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Table 1 The list of popular and known from the literature approximations of 8-point DCT

From: Approximate calculation of 8-point DCT for various scenarios of practical applications

Short name Introduced by No. of additions No. of shifts Orthogonality
SDCT2001 Haweel in [6] 24 0 -
BAS2008I Bouguezel et al. in [7] 18 2 +
BAS2008II Bouguezel et al. in [8] 21 0 (3) -
BAS2010 Bouguezel et al. in [10] 24 4 +
BAS2011 (a=\(\{0,\frac {1}{2},1\}\)) Bouguezel et al. in [9] 16/18/18 0/2/0 +
CB2011 Cintra and Bayer [11] 22 0 -
BC2012 Bayer and Cintra [12] 14 0 +
PMCBR2012 Potluri et al. in [15] 24 6 +
PS2012 Puchala and Stokfiszewski in [13] 18 2 +
DR2014 Dhandapani and Ramachandran in [5] 12 0 -
PMCBKE2014 Potluri et al. in [16] 14 0 +
  1. *The value in brackets indicate the number of operations required in the case of an inverse transformation. It should be noted that approximation BAS2011 is parametrized with the value of one parameter a. In this paper, we consider three values \(a=\{0,\frac {1}{2},1\}\) (also considered in the original paper [9]) which results in three sets of the numbers of additions and bit-shift operations