container : Array, predefined Array for holding results

inplace : truefalse, specifies that output should overwrite input

The BlackmanWindow( A, alpha ) command multiplies the Array A by the Blackman windowing function with parameter alpha and returns the result in an Array having the same length. The length of A must be at least $4$.

The Blackman windowing function $w$ is defined as follows for a sample of $N$ elements.

The default value of the parameter alpha is standard, and in this case, a value of $\mathrm{\alpha }=\mathrm{-0.16}$ is assumed. When alpha is optimal, then a value of $\mathrm{\alpha }=-\frac{0.5}{1+\cos \left(\frac{2\mathrm{\pi }}{N-1}\right)}$ is used. The alpha parameter may also take an arbitrary (real) numeric value.

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.

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

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

$\mathrm{with}\left(\mathrm{SignalProcessing}\right)\:$

$a≔\mathrm{GenerateUniform}\left(10\,-1\,1\right)$

$a≔\left[\begin{array}{cccccccccc}0.995867573674919& 0.408337529411819& 0.167610888327636& \mathrm{-0.246858837322246}& 0.432866472071836& \mathrm{-0.439979858216147}& 0.432901310269353& 0.481379433115581& \mathrm{-0.477697063372826}& 0.0288390346482901\end{array}\right]$

$\mathrm{BlackmanWindow}\left(a\right)$

$\left[\begin{array}{cccccccccc}0.& 0.0207719801199662& 0.0432436932460043& \mathrm{-0.155521067513015}& 0.411712229509390& \mathrm{-0.418477983518514}& 0.272727825469692& 0.124196135157369& \mathrm{-0.0243002741336059}& 0.\end{array}\right]$

$\mathrm{BlackmanWindow}\left(a\,'\mathrm{standard}'\right)$

$\left[\begin{array}{cccccccccc}0.& 0.0207719801199662& 0.0432436932460043& \mathrm{-0.155521067513015}& 0.411712229509390& \mathrm{-0.418477983518514}& 0.272727825469692& 0.124196135157369& \mathrm{-0.0243002741336059}& 0.\end{array}\right]$

$\mathrm{BlackmanWindow}\left(a\,'\mathrm{optimal}'\right)$

$\left[\begin{array}{cccccccccc}0.& 1.05857745610436\times {10}^{\mathrm{-17}}& 0.0232299301958607& \mathrm{-0.132726384850208}& 0.405478026709946& \mathrm{-0.412141332747986}& 0.232754178591409& 0.0667164928279553& \mathrm{-1.23838566311091}\times {10}^{\mathrm{-17}}& 0.\end{array}\right]$

$c≔\mathrm{Array}\left(1..10\,'\mathrm{datatype}'='\mathrm{float}'\left[8\right]\,'\mathrm{order}'='\mathrm{C\_order}'\right)\:$

$\mathrm{BlackmanWindow}\left(a\,'\mathrm{container}'=c\right)$

$\left[\begin{array}{cccccccccc}0.& 0.0207719801199662& 0.0432436932460043& \mathrm{-0.155521067513015}& 0.411712229509390& \mathrm{-0.418477983518514}& 0.272727825469692& 0.124196135157369& \mathrm{-0.0243002741336059}& 0.\end{array}\right]$

$c$

$\left[\begin{array}{cccccccccc}0.& 0.0207719801199662& 0.0432436932460043& \mathrm{-0.155521067513015}& 0.411712229509390& \mathrm{-0.418477983518514}& 0.272727825469692& 0.124196135157369& \mathrm{-0.0243002741336059}& 0.\end{array}\right]$

$a≔\mathrm{GenerateTone}\left(100\,1\,\frac{1}{\mathrm{\pi }}\,\mathrm{\pi }\right)\:$

$\mathbf{use}\mathrm{plots}\mathbf{in}\mathrm{display}\left(\mathrm{Array}\left(\left[\mathrm{listplot}\left(a\right)\,\mathrm{listplot}\left(\mathrm{BlackmanWindow}\left(a\right)\right)\,\mathrm{listplot}\left(\mathrm{BlackmanWindow}\left(a\,\'\mathrm{optimal}\'\right)\right)\right]\right)\right)\;\mathrm{animate}\left(\mathrm{listplot}\,\left[\'\mathrm{BlackmanWindow}\'\left(a\,\mathrm{\α}\right)\right]\,\mathrm{\α}\=-1..1\right)\mathbf{end\; use}$

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

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