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Autocorrelation - Compute autocorrelation of vector or matrix input

Library

Statistics

dspstat3

Description

The Autocorrelation block computes the autocorrelation along each column of a frame-based input, and computes along the first dimension of an N-D sample-based input. The output of the block is always sample-based.

The Autocorrelation block accepts real and complex floating-point and fixed-point inputs except for complex unsigned fixed-point inputs. Fixed-point signals are not supported for the frequency domain.

Autocorrelation of Frame-Based Inputs

When the input to the Autocorrelation block is a frame-based M-by-N matrix u, the output, 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. y_0,j is the zero-lag element in the jth column. When you select Compute all non-negative lags, l=M–1. Otherwise, l is specified as a nonnegative integer by the Maximum non-negative lag (less than input length) 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.

Autocorrelation of Sample-Based Inputs

When the input is a sample-based N-D array, the block computes the autocorrelation along the first dimension of the input. The output is a sample based N-D array, where the size of the first dimension is l+1, and the sizes of all other dimensions match those of the input array. For example, when the input is an M-by-N-by-P array, the Autocorrelation block outputs an (l+1)-by-N-by-P sample-based array.

When you select Compute all non-negative lags, l=M–1. Otherwise, l is specified as a nonnegative integer by the Maximum non-negative lag (less than input length) 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.

Fixed-Point Data Types

The following diagrams show the data types used within the Autocorrelation block for fixed-point signals (time domain only).

You can set the product output, accumulator, and output data types on the Data type attributes pane of the block dialog as discussed in the next section.

The output of the multiplier is in the product output data type when the input is real. When the input is complex, the result of the multiplication is in the accumulator data type. For details on the complex multiplication performed, see Multiplication Data Types.

Dialog Box

The Main pane of the Autocorrelation block dialog appears as follows.

Compute all non-negative lags

Select to compute the autocorrelation over all nonnegative lags in the range [0, length(input)-1].

Maximum non-negative lag (less than input length)

Specify the maximum positive lag, l, for the autocorrelation. This parameter is enabled when you do not select the Compute all non-negative lags check box.

Scaling

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

None — Generates the raw autocorrelation y_i,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.

This parameter is tunable, except in the Simulink external mode.

Computation domain

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

Time — Computes in the time domain, which minimizes memory use
Frequency — Computes in the frequency domain, which might require fewer computations than computing in the time domain, depending on the input length

The Data type attributes pane of the Autocorrelation block dialog appears as follows.

Note Fixed-point signals are only supported for the time domain. To use the parameters on this pane, make sure Time is selected for the Computation domain parameter on the Main pane.

Rounding mode

Select the rounding mode for fixed-point operations.

Overflow mode

Select the overflow mode for fixed-point operations.

Product output data type

Specify the product output data type. See Fixed-Point Data Types and Multiplication Data Types for illustrations depicting the use of the product output data type in this block. You can set it to:

A rule that inherits a data type, for example, Inherit: Inherit via internal rule
An expression that evaluates to a valid data type, for example, fixdt([],16,0)

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Product output data type parameter.

See Using the Data Type Assistant for more information.

Accumulator data type

Specify the accumulator data type. See Fixed-Point Data Types for illustrations depicting the use of the accumulator data type in this block. You can set this parameter to:

A rule that inherits a data type, for example, Inherit: Inherit via internal rule
An expression that evaluates to a valid data type, for example, fixdt([],16,0)

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Accumulator data type parameter.

See Using the Data Type Assistant for more information.

Output data type

Specify the output data type. See Fixed-Point Data Types for illustrations depicting the use of the output data type in this block. You can set it to:

A rule that inherits a data type, for example, Inherit: Same as accumulator
An expression that evaluates to a valid data type, for example, fixdt([],16,0)

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Output data type parameter.

See Specifying Block Output Data Types for more information.

Minimum

Specify the minimum value that the block should output. The default value, [], is equivalent to -Inf. Simulink software uses this value to perform:

Simulation range checking (see Checking Signal Ranges)
Automatic scaling of fixed-point data types

Maximum

Specify the maximum value that the block should output. The default value, [], is equivalent to Inf. Simulink software uses this value to perform:

Simulation range checking (see Checking Signal Ranges)
Automatic scaling of fixed-point data types

Lock scaling against changes by the autoscaling tool

Select this parameter to prevent any fixed-point scaling you specify in this block mask from being overridden by the autoscaling tool in the Fixed-Point Tool.

Supported Data Types

Port	Supported Data Types
Input	Double-precision floating point Single-precision floating point Fixed point (signed and unsigned) 8-, 16-, and 32-bit signed integers 8-, 16-, and 32-bit unsigned integers
Output	Double-precision floating point Single-precision floating point Fixed point (signed and unsigned) 8-, 16-, and 32-bit signed integers 8-, 16-, and 32-bit unsigned integers

Port

Supported Data Types

Input

Double-precision floating point
Single-precision floating point
Fixed point (signed and unsigned)
8-, 16-, and 32-bit signed integers
8-, 16-, and 32-bit unsigned integers

Output

Double-precision floating point
Single-precision floating point
Fixed point (signed and unsigned)
8-, 16-, and 32-bit signed integers
8-, 16-, and 32-bit unsigned integers

Correlation	Signal Processing Blockset
`xcorr`	Signal Processing Toolbox

Autocorrelation - Compute autocorrelation of vector or matrix input

Library

Description

Autocorrelation of Frame-Based Inputs

Autocorrelation of Sample-Based Inputs

Fixed-Point Data Types

Dialog Box

Supported Data Types

See Also

Related Products & Applications