Fast Fourier Transform and Inverse - Maple Programming Help

Fast Fourier Transform and Inverse

 Description Calculate the Fast Fourier transform (FFT) and inverse Fast Fourier transform (iFFT) of an expression.

Define a 1-D vector.

 >
 $\left[\begin{array}{c}{0.944956946300000}{+}{0.327194696800000}{}{I}\\ {0.785887260800000}{+}{0.618369803100000}{}{I}\\ {0.540302305900000}{+}{0.841470984800000}{}{I}\\ {0.235237573600000}{+}{0.971937901300000}{}{I}\\ {-}{0.0957235483500000}{+}{0.995407957700000}{}{I}\end{array}\right]$ (1)

Calculate the Fast Fourier transform of the vector.

 > $\mathrm{DiscreteTransforms}\left[\mathrm{FourierTransform}\right]\left(\right)$
 $\left[\begin{array}{c}{1.07808016684065}{+}{1.67901037959404}{}{I}\\ {0.0427237444135178}{-}{0.741915464460826}{}{I}\\ {0.236451541814053}{-}{0.288930752602944}{}{I}\\ {0.323690442159333}{-}{0.0849440825829593}{}{I}\\ {0.432042072509868}{+}{0.168409503974922}{}{I}\end{array}\right]$ (2)

Calculate the inverse Fast Fourier transform of the result.

 > $\mathrm{DiscreteTransforms}\left[\mathrm{InverseFourierTransform}\right]\left(,\mathrm{inplace}=\mathrm{true}\right)$
 $\left[\begin{array}{c}{0.944956946300000}{+}{0.327194696800000}{}{I}\\ {0.785887260800000}{+}{0.618369803100000}{}{I}\\ {0.540302305900000}{+}{0.841470984800000}{}{I}\\ {0.235237573600000}{+}{0.971937901300000}{}{I}\\ {-}{0.0957235483500000}{+}{0.995407957700000}{}{I}\end{array}\right]$ (3)
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