The Discrete Hilbert Transform for Non-Periodic Signals

This note investigates the size of the guard band for non-periodic discrete Hilbert transform, which has recently been proposed for data hiding and security applications. It is shown that a guard band equal to the duration of the message is sufficient for a variety of analog signals and is, therefore, likely to be adequate for discrete or digital data.

💡 Research Summary

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The paper investigates how large a guard‑band is required when applying the non‑periodic discrete Hilbert transform (DHT) to finite‑length signals. Unlike the many versions of the DHT that assume periodicity, the formulation introduced by Kak treats the signal as non‑periodic and therefore defines the transform over the entire set of integer indices, both positive and negative. In practice, only a finite segment of data is available, so the transform must be approximated using a limited number of samples. The authors formalize the problem as finding the smallest integer m such that the root‑mean‑square (RMS) error between the original signal f(n) and the reconstructed signal f′(n) (obtained by applying the DHT and its inverse over the interval