Question: Draw a diagram of a single stage lattice and write equation for the lattice
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Subject: Speech Processing

Topic: LPC and Parametric Speech Coding

Difficulty: Medium

sp(38) • 251 views
 modified 8 months ago by written 10 months ago by awari.swati831 • 150
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Lattice Structure Realization:

Lattice filters are used in implementation of adaptive filter $y(n) = x(n) + a_1x(n-1)$ as a filter of order 1, then is only one filter coefficient. The filter coefficient $a_1$ is also called the predictor coefficient, as it is used for predicting the current output samples knowing the currents and previous inputs samples. Here, both the inputs are excited by x(n) and the output is taken top of branch. We can write the expression for $f_1(n)$ and $g_1(n)$ $$f_1(n) = x(n) + k_1x(n-1) \\ g_1(n) = kx(n) + x(n-1)$$

*Note that $f_0(n)$ and $g_0(n)$ are both are equal to x(n). $k_1$ is known as the reflection coefficient for stage 1 as $f_0(n)$ and $g_0(n)$ are reflected by factor $k_1$ in the other branch

$$y(n) = x(n) + a_1x(n-1) + a_2x(n-2)$$