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*To*: AUDITORY@xxxxxxxxxxxxxxx*Subject*: Hilbert envelope bandwidth*From*: Christof Faller <cfaller@xxxxxxxxx>*Date*: Mon, 27 Sep 2004 14:02:29 +0200*Delivery-date*: Mon Sep 27 08:26:32 2004*In-reply-to*: <12683.83.116.6.95.1096195467.squirrel@83.116.6.95>*References*: <12683.83.116.6.95.1096195467.squirrel@83.116.6.95>*Reply-to*: Christof Faller <cfaller@xxxxxxxxx>*Sender*: AUDITORY Research in Auditory Perception <AUDITORY@xxxxxxxxxxxxxxx>

Dear list, I am struggling with the following question: Given a signal x(n) with X(f) = 0 for |f| < f1 or |f| > f2 (bandpass filtered signal with bandwidth B = f2-f1) e(n) is the Hilbert envelope of x(n) which can then be written as: x(n) = e(n)y(n), where y(n) is the "temporally flattened" version of x(n). The spectrum of e(n) satisfies: E(f) = 0 for |f| > f3 (Due to its DC offset, the evelope e(n) contains frequencies down to zero). ==> Can f3 be expressed as a function of B (the bandwidth of signal x)? Any comments/suggestions are appreciated. Thanks, Christof Faller

**Follow-Ups**:**Re: Hilbert envelope bandwidth***From:*Tarun Pruthi

**Re: Hilbert envelope bandwidth***From:*Ramin Pichevar

**Re: Hilbert envelope bandwidth***From:*Yadong Wang

**References**:**PhD thesis on music transcription***From:*Taylan Cemgil

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