Discrete Cosine Transform

Parents : Maths for computer science Mathematics In Digital Image Processing

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It separates the images into parts of different frequency regions

DCT Kernels: 2-point DCT:

$$\left[\begin{array}{cc}0.7071& 0.7071\\ 0.7071& -0.7071\end{array}\right]$$

$or$

$$\left[\begin{array}{cc}\frac{\sqrt{2}}{2}& \frac{\sqrt{2}}{2}\\ \frac{\sqrt{2}}{2}& -\frac{\sqrt{2}}{2}\end{array}\right]$$

4-point DCT:

$$\frac{1}{2}\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& \frac{\sqrt{2}}{2}& -\frac{\sqrt{2}}{2}& -1\\ 1& -1& -1& 1\\ 1& -\frac{\sqrt{2}}{2}& \frac{\sqrt{2}}{2}& -1\end{array}\right]$$

$or$

$$\left[\begin{array}{cccc}0.5& 0.5& 0.5& 0.5\\ 0.6533& 0.2706& -0.2706& -0.6533\\ 0.5& -0.5& -0.5& 0.5\\ 0.2706& -0.6533& 0.6533& -0.2706\end{array}\right]$$

References

• Discrete Cosine Transform and Haar transform with Examples - YouTube