# Covariance AR Estimator

Compute estimate of autoregressive (AR) model parameters using covariance method

• Libraries:
DSP System Toolbox / Estimation / Parametric Estimation

## Description

The Covariance AR Estimator block uses the covariance method to fit an autoregressive (AR) model to the input data. This method minimizes the forward prediction error in the least squares sense.

## Ports

### Input

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Specify the input data as a column vector or an unoriented vector. The block assumes that the input data is the output of an AR system driven by white noise and represents a frame of consecutive time samples from a single-channel signal.

Data Types: `single` | `double`

### Output

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Normalized estimate of the AR model polynomial coefficients A(z), returned as a column vector of length p+1 in descending powers of z.

The block computes the estimate of these coefficients independently for each successive input frame.

`$H\left(z\right)=\frac{G}{A\left(z\right)}=\frac{G}{1+a\left(2\right){z}^{-1}+\dots +a\left(p+1\right){z}^{-p}}$`

where,

• H(z) –– Transfer function of the estimated AR model

• G –– Scalar gain

• A(z) –– Polynomial coefficients of the AR model

Data Types: `single` | `double`

Gain of the estimated AR model, returned as a scalar.

`$H\left(z\right)=\frac{G}{A\left(z\right)}=\frac{G}{1+a\left(2\right){z}^{-1}+\dots +a\left(p+1\right){z}^{-p}}$`

where,

• H(z) –– Transfer function of the estimated AR model

• G –– Scalar gain

• A(z) –– Polynomial coefficients of the AR model

Data Types: `single` | `double`

## Parameters

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Specify the estimation order p of the all-pole AR model as a positive integer. To guarantee a nonsingular output, you must set p to be less than or equal to half the input vector length. Otherwise, the output can be singular.

## Block Characteristics

 Data Types `double` | `single` Multidimensional Signals `No` Variable-Size Signals `No`