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Concept of vowel recognition

Vowel recognition is an interesting challenge because it applies system theory to our own physiology. Whenever we attempt to speak, the glottis - the part of the larynx containing the vocal cords - starts to vibrate. These vibrations can be modeled as white noise which become audible and coherent sounds as they pass through the vocal tract. Past experiments have repeatedly confirmed that the vocal tract can be treated as a linear, time-invariant system.

With this, we can proceed in one of three ways: we can model the system as having all zeros (moving average), all poles (autoregressive), or some combination of poles and zeros. Since we can only observe the output of the filter - the speech the escapes the vocal cavity - we choose to model the system as having only poles, because such a model has little dependence on the original input signal. With an autoregressive model, we can generate a transfer function to approximate the filter with a degree of precision proportional to the filter's parameter. It should be noted that a higher order model generally works better but is also more computationally expensive. Once we have the transfer function, we look at the frequency response and determine which frequencies the peaks occur. These frequencies are the formants and we can look at known formant charts to determine which vowel was spoken.

Identifying vowel formants

The term formant refers to peaks in the harmonic spectrum of a complex sound. You can see this spectrum by taking a Fourier transform and looking at the frequency response of the signal. Formants in the sound of the human voice are particularly important because they are essential components in the intelligibility of speech. The distinctness of the vowel sounds can be attributed to the differences in their first three formant frequencies. Producing different vowel sounds amounts to returning these formants within a general range of frequencies depending on the particular person.

Ah frequency response
Formants of an 'Ah' Sound (Adopted from HyperPhysics)

From the frequency response of the vowel formants, we can look at how the peaks of the frequency in the harmonic spectrum line up with the corresponding dark lines in the spectrogram. The dark areas are where the formants are and the graph show them at the same frequency.

specgram of ah sound
Spectrogram of the 'Ah' Sound

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
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2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
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Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
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progressive wave
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A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
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Source:  OpenStax, Vowel recognition using formant analysis. OpenStax CNX. Dec 17, 2014 Download for free at http://legacy.cnx.org/content/col11729/1.5
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