> There doesn't seem to be any limitations -- anything you can do with FFT, you can do here. There's certainly no limitations if all you want to do is to convo

> There doesn't seem to be any limitations -- anything you can do with FFT, you can do here. There's certainly no limitations if all you want to do is to convolve your image with symmetric kernels. But you asked for advantages of the Fourier transform, if any. Convolution of two non-symmetric images is one of them ;) There's also the fact that derivatives have an easier relationship with the DFT than the DHT. If you are interested in discrete linear pde, that's a big advantage. For signal processing, the main advantage of the DFT is that the amplitudes and phases are cleanly separated. For the applications where you only want the amplitude, it is already there in the DFT, but you have to untangle it from the DHT, because the DHT intermingles the phases and amplitudes. An example: imagine that you have an image affected by periodic noise, and you want to remove this noise. This periodic noise appears in the DFT as a frequency with very large amplitude (and an arbitrary phase, corresponding to the phase of the periodic noise, that you don't really care about). Thus, it is easy to locate and filter-out this periodic noise using the DFT: just find the frequency with large amplitude and set it to zero. Now, for the DHT, the frequency that corresponds to the noise period is not necessarily large (in magnitude). It may even be zero, depending on the phase of the noise! To find that frequency, you have to essentially recover the DFT and compute the amplitudes. Of course the DHT and the DFT are equivalent and there's an easy conversion between both, so you can do exactly the same things with either. The difference is just a matter of convenience. It's certainly useful to know both. If you are scared of complex numbers for some reason (e.g., if your programming language makes it difficult to work with them) then you may prefer the DHT. Otherwise, the DFT neatly separates the phases and amplitudes and it's slightly easier to interpret.