🚀 go-pugleaf

In article <10471@csli.Stanford.EDU> poser@csli.stanford.edu (Bill Poser) writes:
>The Fast Hartley Transform is described in great detail in
>Ronald Bracewell's recent book _The Hartley Transform_. Mathematically,
>the Hartley transform is like the Fourier Transform but has a real
>kernel, that is, cos + sin instead of cos + i sin. It is therefore not
>the same as the Fourier Transform. However, the MAGNITUDE of the
>Hartley Transform is the same as that of the Fourier Transform. In the
>many cases in which one only cares about the magnitude, not the phase, 
>the Fourier Transform may be replaced by the Hartley transform.

For use in a one-way transform - perhaps to display frequency spectrum
content of audio data - the FHT might be the choice.

But, since HiFi audio is often discussed in this group, I wanted to point
out that the phase information is necessary to accurately reconstruct the
original signal.  If the goal is to process the frequency domain data
obtained from a Fourier Transform and then reconstruct a modified version
of the original time domain data, it follows that a great deal of
information would be lost without the phase of each frequency component.

Brian Willoughby
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