Theory

Effects of constriction and length of vocal tract.

The effects of the constrictions and the length of the tract can be explained on the basis of the following principles:

· Length of the oral tract –
This depends on the physical size of the speaker. The length affects the frequency location of the formants. This helps us to predict the formants for child, men, and women.

The rule for length and frequency is: The average frequencies of the vowel formants are inversely proportional to the length of the oral tract. Thus we see that for children who have length half that of male the frequencies will be double.
· Location of the constriction in the tract
From the above rule we can get the position of the neutral formants but most vowels are produced by constriction first we consider the change in frequency due to the position of the constriction.
Oral constriction/F1 rule: The frequency of F1 is lowered by any constriction in the half of the oral part of the vocal tract, and greater the constriction the more F1 is lowered.
Pharyngeal constriction/F1 rule: The frequency of F1 is raised by constriction of the pharynx and the greater the constriction, the more is raised.
Back tongue constriction/F2 rule: The frequency of F2 tends to be lowered by a back tongue constriction and the greater the constriction the more F2 is lowered.
Front Tongue constriction/F2 rule: The frequency of F2 is raised by front tongue constriction and the greater the constriction, the more F2 is raised. Lip Rounding Rule: The frequencies of all formants are lowered by lip rounding and more the rounding more the formants are lowered.

Thus we see that these factors affect the output of the filter. It changes the impulse response of the filter. Thus due to this change of impulse response the output changes and we get different vowels.

Filters:-

The filter is a device which filters out the frequency components. It allows only certain frequencies to pass with amplification 1 and stops the other.
There are four types of filters:-
a) Low-pass: allows low frequencies to pass through.
b) High-pass: allows frequencies above a certain value to pass.
c) Band-pass: allows frequencies in a band to pass.
d) Band-stop: allows frequencies outside a band to pass.

An ideal filter is infinitely non-casual, while real filters are casual, so real filters allow some frequencies to pass but not necessarily with unity amplification.