The multiplicative complexity of discrete cosine transforms

Fast Algorithm for the 3-D DCT-II

“…Therefore, although the proposed 3-D VR algorithm does not achieve the theoretical lower bound on the number of multiplications [46], it has the simplest computational structure among all 3-D DCT algorithms. It can be implemented in place using a single butterfly and posses the properties of the Couley-Tukey FFT in 3-D.…”

An FPGA Implementation of HW/SW Codesign Architecture for H.263 Video Coding

“…It was selected due the minimum required number of additions and multiplications (11 Multiplications and 29 additions). This algorithm is obtained by a slight modification of the original Loeffler algorithm [29], which provides one of the most computationally efficient 1-D DCT/IDCT calculation, as compared with other known algorithms [31]- [33]. The modified Loeffler algorithm for calculating 8-point 1-D DCT is illustrated in Fig.14.…”

Fast computing of discrete cosine and sine transforms of types VI and VII

“…[5][6][7] Such transforms are very well studied, and a number of efficient technique exists for their computation. 1,[8][9][10][11][12][13][14] Design of integer approximations of such transforms was also a subject of active study in recent years. 8,15,16 Much less known is a group of so-called "odd" sinusoidal transforms: DST and DCT of types V, VI, VII, and VIII.…”