Could anybody tell me a method to calculate the "4 Hz modulation energy" for a speech signal?



I get some details : 4 Hz modulation energy: Speech has a characteristic energy modulation peak around the 4 Hz syllabic rate [3]. We use a portion of the MFCC algorithm [4] to convert the audio signal into 40 perceptual channels. We extract the energy in each band, bandpass filter each channel with a second order filter with a center frequency of 4 Hz, then calculate the short-term energy by squaring and smoothing the result. We normalize each channel's 4 Hz energy by the overall channel energy in the frame, and sum the result from all channels. Speech tends to have more modulation energy at 4Hz than music does.

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    $\begingroup$ Can you give a reference as to where this terminology is used? Does this help? $\endgroup$ – Peter K. Apr 25 '13 at 19:48
  • $\begingroup$ I already checked this link but it did not give me a big push $\endgroup$ – Maystro Apr 25 '13 at 19:56
  • $\begingroup$ Does my additional information start "pushing" ? :-) $\endgroup$ – Peter K. Apr 25 '13 at 20:00

The link in my comment suggests the following:

I would recommend first extracting the envelope by using either a halfwave rectification (i.e., replace all the negative values in the time waveform with zeros) or a Hilbert Transform and then lowpass filtering the waveform at around 50 Hz (the lowpass is optional if you only care about the 4 Hz component). Once you have the envelope, simply do an fft (making sure that your frequency resolution is at least 1 Hz) and look for the energy around 4 Hz. If any of these steps don't seem obvious too you, let me know and I can send you some Matlab code.

So, what that means is you need to take your speech $s[n]$ and find the envelope:

$$ e[n] = \left | s[n] + j{\bf H}\left[s[n]\right] \right | $$

where ${\bf H}$ is the Hilbert transform of your speech signal.

Then, take the FFT and look at the bin at 4Hz.

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