1. Discrete Cosine Transform (DCT)
DCT is proposed as an alternative approach to DFT
To reduce the complexity in computing complex number
DCT -> DFT keeping only cosine term
Types of DCT
4 types of DCT are proposed in the literature
DCT-I, DCT-II, DCT-III, and DCT-IV

2. DCT-I
Forward DCT-I
Inverse DCT-I

3. DCT-II (most popular)
Forward DCT-II
Inverse DCT-II

4. DCT-III
Forward DCT-III
Inverse DCT-III

5. DCT-IV
Forward DCT-IV
Inverse DCT-IV

6. Extension of the Original function

7. Power Spectrum Comparison

8. DCT-II Basis Function (n=8)

9. 2D-DCT-II
Forward DCT
Inverse DCT

10. Coefficient Comparison
DCT
DFT

11. 2D-DCT Separable

12. Fast DCT Algorithm (Lee’s algorithm)
DIF-DCT (Radix-2) -> Similar to DIF-DFT