A DHT Based Measure of Randomness

This paper presents a new discrete Hilbert transform (DHT) based measure of randomness for discrete sequences. The measure has been used to test three different classes of sequences with satisfactory results.

💡 Research Summary

The paper introduces a novel randomness metric for discrete binary sequences that is based on the discrete Hilbert transform (DHT). Traditional randomness tests—such as frequency tests, runs tests, entropy measures, and linear complexity—often struggle to provide reliable discrimination when the sequence length is short or when the underlying structure is subtle. To address these shortcomings, the authors exploit a characteristic of the DHT: it generates a quadrature (90‑degree phase‑shifted) component of a real‑valued signal, thereby emphasizing asymmetry and non‑linear features that are otherwise hidden in the original domain.

Mathematically, for a sequence (x