Subject: Speech Processing

Topic: Homomorphic Speech Processing

Difficulty: Low

The homomorphic processing is generally applied to a class of systems that obeys a generalized principal of superposition.

Principal of superposition:

If x$_1$(n) and x$_2$(n) are input to a homomorphic system and y$_1$(n) and y$_2$(n) are the respective output and 'c' scaling factor, then if $$ y_1(n) = T[x_1(n)] \\ y_2(n) = T[x_2(n)] $$

Then, $$ T[x_1(n) + x_2(n)] = T[x_1(n)] + T[x_2(n)] \\ T[c \times x_1(n)] = CT[x_1(n)] $$

Then importance of this type of system lies in the fact that operates T of the homomorphic processing can be decomposed into cascade operation,

The system A$_0$ and A$_0^{-1} $ are inverse system and are called canonical.

The system 'L' $\to$ Linear Time Invariant (LTI)

We have seen that voice or unvoiced speech is produced when the output of either the pulse train generator or the random generator respectively convoles the impulse response of a vocal tract.