FHSS signal sparsification in the Hermite transform domain
Miloš Brajović, Andjela Draganić, Irena Orović, Srdjan S. Stankovic · 2016
Signal sparsity is exploited in various signal processing approaches. The applicability ranges from compression, signal classification, coding, etc. Finding a suitable basis where the signal exhibits a compact (sparse) support is a challenging task and the result mainly depends on the signal nature. In this paper, we observed sinusoidally modulated signals appearing in wireless communications, namely the FHSS signals. As a sparsity domain, the Hermite transform domain is considered. The Hermite basis functions resemble the shapes of the FHSS signal components, and therefore these are considered as suitable for compact representation. In order to improve the sparsity of the observed signal components, we propose to employ a procedure for the Hermite transform optimization. As a result, the discrete Hermite functions better fit the signal components, producing just negligible errors between the original and optimized signal. The theory is verified by the experimental results. The procedure is tested on synthetic FHSS signal.