[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

*To*: AUDITORY@xxxxxxxxxxxxxxx*Subject*: Hilbert Transform*From*: Fred Herzfeld <herzfeld@xxxxxxxxxxxx>*Date*: Mon, 27 Nov 2006 21:37:25 -0500*Delivery-date*: Mon Nov 27 21:48:22 2006*List-archive*: <http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>*List-help*: <http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>, <mailto:LISTSERV@LISTS.MCGILL.CA?body=INFO AUDITORY>*List-owner*: <mailto:AUDITORY-request@LISTS.MCGILL.CA>*List-subscribe*: <mailto:AUDITORY-subscribe-request@LISTS.MCGILL.CA>*List-unsubscribe*: <mailto:AUDITORY-unsubscribe-request@LISTS.MCGILL.CA>*Reply-to*: Fred Herzfeld <herzfeld@xxxxxxxxxxxx>*Sender*: AUDITORY - Research in Auditory Perception <AUDITORY@xxxxxxxxxxxxxxx>*User-agent*: Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:1.0.2) Gecko/20030208 Netscape/7.02 (VAUSSU03)

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 !)

Thus far no problem.

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

- Prev by Date:
**Re: HILBERT TRANSFORM** - Next by Date:
**Research Fellow in Auralisation** - Previous by thread:
**Re: HILBERT TRANSFORM** - Next by thread:
**Research Fellow in Auralisation** - Index(es):