The Speech Envelope
A complex signal such as speech has many frequencies and the amount of energy in each frequency is rapidly changing, over time. In the figure below represents the speech signal for the phrase “Mary Mary quite contrary”. The red line is the Hilbert envelope low pass filtered below 50 Hz, representing the overall slower rate modulation of energy in the speech. Another approach to extracting the envelope is the Probabilistic Amplitude Demodulation (PAD, Turner, 2010; Turner & Sahani, 2011) method. This generates a 'model' of the signal (where the model comprises a positive slow envelope, and a fast carrier), and uses Bayesian statistical inference to identify the envelope with the best fit to the data. See the research dissertation of Leong (2012) for further discussion regarding envelope extraction.
The MATLAB code to extract, filter and plot the Hilbert envelope from a sound file (.wav) can be found here HERE.