Fourier Transforms in MapleFourier transforms in Maple can be categorized as either transforms on expressions or transforms on signal data.To compute the Fourier transform of an expression, use the inttrans[fourier] command. For more details on this command, see the inttrans[fourier] help page.To compute the Fourier transform of signal data, the following commands are available: SignalProcessing[DFT] : This command computes the discrete Fourier transform of an Array of signal data points. The SignalProcessing[DFT] command works for any size Array. For more information, see SignalProcessing[DFT].SignalProcessing[FFT] : Similar to the SignalProcessing[DFT] command, SignalProcessing[FFT] computes the discrete Fourier transform of an Array of signal data points. The difference between the two commands is that the SignalProcessing[FFT] command uses the fast Fourier transform algorithm. Note: SignalProcessing[FFT] requires that the size of the Array must be a power of 2, greater than 2. If the Array passed to SignalProcessing[FFT] does not meet this requirement, the SignalProcessing[DFT] command is used instead. Similarly, SignalProcessing[InverseFFT] calls SignalProcessing[InverseDFT] when the passed Array does not meet this requirement. For more information, see SignalProcessing[FFT].DiscreteTransforms[FourierTransform] : The DiscreteTransforms[FourierTransform] provides similar functionality to that of SignalProcessing[DFT]. There are some options available in DiscreteTransforms[FourierTransform], such as padding, that are not available in SignalProcessing[DFT]. For more information, see DiscreteTransforms[FourierTransform].Note: Typically, SignalProcessing[DFT] and SignalProcessing[FFT] are slightly more efficient than DiscreteTransforms[FourierTransform]. The table below provides a summarized comparison of the discrete Fourier transform commands mentioned above.FeatureSignalProcessing[FFT]SignalProcessing[DFT]DiscreteTransforms[Fourier Transform]input single rtableyesyesyesinput two rtables (Re/Im)yesyesyeshigher-dimensional transformsyesyesyesspecify single dim for higher-dimensional transformsnonoyesoutput single rtableyesyesyesoutput two rtables (Re/Im)yesyesyespaddingnonoyesapply transform only to initial segmentnonoyesin placeyesyesyesspecify output rtableyesyesnospecify working storagenonoyessize of Array: power of 2yesyesyessize of Array: otheryes (dispatch to DFT)yesyes