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# lev

Yule-Walker equations (Levinson's algorithm)

### Syntax

`[ar, sigma2, rc]=lev(r)`

### Arguments

r

correlation coefficients

ar

auto-Regressive model parameters

sigma2

scale constant

rc

reflection coefficients

### Description

This function resolves the Yule-Walker equations using Levinson's algorithm. Generally, it is used to estimate the coefficients of an autoregressive process.

### Example

```b=1; //numerator
a=[1 -0.7 0.8]; //denominator
x=[1 zeros(1,99)]; //input=impulse
data=filter(b,a,x); //real data
a2=lev(data); //modelized data
a2=a2/a2(1); //normalization
m_data=filter(1,a2,x);
// Compare real data and modelized data
plot(data,"color","blue","lineStyle","none","marker","d");
plot(m_data,"color","red","lineStyle","none","marker","d");```
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