Causality Determination and Time Delay Extraction by Means of the Eigenfunctions of the Hilbert Transform

Frequency domain causality is determined by means of the Hilbert transform relating the imaginary part to the real part of the transfer function. Projecting on the eigenfunctions of the Hilbert transform leads to a simple and easily understood causality determination algorithm for measured (sampled) transfer functions. The causality determination algorithm can then easily be transformed into a delay estimation algorithm, by introducing a linearly varying phase factor. Several examples, both analytical and numerical, demonstrate the strength and accuracy of the proposed algorithm.