LPC to/from RC

Convert linear prediction coefficients to reflection coefficients or reflection coefficients to linear prediction coefficients

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Libraries:
DSP System Toolbox / Estimation / Linear Prediction

Description

The LPC to/from RC block can convert linear prediction coefficients (LPCs) to reflection coefficients (RCs) or reflection coefficients to linear prediction coefficients. Set the Type of conversion parameter to LPC to RC or RC to LPC to select the domain for converting your coefficients. For more information, see Algorithm.

Consider a signal, x (n), as the input to an FIR analysis filter represented by LPC coefficients. The output of the analysis filter, e (n), is known as the prediction error signal. The power of this error signal is denoted by P. When the zero lag autocorrelation coefficient of x (n) is 1, the autocorrelation sequence and prediction error power are said to be normalized.

Ports

Input

K — RC coefficients

vector | matrix

Specify the RC coefficients as a vector or a matrix. The block treats each column of the matrix as a channel. When you specify an unoriented vector, the block treats the input as one channel.

Dependencies

To enable this input port, set Type of conversion to RC to LPC.

Data Types: single | double

A — LPC coefficients

vector | matrix

Specify the LPC coefficients as a vector or a matrix. The block treats each column of the matrix as a channel. When you specify an unoriented vector, the block treats the input as one channel.

Dependencies

To enable this input port, set Type of conversion to LPC to RC.

Data Types: single | double

Output

K — RC coefficients

vector | matrix

RC coefficients, returned as a vector or a matrix.

Dependencies

To enable this output port, set Type of conversion to LPC to RC.

Data Types: single | double

A — LPC coefficients

vector | matrix

LPC coefficients, returned as a vector or a matrix. Each channel of the input must have at least two samples.

Dependencies

To enable this output port, set Type of conversion to RC to LPC.

Data Types: single | double

P — Normalized prediction error power

vector

Normalized prediction error power, returned as a vector with one element per input channel. Each element varies between 0 and 1.

Dependencies

To enable this port, select the Output normalized prediction error power check box.

Data Types: single | double

S — Filter stability output

vector

Filter stability output, returned as a vector with one element per input channel. The filter is represented by the LPCs or RCs.

The synthesis filter represented by the LPCs is stable when the absolute value of each of the roots of the LPC polynomial is less than 1. The lattice filter represented by the RCs is stable when the absolute value of each reflection coefficient is less than 1. When the filter is stable, the block outputs a Boolean value of 1 for each input channel. When the filter is unstable, the block outputs a Boolean value of 0 for each input channel.

Dependencies

To enable this port, select the Output LPC filter stability check box.

Data Types: Boolean

Parameters

Type of conversion — Type of conversion

RC to LPC (default) | LPC to RC

Select LPC to RC or RC to LPC to select the domain for converting your coefficients.

Output normalized prediction error power — Output normalized prediction error power

on (default) | off

Select this check box to output the normalized prediction error power on port P.

Output LPC filter stability — Output LPC filter stability

off (default) | on

Select this check box to output the stability of the filter.

The synthesis filter represented by the LPCs is stable when the absolute value of each of the roots of the LPC polynomial is less than 1. The lattice filter represented by the RCs is stable when the absolute value of each reflection coefficient is less than 1. When the filter is stable, the block outputs a Boolean value of 1 for each input channel at the S port. When the filter is unstable, the block outputs a Boolean value of 0 for each input channel at the S port.

If first input value is not 1 — Action to take if first input value is not 1

Replace it with 1 (default) | Normalize | Normalize and warn | Error

Specify the action to take if the first coefficient of the LPC coefficient vector in any channel is not a 1. You can set this parameter to one of the following:

• Replace it with 1 — Changes the first value of the coefficient channel to 1. The other coefficient values are unchanged.

• Normalize — Divides the entire channel of coefficients by the first coefficient so that the first coefficient of the LPC coefficient vector is 1.

• Normalize and Warn — Divides the entire channel of coefficients by the first coefficient so that the first coefficient of the LPC coefficient vector is 1. The block displays a warning message telling you that your vector of coefficients has been normalized.

• Error — Displays an error telling you that the first coefficient of the LPC coefficient channel is not 1.

Dependencies

To enable this parameter, set Type of conversion to LPC to RC.

Block Characteristics

Data Types	double | single
Direct Feedthrough	no
Multidimensional Signals	no
Variable-Size Signals	no
Zero-Crossing Detection	no

Algorithms

LPC to RC

In this mode, the block uses backward Levinson recursion to convert linear prediction coefficients (LPCs) to reflection coefficients (RCs). For a given Nth order LPC vector, $$LP{C}_N=\left[\begin{array}{ccccc}1& a_{N1}& a_{N2}& \dots & a_{NN}\end{array}\right]$$, the block calculates the Nth reflection coefficient value using the formula $${\gamma }_N=-a_{NN}$$. The block then finds the lower order LPC vectors , $$LP{C}_{N-1},LP{C}_{N-2},\mathrm{...}\text{, }LP{C}_1$$, using the following recursion.

for p = N, N – 1, ..., 2,

$$\begin{array}{l}{\gamma }_p=a_{pp}\hfill \\ F=1-{\gamma }_p{}^2\hfill \\ a_{p-1,m}=\frac{a_{p,m}}{F}-\frac{{\gamma }_p{a}_{p,p-m}}{F},1\le m<p\hfill \end{array}$$

end

Finally, $${\gamma }_1=-a_{11}$$. The reflection coefficient vector is $$\left[\begin{array}{cccc}{\gamma }_1,& {\gamma }_2,& \dots ,& {\gamma }_N\end{array}\right]$$.

RC to LPC

When in this mode, this block uses Levinson recursion to convert reflection coefficients (RCs) to linear prediction coefficients (LPCs). In this case, the input to the block is $$RC=\left[\begin{array}{cccc}{\gamma }_1& {\gamma }_2& \mathrm{...}& {\gamma }_N\end{array}\right]$$. The zeroth order LPC vector term is 1. Starting with this term, the block uses recursion to calculate the higher order LPC vectors, $$LP{C}_2,LP{C}_3,\mathrm{...}LP{C}_N$$, until it has calculated the entire LPC matrix.

$$LP{C}_{matrix}=\left[\begin{array}{c}LP{C}_0\\ LP{C}_1\\ LP{C}_2\\ \cdots \\ LP{C}_N\end{array}\right]=\left[\begin{array}{cccccc}1& 0& 0& 0& \cdots & 0\\ 1& a_{11}& 0& 0& \cdots & 0\\ 1& a_{21}& a_{22}& 0& \cdots & 0\\ 1& a_{31}& a_{32}& a_{33}& \cdots & 0\\ \cdots & \cdots & \cdots & \cdots & \cdots & \cdots \\ 1& a_{N1}& a_{N2}& a_{N3}& \cdots & a_{NN}\end{array}\right]$$

This LPC matrix consists of LPC vectors of order 0 through N found by using the Levinson recursion. The following are the formulas for the recursion steps, for p = 0, 1, ...,N – 1.

$$\begin{array}{l}{a}_{p+1,m}=a_{p,m}+{\gamma }_{p+1}{a}_{p,p+1-m},1\le m\le p\hfill \\ a_{p+1,p+1}={\gamma }_{p+1}\hfill \end{array}$$

References

[1] Makhoul, J Linear Prediction: A tutorial review. Proc. IEEE. 63, 63, 56 (1975).

[2] Markel, J.D. and A. H. Gray, Jr., Linear Prediction of Speech. New York, Springer-Verlag, 1976.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced before R2006a