Subject: Hilbert Transform From: Fred Herzfeld <herzfeld@xxxxxxxx> Date: Mon, 27 Nov 2006 21:37:25 -0500 List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>Hello List, Earlier today I asked two questions about the Hilbert Transform. From the response I now realize that I did not make myself very clear. The problem is a real one which I believe the mamalian auditory system has solved. I too have solved the problem but require an exact knowledge of the frequency of the sinusoidal signal of the collected sampled data S(n). ( S(t) = A*Cos(2*pi*f*t - phi) ) I have absolutely no knowldge of A or of phi but I do know that the frequency is absolutely constant. If I have exact knowledge of the frequency f then I can determine the sampling frequency so that DFT[ S(n) ] has no "leakage" and all bins are exactly zero except for a single bin showing the single frequency component (real and imaginary) of S(t) from which I can recover both A and phi. I now calculate IDFT {DFT [S(n)]} and find that this is exactly equal to S(n) (to 14 decimal digits !) If I take G(t) = A*Sin(2*pi*f*t - phi) )using the same conditions as above then G(n)= IDFT {DFT [G(n)]}. I can now take the DFT of S(n) modift the phase of the components and then I have IDFT {modified-phase-DFT [S(n)]}= G(n) (exactly and again to 14 decimal digits). Thus far no problem. Now if I change the frequency in S(t) and call the new function SS(t) so that the components of DFT(SS(n)) no longer fall into a single bin and then do IDFT{DFT(SS(n))} I also get IDFT{DFT(SS(n))}=SS(n) exactly (again to 14 digits of accuracy). When I form the equivalent GG(t) and GG(n) I get the same results. What I am looking for is the transformation that I need (call it "TRANS" ) so that IDFT {TRANS-DFT [S(n)]}= G(n)} Thats my problem in a nutshell. Any ideas ? Fred -- Fred Herzfeld, MIT '54 78 Glynn Marsh Drive #59 Brunswick, Ga.31525 USA