Adam Wyatt

Great.

Suggestion - can you add support for bold text to. I presume its doable since the command window already utilizes bold text.

The example given in the code does not scale the amplitudes of the angular distribution because it is not necessary (since it is only necessary to multiply by a phase factor and so the scaling required will be undone again before transforming back). However, strictly speaking this should be done as follows:

H = hankel_matrix(0, rmax, samples);
HT = @(f) (H.T*(f./H.JR)).*H.JV;
IHT = @(F) (H.T*(F./H.JV)).*H.JR;

Note that two scaling vectors are supplied:

H.JR
H.JV

Therefore I agree that the example is misguiding from a physical point of view, but not computationally, but it is not incomplete.

Note that there is a difference between the Hankel transform (HT) and the quasi discrete Hankel transform (qDHT). This code provides a way of performing the qDHT and the scaling vectors to turn it into an accurate estimation of the HT.

Indeed there is a factor of 2pi, but as stated this does depend on the definition of the HT used - so long as f = IHT(HT(f)), its all good. So using the definition consistent with the code:

HT{exp(-br^2)} = pi/b * exp{-k^2/(2*b)];

Further details can be found in the references given in the code.

your delay is always half of the signal
the matrix can be too large
for chirp test the max locations should be at phase 2*f*b*t but the max is alwayes at the center

I wrote my own program, starting with this one. (You can find it posted under the same title as this one). I found this program to be a nice starting point to use. I found plenty of room for improvements and additions, but I don't remember finding any bugs that would noticeably impact the results.