reddy, Arikatla Satyanarayana
Format: Article
Language:English
Subjects:
ccps
ccs
Complex conjugate pair
Computation
Computational complexity
Conjugates
Convolution
derivative
Edge detection
Equivalence
Image detection
Image edge detection
Impulse response
Indexes
Linear systems
projections
Radar tracking
shift-invariant
Subspaces
Sums
Transforms
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Summary: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.
ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2019.2932717