A new two-dimensional fast cosine transform algorithm

Split-radix fast cosine transform algorithm

“…Furthermore, two additions and one multiplication are required for each radix-2 butterfly. Therefore, the computational complexity for the calculation of the butterflies equals: It should be noted here, that scaling by 2 has not been considered (Arguello andZapata 1990, Chan andHo 1991). The recursive additions are performed after the bit reversal stage in order to be implemented in a very regular way.…”

“…The even indexed components of X , can be computed as (Chan and Ho 1991) N I Z -I X2t= C (f,+i,+N1,)Cfvp, k = 0 , 1 , . .…”

“…Many fast algorithms have been proposed for computing the DCT. These fast cosine transform (FCT) algorithms could be classified according to their method of approach into: (a) indirect, when computation is achieved by means of the FFT or the fast Hartley transform or other transforms (Malvar 1986, Narasimha andPeterson 1978); and (b) direct, when computation is performed through matrix factorization or recursively (Hou 1987, Chan and Ho 1991, Arguello and Zapata 1990, Lee 1984, Vetterli and Nussbaumer 1984.…”

Fast 2-D 8×8 discrete cosine transform algorithm for image coding

“…There are tremendous DCT fast algorithms in refs. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. The most influential algorithms nowadays are listed in Table 1.…”

A fast algorithm for the computation of 2-D forward and inverse MDCT

“…Among them, by using a polynomial transform (PT), Duhamel and Guillemot [24] [27][28][29][30][31], matrix factorization or recursive computation [32][33][34][35][36][37], constant geometry algorithm [38,39], and Chebyshev polynomial [40]. Among them, Britanak and Rao [36] developed an efficient recursive 2-D DCT algorithm for a rectangular 2 m ×2 n block sizes.…”