I am new to signal processing.

I want to find the envelope of a given speech signal.

When I searched about it, I found about Mean Hilbert envelope function. I want to know what other functions/methods can do the same and why Mean Hilbert envelope is considered the best?


The notion of envelope is an ill-defined concept that describes the smooth upper and lower boundaries of more or less oscillating signals.

enter image description here

The most classical technique rectifies the signal (take the absolute value) and low-pass filters the result. Of course, results are not unique.

Other techniques identify local extrema and fit them with low-order functions like polynomials or splines. This is used for instance in some implementations of the Empirical Mode Decomposition.

The Hilbert transform sometimes offers a more solid alternative. Roughly speaking, suppose the signal can be written as the product of an envelope times an oscillation: $s(t) = e(t).o(t)$. Then, with other technical conditions, if the spectra of $e$ and $o$ are well separated, $H(s(t)) =e(t).H(o(t))$, where $H$ is the Hilbert transform. This is a loose transcription of the Bedrosian identity.

If $o(t)$ is a fine pass-band oscillations (the purest being a sine or a cosine), and $e(t)$ is lower in frequency, the Hilbert transform can separate them. This is why for speech, the signal is often decomposed first through a multirate filter bank.

All these techniques are often post-filtered in practice.

More recent approaches try to better define the regularity or smoothness of the envelope, using optimization techniques.

|improve this answer|||||

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.