Eigensignals of Downsamplers in Time and Transform Domains
S. Samadi, M.O. Ahmad, Akinori Nishihara, M.N.S. Swamy · IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences · 2007
As a fundamental building block of multirate systems, the downsampler, also known as the decimator, is a periodically time-varying linear system.An eigensignal of the downsampler is defined to be an input signal which appears at the output unaltered or scaled by a non-zero coefficient.In this paper, the eigensignals are studied and characterized in the time and z domains.The time-domain characterization is carried out using number theoretic principles, while the one-sided z-transform and Lambertform series are used for the transform-domain characterization.Examples of non-trivial eigensignals are provided.These include the special classes of multiplicative and completely multiplicative eigensignals.Moreover, the locus of poles of eigensignals with rational z transforms are identified.