Inverse discrete cosine transform

Patent Pending Using the normalization conventions above, the inverse of DCT-I is DCT-I multiplied by 2/(N-1). The inverse of DCT-IV is DCT-IV multiplied by 2/N. The inverse of DCT-II is DCT-III multiplied by 2/N and vice versa.[2] Like for the DFT, the normalization factor in front of these transform definitions is merely a convention and differs between treatments. For example, some authors multiply the transforms by \sqrt{2/N} so that the inverse does not require any additional multiplicative factor. Combined with appropriate factors of √2 (see above), this can be used to make the transform matrix orthogonal.