Crosscorrelation of two inputs
Statistics
dspstat3
The Correlation block computes the crosscorrelation of two ND input arrays. The block computes the correlation columnwise, so both inputs must have the same number of columns. If one input is a column vector and the other is an ND array, the Correlation block computes the crosscorrelation of the vector with each column of the ND array.
When the input to the Correlation block is an M_{u}byN input matrix u and an M_{v}byN matrix v, the output, y, is a (M_{u}+M_{v}–1)byN matrix whose jth column has elements
$$\begin{array}{l}{y}_{uv(i,j)}={\displaystyle \sum _{k=0}^{\mathrm{max}({M}_{u},{M}_{v})1}{u}_{k,j}^{}{v}_{(ki),j}^{*}}\text{}0\le i{M}_{v}\\ \\ {y}_{uv(i,j)}={y}_{vu(i,j)}^{*}\text{}{M}_{u}i0\end{array}$$
where * denotes the complex conjugate. Inputs u and v are zero when indexed outside of their valid ranges. When both inputs are real, the output is real; when one or both inputs are complex, the output is complex.
When one input is a column vector and the other is an ND array, the Correlation block independently crosscorrelates the input vector with each column of the ND array. For example, when u is a M_{u}by1 column vector and v is an M_{v}byN matrix, the output is an (M_{u}+M_{v}–1)byN matrix whose jth column has elements
$$\begin{array}{l}{y}_{uv(i,j)}={\displaystyle \sum _{k=0}^{\mathrm{max}({M}_{u},{M}_{v})1}{u}_{k}^{}{v}_{(ki),j}^{*}}\text{}0\le i{M}_{v}\\ \\ {y}_{uv(i,j)}={y}_{vu(i,j)}^{*}\text{}{M}_{u}i0\end{array}$$
The Correlation block also accepts two column vector inputs. When u and v are column vectors with lengths M_{u} and M_{v}, the Correlation block performs the vector crosscorrelation according to the following equation:
$$\begin{array}{l}{y}_{uv(i)}={\displaystyle \sum _{k=0}^{\mathrm{max}({M}_{u},{M}_{v})1}{u}_{k}^{}{v}_{(ki)}^{*}}\text{}0\le i{M}_{v}\\ \\ {y}_{uv(i)}={y}_{vu(i)}^{*}\text{}{M}_{u}i0\end{array}$$
The output is a (M_{u}+M_{v}–1)by1 column vector.
The following diagram shows the data types used within the Correlation block for fixedpoint signals (time domain only).
You can set the product output, accumulator, and output data types in 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.
Note: When one or both of the inputs are signed fixedpoint signals, all internal block data types are signed fixed point. The internal block data types are unsigned fixed point only when both inputs are unsigned fixedpoint signals. 
The Main pane of the Correlation block dialog appears as follows.
Set the domain in which the block computes correlations:
Time
— The block
computes in the time domain, which minimizes memory use.
Frequency
— The
block computes in the frequency domain, which might require fewer
computations than computing in the time domain, depending on the input
length.
Fastest
— The block
computes in the domain, which minimizes the number of computations.
The Data Types pane of the Correlation block dialog appears as follows.
Note:
Fixedpoint signals are only supported for the time domain.
To use the parameters on this pane, make sure 
Select the rounding mode for fixedpoint operations.
Note: The Rounding mode and Overflow mode settings have no effect on numerical results when all the following conditions exist:
With these data type settings, the block is effectively operating in full precision mode. 
Select the overflow mode for fixedpoint operations.
Specify the product output data type. See FixedPoint 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 Specify Data Types Using Data Type Assistant for more information.
Specify the accumulator data type. See FixedPoint 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 Specify Data Types Using Data Type Assistant for more information.
Specify the output data type. See FixedPoint 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 Specify Block Output Data Types for more information.
Specify the minimum value that the block should output. The
default value is []
(unspecified). Simulink^{®} software
uses this value to perform:
Simulation range checking (see Signal Ranges)
Automatic scaling of fixedpoint data types
Specify the maximum value that the block should output. The
default value is []
(unspecified). Simulink software
uses this value to perform:
Simulation range checking (see Signal Ranges)
Automatic scaling of fixedpoint data types
Select this parameter to prevent the fixedpoint tools from overriding the data types you specify on the block mask.
Port  Supported Data Types 

Input 

Output 

Autocorrelation  DSP System Toolbox 
Convolution  DSP System Toolbox 
xcorr  Signal Processing Toolbox 