Discrete Fourier Transform

Parents : Mathematics In Digital Image Processing Maths for computer science

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DFT in case of Image Processing

Kernels used are:

DFT Kernels:

2-point DFT:

$$\left[\begin{array}{cc}1& 1\\ 1& -1\end{array}\right]$$

4-point DFT:

$$\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& i& -1& -i\\ 1& -1& 1& -1\\ 1& -i& -1& i\end{array}\right]$$

Inverse DFT kernels

2-point DFT: $\frac{1}{\sqrt{2}}\left[\begin{array}{cc}1& 1\\ 1& -1\end{array}\right]$ For 4-point DFT $\frac{1}{2}\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& i& -1& -i\\ 1& -1& 1& -1\\ 1& -i& -1& i\end{array}\right]$

References

• Image Transforms and DFT (Discrete Fourier Transform) With Examples - YouTube