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) :

enter image description here

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 ?

  • $\begingroup$ Why are you filtering after taking the modulus of the hilbert transform? Do not do it this way. Instead, low-pass (or band pass) your signal prior, perform the hilbert transform, and take the modulus to get the envelope. $\endgroup$ Commented Nov 12, 2013 at 16:38
  • $\begingroup$ Thanks user4619, I tried, but this doesn't give good results... Here is my code : pastebin.com/kz2yhHu3. Do you have an idea of what to modify ? (Unfortunately I cannot paste a figure.png here in the comment to show you the result !) $\endgroup$
    – Basj
    Commented Nov 12, 2013 at 16:57
  • $\begingroup$ What is the nature of your data? Is it narrow-band, or is it broad-band? Usually voice is broadband, in which case you cannot use the Hilbert Transform. $\endgroup$ Commented Nov 12, 2013 at 18:20
  • $\begingroup$ A few weeks ago I needed it for broadband, but now for narrow-band : I need the envelope of a single harmonic of a soundfile, example : I need the envelop of a signal whose spectrum is 470-500 Hz $\endgroup$
    – Basj
    Commented Nov 13, 2013 at 11:23
  • $\begingroup$ If you bandpass your signal through a filter centered at 485 Hz, with the same bandwidth, computed the hilbert transform, and take the modulus, what do you get? $\endgroup$ Commented Nov 13, 2013 at 15:13

1 Answer 1


Using a Hilbert transform with a sufficiently narrow-band signal, the low pass filter may not be needed even for continuous envelope estimation.

  • $\begingroup$ So you're saying that Hilbert transform is used to avoid the use of low pass filter? $\endgroup$
    – Basj
    Commented Nov 12, 2013 at 15:39
  • $\begingroup$ Avoid the use of a lowpass filter, thanks to Hilbert transform is a bit strange : isn't a 1-pole IIR low pass filter much much faster than a FIR with thousands of coefficients (needed for Hilbert transform)? $\endgroup$
    – Basj
    Commented Nov 12, 2013 at 15:56
  • $\begingroup$ Faster? Likely yes. Produce identical results, depending on the signal and the answer required? Possibly not. $\endgroup$
    – hotpaw2
    Commented Nov 12, 2013 at 16:36
  • $\begingroup$ ok! thanks! I'll investigate more on the hilbert transform then! $\endgroup$
    – Basj
    Commented Nov 12, 2013 at 16:50

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