fft - Maple Help

Matlab

 fft
 compute the discrete Fourier transform of a vector in MATLAB(R)

 Calling Sequence fft(X) fft(X, n)

Parameters

 X - MapleMatrix or MatlabMatrix n - (optional) integer

Description

 • The fft command uses MATLAB® to compute the discrete Fourier transform of a vector, X.
 • If the optional parameter n is specified, then only the first n elements of vector X are used in the computation. If X has fewer than n elements, the missing elements are replaced with zeros (that is, X is padded with zeros up to the value of n).
 • Executing the fft command returns a Vector.

Examples

To see the result of the MATLAB® calls, copy the examples to a worksheet and execute them. For help setting up MATLAB® to work with Maple, see Matlab[setup].

Define the Maple matrix

 > $\mathrm{with}\left(\mathrm{Matlab}\right):$
 > $v≔⟨1,2,3,4,3,2,1,2,3,4⟩$
 ${v}{≔}\left[\begin{array}{c}{1}\\ {2}\\ {3}\\ {4}\\ {3}\\ {2}\\ {1}\\ {2}\\ {3}\\ {4}\end{array}\right]$ (1)

The Fourier transform is computed as

 > $\mathrm{Matlab}\left[\mathrm{fft}\right]\left(v\right)$

 [                 25. + 0. I                  ] [                                             ] [0.618033988749894901 - 1.90211303259030706 I ] [                                             ] [-3.61803398874989490 + 4.97979656976556040 I ] [                                             ] [-1.61803398874989490 + 1.17557050458494626 I ] [                                             ] [-1.38196601125010509 + 0.449027976579585484 I] [                                             ] [                 -3. + 0. I                  ] [                                             ] [-1.38196601125010509 - 0.449027976579585484 I] [                                             ] [-1.61803398874989490 - 1.17557050458494626 I ] [                                             ] [-3.61803398874989490 - 4.97979656976556040 I ] [                                             ] [0.618033988749894901 + 1.90211303259030706 I ]

To obtain the fft of only the first two elements of v

 > $\mathrm{Matlab}\left[\mathrm{fft}\right]\left(v,2\right)$

 [3. ] [   ] [-1.]