Digital voice Signal Processing learning notes-homomorphic processing voice signals (1)

5.1 Overview

The method of processing, which can be two signals by multiplying the signal by multiplication, or by convolution synthesis signal separation.

for voice signals. Our aim is to separate the original components from the convolution of the channel impulse corresponding to the excitation component.

Each signal component obtained by convolution is a task involved in the theory of digital signal processing, called "deconvolution" or "deconvolution".

After the same state analysis of the speech signal. The cepstrum parameters of the speech signal are obtained, so homomorphic analysis is also called cepstrum analysis or homomorphic processing.

5.2 Superposition principle and generalized superposition principle

for a linear system, the relationship of its input and output is subject to the superposition principle. The superposition principle can be described as follows: Assuming that the input signal is a linear combination of several primitive signals, the system output is a linear combination of each corresponding system.

By imitating the superposition principle of a common linear system, we can define a class of systems that obey the generalized superposition principle, in which addition can be replaced by convolution. That is:

So. Suppose a system has the properties represented by the above, it is called "convolution homomorphism system".

5.3 Convolution homomorphism system

for convolution homomorphism system:

A model for convolution homomorphism systems for example, as seen, it consists of three parts: characteristic system, linear system L and inverse characteristic system

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The first part is the characteristic system. The input is a convolution combination of several signals, and the output is an addition combination of several signals. The characteristic system has the following properties:

The second part is an ordinary linear system, which obeys the general superposition principle, as seen in the following formula:

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The third part is the inverse system of the characteristic system, which transforms the addition combination of the signal back into the convolution combination.

The inverse characteristic system has the following properties:

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According to convolution theorem, the time domain is a convolution of two signals, then its Z-transform is the product of two signal Z-transformations, namely:

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Its Z-transform is:

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Represented by the Z-transform. The convolution combination can become a multiplication combination. By using the Logarithmic property, the multiplication combination can be changed into the addition combination, then the inverse Z-transform, and the output signal is still an additive combination, which constitutes the characteristic system of the convolution homomorphism system:

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The inverse system of convolution homomorphism system is:

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Digital voice Signal Processing learning notes-homomorphic processing voice signals (1)