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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 N, storing the result in an Array C having the same length, which is then returned.

• 

The autocorrelation is defined by the formula

Ck=i=1NAi&conjugate0;Ai+k1

  

for each k from 1 to N, with Aj&equals;0 for N<j. 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 1N. If scaling is set to unbiased, then the k-th element of C is scaled by 1Nk.

• 

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

withSignalProcessing&colon;

aGenerateUniform10&comma;1&comma;1

a:=0.7852184921503080.5884139649570000.9931658226996680.9215782885439710.03878017095848920.01360579254105690.2107569728977980.7496002158150090.1389663578011100.212285134010017

(1)

AutoCorrelationa

3.470868599012912.025154107915381.521388597762801.026120416129290.9360878204414270.7593372566058070.6641862410004680.7176645453543910.01579258347205470.166690212833272

(2)

cArray1..numelemsa&comma;&apos;datatype&apos;&equals;&apos;float&apos;8&colon;

AutoCorrelationa&comma;&apos;container&apos;&equals;c

3.470868599012912.025154107915381.521388597762801.026120416129290.9360878204414270.7593372566058070.6641862410004680.7176645453543910.01579258347205470.166690212833272

(3)

c

3.470868599012912.025154107915381.521388597762801.026120416129290.9360878204414270.7593372566058070.6641862410004680.7176645453543910.01579258347205470.166690212833272

(4)

AutoCorrelationa&comma;&apos;scaling&apos;&equals;&apos;biased&apos;

0.3470868650732880.2025154138092520.1521388620433260.1026120431419670.09360878343902230.07593372679208140.06641862508976140.07176645560484260.001579258370738250.0166690215317150

(5)

AutoCorrelationa&comma;&apos;scaling&apos;&equals;&apos;unbiased&apos;&comma;&apos;container&apos;&equals;c

0.3470868599012910.2250171231017090.1901735747203500.1465886308756120.1560146367402380.1518674513211610.1660465602501170.2392215151181300.007896291736027340.166690212833272

(6)

c

0.3470868599012910.2250171231017090.1901735747203500.1465886308756120.1560146367402380.1518674513211610.1660465602501170.2392215151181300.007896291736027340.166690212833272

(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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