RiemannWindow - Maple Help

SignalProcessing

 RiemannWindow
 multiply an array of samples by a Riemann windowing function

 Calling Sequence RiemannWindow(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 RiemannWindow(A) command multiplies the Array A by the Riemann windowing function and returns the result in an Array having the same length.
 • The Riemann windowing function $w\left(k\right)$ is defined as follows for a sample with $N$ points.

$\left\{\begin{array}{cc}1& k=\frac{N}{2}\\ \frac{\mathrm{sin}\left(\left(\frac{2k}{N}-1\right)\mathrm{\pi }\right)}{\left(\frac{2k}{N}-1\right)\mathrm{\pi }}& \mathrm{otherwise}\end{array}\right\$

 • 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[RiemannWindow] command is thread-safe as of Maple 18.

Examples

 > $\mathrm{with}\left(\mathrm{SignalProcessing}\right):$
 > $N≔1024:$
 > $a≔\mathrm{GenerateUniform}\left(N,-1,1\right)$
 ${{\mathrm{_rtable}}}_{{36893628315422794084}}$ (1)
 > $\mathrm{RiemannWindow}\left(a\right)$
 ${{\mathrm{_rtable}}}_{{36893628315267284988}}$ (2)
 > $c≔\mathrm{Array}\left(1..N,'\mathrm{datatype}'='\mathrm{float}'\left[8\right],'\mathrm{order}'='\mathrm{C_order}'\right):$
 > $\mathrm{RiemannWindow}\left(\mathrm{Array}\left(1..N,'\mathrm{fill}'=1,'\mathrm{datatype}'='\mathrm{float}'\left[8\right],'\mathrm{order}'='\mathrm{C_order}'\right),'\mathrm{container}'=c\right)$
 ${{\mathrm{_rtable}}}_{{36893628315267260652}}$ (3)
 > $u≔\mathrm{~}\left[\mathrm{log}\right]\left(\mathrm{FFT}\left(c\right)\right):$
 > $\mathbf{use}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathrm{plots}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{in}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathrm{display}\left(\mathrm{Array}\left(\left[\mathrm{listplot}\left(\mathrm{ℜ}\left(u\right)\right),\mathrm{listplot}\left(\mathrm{ℑ}\left(u\right)\right)\right]\right)\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{end use}$

 > 

Compatibility

 • The SignalProcessing[RiemannWindow] command was introduced in Maple 18.