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Splines - A Match for Pulse Shaping Filters with ISI Free Properties

Ayush Bhandari, N.V. Kalpakam

Abstract

In this paper, we revisit the problem of intersymbol interference in digital communications. We reinterpret the Nyquist Criteria for distortionless transmission in connection with "Ideal Shape Factors". Based on this reinterpretation, we propose a new family of ISI-free pulses (after matched filtering is performed) which is pivoted on the B-spline signal processing theory. In particular, we show that cardinal splines are a perfect match for pulse shaping and ISI avoidance. Their spectral properties are in full consensus with the "shape factors" which are sufficient and necessary to ascertain ISI-free transmission. The fact that cardinal splines fuse into an ideal Nyquist Pulse in Lp, further strengthens our claim.

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Key concepts: Intersymbol interference, Nyquist ISI criterion, Pulse shaping, Nyquist–Shannon sampling theorem, Ideal (ethics), Computer science, Algorithm, Pulse (music)