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Hilbert envelope bandwidth
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
Can f3 be expressed as a function of B (the bandwidth of signal x)?
Any comments/suggestions are appreciated. Thanks,