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I didn't know the convolution theorem for the DHT before, but it's pretty clear that if it exists, it must be about circular convolution, just like for the DFT. You're comparing that with acyclic convolution, so the results differing is no surprise.


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I´m not sure if this really applies to your problem since it may be another issue, but I can tell from my experience with acoustic impulse response measurements (only there you want to estimate the response from the input signal, but the deconvolution should be the same): In case your transfer function E is somehow bandlimited and has zero (or very low) ...


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