DSP Blockset

Autocorrelation

Compute the autocorrelation of a vector input.

Library

Statistics

Description

The Autocorrelation block computes the autocorrelation of each channel in an input matrix or vector, u. The block computes the autocorrelation along each column of a frame-based input, and computes along the vector dimension of a sample-based vector input. The block does not accept sample-based matrix inputs. Outputs are always sample-based.

M-by-N matrix inputs must be frame-based. The result, y, is a sample-based (l+1)-by-N matrix whose jth column has elements

where * denotes the complex conjugate, and l represents the maximum lag. Note that y_1,j is the zero-lag element in the jth column. When Compute all non-negative lags is selected, l=M. Otherwise, l is specified as a nonnegative integer by the Maximum positive lag parameter.

Input u is zero when indexed outside of its valid range. When the input is real, the output is real; otherwise, the output is complex.

If the input is a sample-based vector (row, column, or 1-D), the output is sample-based, with the same shape as the input and length l+1. The block computes the autocorrelation of sample-based vector inputs along the vector dimensions. The Autocorrelation block does not accept a sample-based full-dimension matrix input.

The Scaling parameter controls the scaling that is applied to the output. The following options are available:

• None -- Generates the raw autocorrelation, yi,j, without normalization.
• Biased -- Generates the biased estimate of the autocorrelation.

• Unbiased -- Generates the unbiased estimate of the autocorrelation.

• Unity at zero-lag -- Normalizes the estimate of the autocorrelation for each channel so that the zero-lag sum is identically 1.

The Computation domain parameter sets the domain in which the block computes convolutions to one of the following settings:

• Time -- The block computes in the time domain, which minimizes memory use.
• Frequency -- The block computes in the frequency domain, which may require fewer computations than computing in the time domain (depending on the input length).

Dialog Box

Compute all non-negative lags

When selected, computes the autocorrelation over all non-negative lags in the range [0, length(input)-1].

Maximum positive lag

The maximum positive lag, l, for the autocorrelation. This parameter is enabled when the Compute all non-negative lags check box is unselected.

Scaling

The type of scaling for the autocorrelation: None, Biased, Unbiased, or Unity at zero-lag. Tunable, except in the Simulink external mode.

Computation domain

The domain in which the block computes convolutions: Time or Frequency. To minimize memory use, select Time; frequency domain computations may require fewer computations than those in the time domain depending on the input length.

Supported Data Types

• Double-precision floating point
• Single-precision floating point

To learn how to convert to the above data types in MATLAB and Simulink, see Supported Data Types and How to Convert to Them.

See Also

Correlation	DSP Blockset
xcorr	Signal Processing Toolbox

Also see Statistics for a list of all the blocks in the Statistics library.

Analytic Signal

Autocorrelation LPC