I’m currently doing research investigating endogenously generated whole body vibrations. Firstly, I would like to prove that vibration can be detected on the skeletal system (using accelerometer) during vocalization (voice recorder) and I need to prove that the skeletal vibration is indeed coming from the vocal cord/tract. My supervisor had suggested I do FFT of both signals (voice and vibration) and compare their fundamental and harmonic signatures. I have since noted that LPC with formant analysis appeared to be the standard in voice analysis. I also thought that I could gain more information using LPC; i.e comparing voice/voiceless phonemes, able to determine which voice components are better transmitted and etc. I understand that FFT and LPC has different mathematical algorithm hence giving rise to different sets of deconvoluted frequencies. For example, analysis of a short 320ms /a/ phoneme gave the following; FFT: F0 134.3 Hz, H1 266.2 Hz, H2 398.8 Hz and H3 529.3 Hz versus LPC: F0 132.77 Hz, F1 452.3 Hz, F2 1391.2 Hz and F3 2390 Hz.
What I am puzzle is that both claim the same thing. THAT THE COMPOSITE WAVEFORM /a/ IS THE COMBINATION OR CONVOLUTION OF CONSITUENT WAVEFORMS WITH THE DERIVED FREQUENCIES. How two sets of waves with vastly different frequency values convolute into the same product. Which one is more accurate? I wonder if anyone could point out to me, where did I go wrong. Thanks.
Abu Dzarr wrote:
> Firstly, I would like to proof that vibration can be detected
> on the skeletal system (using accelerometer) during
> vocalization (voice recorder) and I need to prove
> that the skeletal vibration is indeed coming from
> the vocal cord/tract.
There are some products on the market
that use bone sound conduction.
http://www.ruf.rice.edu/~mobile/osteoconduct.html
http://www.scienceandsociety.net/podcasts/archives/2007/06/dr_michael_lieb_1.html
http://www.technologyreview.com/view/427887/a-phone-you-can-hear-in-your-bones/
http://www.wired.com/gadgetlab/2006/07/bone_conduction/
Regards,
Joachim
Joachim wrote ‘Abu Dzarr wrote: > Firstly, I would like to proof that vibration can be detected > on the skeletal system (using accelerometer) during > vocalization (voice recorder) and I need to prove > that the skeletal vibration is indeed coming from > the vocal cord/tract. There are some products on the market that use bone sound conduction. ……… ‘
I suppose, what we plan to do is not original but we wanted to at least with our limited resources, prove to ourselves that we could detect the signals and confirm it before we move on to the next stage of research. By the way thanks for the link Joachim. I will trace back Prof. Liebschner's group’s work.
Just made a small heart warming step. I’m beginning to get an idea what I am talking about. On a narrow band spectrogram the first dark horizontal stripe at the bottom is the fundamental frequency, F0. Both FFT and LPC agreed to the same value (more or less). The subsequent stripes are the harmonics of F0 all the way up to 5000 Hz. This is from FFT. Along the way there are groups of these harmonics that become darker than the rest, corresponding to the dark wideband. These are the formants. LPC lets us derive it? (Not sure of this statement yet) I suppose the peak within the band is the formant frequency. So formant frequencies are harmonic frequencies that are more energized then the rest of the harmonics. Like a secondary harmonics of the harmonics … (sort of: the formant position are not integer multiples).
On spectrum slice I could see the harmonics peaking at the corresponding frequency right up to 5000Hz.. Ok, I got it. What I still don’t understand, why did the calculated FFT failed to produce peaks at the 11, 12 or 16, 17th harmonics, corresponding to the 2nd and 3rd formant? Instead the peak amplitude just got shorter and shorter from H1 to H4 and gone?
An LPC is an estimation of the filter function (resonators) of the vocal tract (formants), while an FFT is an application of a fourier transform to a signal do decompoe it into its simple wave (sine) components. In this way an FFT isn't really the "harmonics" but it can be used to measure harmonics (given the right settings. Harmonics are whole number multiples of the periodic fundamental: in the case of speech the fundamental is rate of vibration of the vocal folds. You can think of each vibration of the vocal folds as equivalent to a hand-clap (a 1/4 cycle damped source). Each puff of air released by the vocal folds excites the resonators of the vocal tract; the shape of the (air trapped in the) series of resonators allows some harmonics to pass while attenuating others, creating the shaping of the harmonics. The signal generated buy the vocal source is already complex, the the formants are the filter peaks of the resonators that shape the vocal-source harmonics. You can measure both formants and harmonics with an FFT depending on the settings.
An excellent engineering introduction to the relationship between harmonics and formants can be found in: Stevens 1998 "Acoustic Phonetics", MIT Press.
The harmonics are integer multiples of the fundamental frequency. As you said yourself, if F0 is 134.3 Hz, then H1 (= 2 * F0) is 266.2 Hz and H2 (=3 * F0) is 398.8 Hz and H3 (=4 * F0) is 529.3 Hz etc.
The formants now are a different thing. The formants are frequency "regions" (they have a bandwidth), in which the harmonics are less damped than in other regions. These formant frequency (regions) come from the actual form of the vocal tract (opening of the mouth, rounding of the lips, position of the tongue etc.).
For the vowel /a/ for example the mouth is quite opened, the lips are not rounded and the horizontal position of the tongue is kind of "in the middle". These leads to the typical formant frequencies of an /a/ (for a male vocaltract with a certain length):
F1: 452.3 Hz, F2: 1391.2 Hz, F3: 2390 Hz
In these regions the energy of the (source) signal can get through very well. In other frequency regions the energy can not pass so easily.
The harmonics and the formants are independent from one another. You can alter the harmonics by changing F0 (speak higher, speak lower) - and at the same time you can alter the formant frequency (regions) by changing the vocal tract.
F0 and the harmonics can also be called as the "source" part of speech. With the formant frequencies you have the so called "filter" part of speech. With these two elements you build the source-filter-composition of speech, which still is the common model for speech (Gunnar Fant, 1960).
Dear Abu Dzarr, I supervised a project where a group of my student each recorded the sound of the word "Hello" in his own voice then decomposed it to different sine wave using FFT, and then by using SCILAB, they reproduced the original voice! They also went further and made a program to recognize the voice of them when they say "Bye" using neural network methods to compare the new captured pattern with the pattern of a different word they already have in their databank. All these I said, to tell you, in this case which we have done, FFT did work fine!
Dear Omid,
Thanks for the input. I have already got the above confusion resolved as in this following thread https://www.researchgate.net/post/Why_is_formant_frequency_different_from_the_harmonic_frequency
I have already purchased the student version of mathlab. I wish not to go into perpetual learning curve familiarizing with softwares but not getting anywhere with my objectives. I will keep note of SCILAB in case I lost my way with Mathlab. Thanks again.