We can often read that Hilbert transform is useful for envelope detection (e.g. Hilbert transform to compute signal envelope?)
I have done some tests with various soundfiles, and
x[n] -> absolue value -> 1-pole low pass filter -> envelope
x[n] -> Hilbert transform -> absolute value -> 1-pole low pass filter -> envelope
gives the same kind of result, it's not better with a Hilbert transform (top : envelope computed with hilbert, bottom : envelope computed without hilbert) :
Moreover, I know that computing the Hilbert transform is very time-consuming (big FIR filters involved).
So it is really a good method for envelope detection ?