# Modified Covariance AR Estimator

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

Libraries:
DSP System Toolbox / Estimation / Parametric Estimation

## Description

The Modified Covariance AR Estimator block uses the modified covariance method to fit an autoregressive (AR) model to the input data. This method minimizes the forward and backward prediction errors 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 AR model (all-pole model) as a positive integer. To guarantee a nonsingular output, you must set the Estimation order parameter to be less than or equal to two thirds the input vector length. Otherwise, the output might be singular.

## Block Characteristics

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

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## References

[1] Kay, S. M. Modern Spectral Estimation: Theory and Application. Englewood Cliffs, NJ: Prentice-Hall, 1988.

[2] Marple, S. L., Jr., Digital Spectral Analysis with Applications. Englewood Cliffs, NJ: Prentice-Hall, 1987.

## Version History

Introduced before R2006a