Enumerative combinatorics
Multirate systems and filter banks
Multirate systems and filter banks
Multirate Digital Signal Processing
Multirate Digital Signal Processing
IEEE Transactions on Signal Processing - Part I
Characterization of nonuniform perfect-reconstruction filterbanks using unit-step signal
IEEE Transactions on Signal Processing
A multirate autotuning PI with improved static performance
ACC'09 Proceedings of the 2009 conference on American Control Conference
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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 Lambert-form 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.