\(\text{InverseDFT}\)

Calculates the inverse discrete Fourier transform (DFT) of a matrix in one or two dimensions.

You can use the \idft backslash command to insert this function.

The following variants of this function are available:

  • \(\text{complex matrix } \text{InverseDFT} \left ( \text{<matrix>} \right )\)

The \(\text{InverseDFT}\) always returns a complex matrix independent of the type of the supplied input. Also note that the function assumes a cartesian representation of complex values rather than a polar representation. The returned matrix will have the same dimensions as the supplied input matrix.

This function calculates the inverse DFT in one dimension using the relation:

\[f _ { k + 1 } = \sum_{n=0}^{N-1} F _ { n + 1 } e ^ { \frac{2 \pi i}{N} k n }\]

In two dimensions, this function calculates the DFT using the relation:

\[f _ { k + 1, l + 1 } = \sum_{m=0}^{\text{nrows} \left ( F \right ) - 1 } \sum_{n=0}^{\text{ncols} \left ( F \right ) - 1 } F _ { m + 1, n + 1 } e ^ { 2 \pi i \left [ \frac{ k m }{ \text{nrows} \left ( F \right ) } + \frac{ l n }{ \text{ncols} \left ( F \right ) } \right ] }\]

Figure 156 shows the basic use of the \(\text{InverseDFT}\) function.

../_images/inverse_dft_example.png

Figure 156 Example Use of The Inverse DFT Function