container : Array, predefined Array for holding results

inplace   : truefalse, specifies that output should overwrite input

The DCT(A) command computes the discrete cosine transform (DCT) of the Array A and returns the result in an Array with datatype float[8].

The InverseDCT(A) command computes the inverse discrete cosine transform of the Array A and returns the result in an Array with datatype float[8].

Before the code performing the computation runs, A is converted to datatype float[8] if it does not have that datatype already. For this reason, it is most efficient if A has this datatype beforehand.

The discrete cosine transform B of a sample of $N$ elements with initial index 1 is defined by the formula

where $C_k$ is given by

Samples may be of arbitrary length, but when the length is a power of $2$, a faster algorithm is used,

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 float[8] 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 datatype float[8].

The SignalProcessing[DCT] and SignalProcessing[InverseDCT] commands are thread-safe as of Maple 17.

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

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

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

$N≔10\:$

$A≔\mathrm{GenerateTone}\left(N\,1\,0.1\,0\right)+\mathrm{GenerateTone}\left(N\,3\,0.4\,0.2\right)\:$

$B≔\mathrm{DCT}\left(A\right)$

$B≔\left[\begin{array}{cccccccccc}\mathrm{-5.61733354972272}\times {10}^{\mathrm{-16}}& 1.84081507493747& 2.12662702088010& 1.07340522632521& \mathrm{-5.99869680619447}\times {10}^{\mathrm{-16}}& 1.86744934354457& \mathrm{-1.23392200523572}\times {10}^{\mathrm{-15}}& 4.53201776089782& 3.29911475027503& \mathrm{-2.45478072804124}\end{array}\right]$

$\mathrm{display}\left(⟨⟨⟨\mathrm{listplot}\left(A\,'\mathrm{title}'=''Signal''\right)⟩\,⟨\mathrm{listplot}\left(B\,'\mathrm{title}'=''Cosine\; Transform''\right)⟩⟩⟩\right)$

$C≔\mathrm{InverseDCT}\left(B\right)$

$C≔\left[\begin{array}{cccccccccc}3.94019973352373& \mathrm{-1.91997926507489}& 1.78442596381239& 0.0327174052186558& \mathrm{-2.83736383747988}& 1.94019973352373& \mathrm{-3.53801325382479}& 1.16639197506249& 0.650751393968551& \mathrm{-1.21932984872999}\end{array}\right]$

$\mathrm{map}\left(\mathrm{fnormal}\,A-C\right)$

$\left[\begin{array}{cccccccccc}0.& \mathrm{-0.}& 0.& 0.& 0.& 0.& \mathrm{-0.}& \mathrm{-0.}& 0.& 0.\end{array}\right]$

$A≔\mathrm{GenerateJaehne}\left(10\,3\right)$

$A≔\left[\begin{array}{cccccccccc}0.& 0.469303395120693& 1.76335575687742& 2.96306502178541& 1.76335575687742& \mathrm{-2.12132034355964}& \mathrm{-1.76335575687742}& 2.96306502178541& \mathrm{-1.76335575687742}& 0.469303395120694\end{array}\right]$

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

$\mathrm{DCT}\left(A\,'\mathrm{container}'=C\right)$

$\left[\begin{array}{cccccccccc}1.50000000000000& 1.53435101970163& \mathrm{-0.303665947951025}& \mathrm{-2.52783090094747}& \mathrm{-2.06039897562768}& 2.24801372960734& 1.27812042982672& \mathrm{-2.67811620958831}& 2.16323992827129& \mathrm{-1.03295888501124}\end{array}\right]$

$C$

$\left[\begin{array}{cccccccccc}1.50000000000000& 1.53435101970163& \mathrm{-0.303665947951025}& \mathrm{-2.52783090094747}& \mathrm{-2.06039897562768}& 2.24801372960734& 1.27812042982672& \mathrm{-2.67811620958831}& 2.16323992827129& \mathrm{-1.03295888501124}\end{array}\right]$

$\mathrm{InverseDCT}\left(C\,'\mathrm{inplace}'\right)$

$\left[\begin{array}{cccccccccc}\mathrm{-1.38777878078145}\times {10}^{\mathrm{-16}}& 0.469303395120693& 1.76335575687742& 2.96306502178541& 1.76335575687742& \mathrm{-2.12132034355964}& \mathrm{-1.76335575687742}& 2.96306502178541& \mathrm{-1.76335575687742}& 0.469303395120694\end{array}\right]$

$C$

$\left[\begin{array}{cccccccccc}\mathrm{-1.38777878078145}\times {10}^{\mathrm{-16}}& 0.469303395120693& 1.76335575687742& 2.96306502178541& 1.76335575687742& \mathrm{-2.12132034355964}& \mathrm{-1.76335575687742}& 2.96306502178541& \mathrm{-1.76335575687742}& 0.469303395120694\end{array}\right]$

$\mathrm{map}\left(\mathrm{fnormal}\,A-C\right)$

$\left[\begin{array}{cccccccccc}0.& \mathrm{-0.}& \mathrm{-0.}& 0.& 0.& 0.& 0.& 0.& 0.& 0.\end{array}\right]$

The SignalProcessing[DCT] and SignalProcessing[InverseDCT] commands were introduced in Maple 17.

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