The discrete cosine transform is a frequency representation similar to the Fourier transform, but it uses only real-valued functions and is more efficient for processing data that has symmetric properties. There are several variations of the DCT, including the Type I, II, III, and IV transforms. The most commonly used form is the DCT-II, often simply referred to as "the DCT": $ X(k) = \sum_{n=0}^{N-1} x(n) \cos\left( \frac{\pi}{N} \left( r+ \frac{1}{2} \right)k \right) \; $ for $k=0, \dots, N-1$.