# Why do we read that Hilbert transform can be used for envelope detection?

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


or

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 ?

• 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. Nov 12, 2013 at 16:38
• 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 !)
– Basj
Nov 12, 2013 at 16:57
• 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. Nov 12, 2013 at 18:20
• 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
– Basj
Nov 13, 2013 at 11:23
• 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? Nov 13, 2013 at 15:13

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

• So you're saying that Hilbert transform is used to avoid the use of low pass filter?
– Basj
Nov 12, 2013 at 15:39
• 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)?
– Basj
Nov 12, 2013 at 15:56
• Faster? Likely yes. Produce identical results, depending on the signal and the answer required? Possibly not. Nov 12, 2013 at 16:36
• ok! thanks! I'll investigate more on the hilbert transform then!
– Basj
Nov 12, 2013 at 16:50