HammingWindow - Maple Help
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SignalProcessing

 HammingWindow
 multiply an array of samples by a Hamming windowing function

 Calling Sequence HammingWindow(A)

Parameters

 A - Array of real or complex numeric values; the signal

Options

 • container : Array, predefined Array for holding results
 • inplace : truefalse, specifies that output should overwrite input

Description

 • The HammingWindow(A) command multiplies the Array A by a Hamming windowing function and returns the result in an Array having the same length. The length of A must be at least $3$.
 • The Hamming windowing function $w$ is defined as follows for a sample with $N$ points.

$w\left(k\right)=0.54-0.46\mathrm{cos}\left(\frac{2\mathrm{\pi }k}{N-1}\right)$

 • For an Array with complex values, the real and imaginary parts are multiplied by the same windowing function.
 • Before the code performing the computation runs, A is converted to datatype float[8] or complex[8] if it does not have one of those datatypes already. For this reason, it is most efficient if A has one of these datatypes beforehand. This does not apply if inplace is true.
 • 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.
 • If the inplace or inplace=true option is provided, then A is overwritten with the results. In this case, the container option is ignored.

Thread Safety

 • The SignalProcessing[HammingWindow] command is thread-safe as of Maple 17.
 • For more information on thread safety, see index/threadsafe.

Examples

 > $\mathrm{with}\left(\mathrm{SignalProcessing}\right):$
 > $a≔\mathrm{GenerateUniform}\left(10,-1,1\right)$
 $\left[\begin{array}{cccccccccc}0.9958675736749194& 0.4083375294118188& 0.1676108883276358& -0.24685883732224634& 0.43286647207183604& -0.43997985821614727& 0.43290131026935325& 0.4813794331155813& -0.47769706337282575& 0.028839034648290067\end{array}\right]$ (1)
 > $\mathrm{HammingWindow}\left(a\right)$
 $\left[\begin{array}{cccccccccc}0.07966940589399357& 0.07661210603386838& 0.07712143005191785& -0.1900813047381297& 0.42085815253089703& -0.4277742034243857& 0.33333400890740206& 0.22149318967205803& -0.0896253110114625& 0.0023071227718632057\end{array}\right]$ (2)
 > $c≔\mathrm{Array}\left(1..10,'\mathrm{datatype}'={'\mathrm{float}'}_{8},'\mathrm{order}'='\mathrm{C_order}'\right):$
 > $\mathrm{HammingWindow}\left(a,'\mathrm{container}'=c\right)$
 $\left[\begin{array}{cccccccccc}0.07966940589399357& 0.07661210603386838& 0.07712143005191785& -0.1900813047381297& 0.42085815253089703& -0.4277742034243857& 0.33333400890740206& 0.22149318967205803& -0.0896253110114625& 0.0023071227718632057\end{array}\right]$ (3)
 > $c$
 $\left[\begin{array}{cccccccccc}0.07966940589399357& 0.07661210603386838& 0.07712143005191785& -0.1900813047381297& 0.42085815253089703& -0.4277742034243857& 0.33333400890740206& 0.22149318967205803& -0.0896253110114625& 0.0023071227718632057\end{array}\right]$ (4)
 > $a≔\mathrm{GenerateTone}\left(100,1,\frac{1}{\mathrm{Pi}},\mathrm{Pi}\right):$
 > $\mathbf{use}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathrm{plots}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{in}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathrm{display}\left(\mathrm{Array}\left(\left[\mathrm{listplot}\left(a\right),\mathrm{listplot}\left(\mathrm{HammingWindow}\left(a\right)\right)\right]\right)\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{end use}$

Compatibility

 • The SignalProcessing[HammingWindow] command was introduced in Maple 17.
 • For more information on Maple 17 changes, see Updates in Maple 17.

 See Also