Contents
Properties of the System
1.Linearity
We have tried to represent the speech production using the source filter theory. According to it larynx acts as source and the vocal tract as a filter and the combination of the two gives the speech.
2.Memory:-
The source system has memory as the pulse creation of the larynx is memory dependent the present air output depends on the crosssection which is decided by the previous output as a result of Bernoulli’s theorem.The filter is not memory less as the frequency response is not a constant which should be for a memory less system (impulse response of a memory less system is an impulse).
The system describing the effects of the length and constriction is memory less as the frequency response of the system will depend on the present input only.
3.Shift invariant:-
The source system is shift invariant as if the air from the lungs came after a time interval then also the pulses produced will remain the same.The filter system is also shift invariant. The constriction system is also shift invariant.
4.Causality:-
The source system is casual. Since if the input is zero up to a certain time the output will also remain the same as without the air from the lungs the source cannot give an output air pulses. The filter system is also casual, since we can’t expect to have speech without giving any input.The constriction is casual as it is memory less.
5.Stability:-
The source system is stable as the filter system is bounded and so x(t) is bounded. The filter system is bounded as it limits the frequencies and thus decreases the energy in the spectrum. Also the amplification of the filter is not unbounded.The constriction system ideally is not bounded as for zero length the lowest formant frequency also becomes very high ,but in reality we never expect the length to decrease to zero and similarly for the other inputs. So within actual variable values of the system the system is stable.
6.Invertibility:-
The source system is invertible.The filter system is not invertible as many inputs may have same output. The constriction system is not invertible as different set of inputs may lead to same output.
