absolutevalue : truefalse, specifies whether or not to use absolute values when thresholding

container : Array, predefined Array for holding results

comparison : lessthan, greaterthan, or lessgreater; type of comparison

inplace : truefalse, specifies that output should overwrite input

value : realcons or [realcons, realcons], alternative values to replace level values

The Threshold command performs thresholding operations on samples, which means retaining or discarding data points that do not meet some kind of minimality criterion.

If the comparison option is lessthan (the default), then "less-than" thresholding is done on the Array A and the result, an Array B having the same length and datatype, is returned. The threshold is determined by the value of the parameter level as follows for real data.

For a complex Array A, the value of the level parameter must be real and non-negative. In this case, the formula governing the thresholding function is given by

If the comparison option is greaterthan, then "greater-than" thresholding is done on the Array A. This is similar to the process described for comparison=lessthan, except that the less-than symbol is replaced by the greater-than symbol in the definitions shown above.

If the absolutevalue option is set to true then thresholding is done on absolute values. The formula in this case, with comparison=lessthan, is shown below. With comparison=greaterthan, the inequality $\left|A_k\right|<\mathrm{level}$ is replaced by $\mathrm{level}<\left|A_k\right|$. Note that this option works with real data only. The default value is false.

The value option allows you to specify an alternative real value to place in the output Array instead of level, as shown in the formulae below, with comparison=lessthan:

for real Arrays, and

for complex Arrays.

The value option also works with comparison=greaterthan, and in this case, the inequalities in the formulae above are reversed. In addition, the comparison option  can also take the lessgreater value, where both "less-than" and "greater-than" conditions are used. In this case, the level parameter and the value option should each be a list of two real values, and level[1] must be less than level[2].

By default, the value option is equal to level. Values in the Array A that are less than level[1] are set to value[1] in B, while those values in A that are greater than level[2] are set to value[2] in B. The precise formula used is

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 having datatype and size equal to those of 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. Furthermore, A must have one of the datatypes float[8] and complex[8].

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

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

$\mathrm{with}\left(\mathrm{SignalProcessing}\right)\&colon;$

$a≔\mathrm{GenerateUniform}\left(10\&comma;-1\&comma;1\right)$

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

$\mathrm{Threshold}\left(a\&comma;0.2\right)$

$\left[\begin{array}{cccccccccc}0.995867573674919& 0.408337529411819& 0.200000000000000& 0.200000000000000& 0.432866472071836& 0.200000000000000& 0.432901310269353& 0.481379433115581& 0.200000000000000& 0.200000000000000\end{array}\right]$

$\mathrm{Threshold}\left(a\&comma;0.2\&comma;'\mathrm{absolutevalue}'\right)$

$\left[\begin{array}{cccccccccc}0.995867573674919& 0.408337529411819& 0.200000000000000& \mathrm{-0.246858837322246}& 0.432866472071836& \mathrm{-0.439979858216147}& 0.432901310269353& 0.481379433115581& \mathrm{-0.477697063372826}& 0.200000000000000\end{array}\right]$

$\mathrm{Threshold}\left(a\&comma;0.2\&comma;'\mathrm{comparison}'='\mathrm{greaterthan}'\right)$

$\left[\begin{array}{cccccccccc}0.200000000000000& 0.200000000000000& 0.167610888327636& \mathrm{-0.246858837322246}& 0.200000000000000& \mathrm{-0.439979858216147}& 0.200000000000000& 0.200000000000000& \mathrm{-0.477697063372826}& 0.0288390346482901\end{array}\right]$

$\mathrm{Threshold}\left(a\&comma;0.2\&comma;'\mathrm{value}'=\mathrm{\pi }\right)$

$\left[\begin{array}{cccccccccc}0.995867573674919& 0.408337529411819& 3.14159265400000& 3.14159265400000& 0.432866472071836& 3.14159265400000& 0.432901310269353& 0.481379433115581& 3.14159265400000& 3.14159265400000\end{array}\right]$

$\mathrm{Threshold}\left(a\&comma;\left[-0.3\&comma;0.2\right]\&comma;'\mathrm{comparison}'='\mathrm{lessgreater}'\right)$

$\left[\begin{array}{cccccccccc}0.200000000000000& 0.200000000000000& 0.167610888327636& \mathrm{-0.246858837322246}& 0.200000000000000& \mathrm{-0.300000000000000}& 0.200000000000000& 0.200000000000000& \mathrm{-0.300000000000000}& 0.0288390346482901\end{array}\right]$

$\mathrm{Threshold}\left(a\&comma;\left[-0.3\&comma;0.2\right]\right)$

$\left[\begin{array}{cccccccccc}0.200000000000000& 0.200000000000000& 0.167610888327636& \mathrm{-0.246858837322246}& 0.200000000000000& \mathrm{-0.300000000000000}& 0.200000000000000& 0.200000000000000& \mathrm{-0.300000000000000}& 0.0288390346482901\end{array}\right]$

$\mathrm{Threshold}\left(a\&comma;\left[-0.3\&comma;0.2\right]\&comma;'\mathrm{value}'=\left[-\mathrm{\pi }\&comma;\mathrm{\pi }\right]\right)$

$\left[\begin{array}{cccccccccc}3.14159265400000& 3.14159265400000& 0.167610888327636& \mathrm{-0.246858837322246}& 3.14159265400000& \mathrm{-3.14159265400000}& 3.14159265400000& 3.14159265400000& \mathrm{-3.14159265400000}& 0.0288390346482901\end{array}\right]$

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

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