AutoCorrelation - Maple Help
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SignalProcessing

  

AutoCorrelation

  

estimate the autocorrelation of an array of samples

 

Calling Sequence

Parameters

Options

Description

Thread Safety

Examples

Compatibility

Calling Sequence

AutoCorrelation(A)

Parameters

A

-

Array with complex or real numeric values; the signal

Options

• 

container : Array, predefined Array for holding result

• 

scaling : none, biased or unbiased

Description

• 

The AutoCorrelation(A) command estimates the autocorrelation of the Array A of length , storing the result in an Array C having the same length, which is then returned.

• 

The un-scaled autocorrelation of Array A of length  and initial index 1 is defined by the formula

  

for each  from  to . Note that this routine computes estimates for positive lags only, since the autocorrelation for a negative lag value is the complex conjugate of the autocorrelation for the equivalent positive lag.

• 

The formula shown above is for the default value of the scaling option, none. If scaling is set to biased, then each value of C is scaled by . If scaling is set to unbiased, then the -th element of C is scaled by .

• 

Before the code performing the computation runs, Maple converts A to a hardware datatype, first attempting float[8] and subsequently complex[8], unless it already has one of these datatypes. For this reason, it is most efficient if A has one of these datatypes beforehand.

• 

If the container=C option is provided, then the results are put into C and C is returned. With this option, no additional memory is allocated to store the result. The container must be an Array of the same size and datatype as A.

Thread Safety

• 

The SignalProcessing[AutoCorrelation] command is thread-safe as of Maple 17.

• 

For more information on thread safety, see index/threadsafe.

Examples

(1)

(2)

(3)

(4)

(5)

(6)

(7)

Compatibility

• 

The SignalProcessing[AutoCorrelation] command was introduced in Maple 17.

• 

For more information on Maple 17 changes, see Updates in Maple 17.

See Also

SignalProcessing[Convolution]

SignalProcessing[CrossCorrelation]

 


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