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Table 6 The results of analysis of known approximations of DCT in the case of the symmetric scenario (π(V)=0.131042)

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

Type Adds Shifts \(\chi _{3}(U,\overline {U})\) \(\epsilon _{A}^{(III)}(U,\overline {U})\) \(\text {tr}(\overline {U}^{T}\overline {U})/N\) π(U) Orthogonality
DR2014 12 0 5.782034 0.000000 3.000000 0.542537 -
    (2.545508) (1.100000) (0.750000)   
BC2012 14 0 0.656552 0.000000 1.000000 0.184816 +
PMCBKE2014 14 0 0.656552 0.000000 1.000000 0.184816 +
BAS2008III (a=0.0) 16 0 0.574577 0.000000 1.000000 0.161740 +
BAS2008III (a=1.0) 18 0 0.574474 0.000000 1.000000 0.161711 +
BAS2008III (a=0.5) 18 2 0.547763 0.000000 1.000000 0.154192 +
BAS2008I 18 2 0.547763 0.000000 1.000000 0.154192 +
PS2012 18 2 0.534894 0.000000 1.000000 0.150570 +
BAS2008II 21 0 1.032007 0.000000 1.781250 0.163090 -
    (0.794446) (0.215074) (1.000000)   
CB2011 22 0 0.539839 0.000000 1.000000 0.151962 +
SDCT2001 24 0 0.886988 0.000000 1.500000 0.166455 -
    (0.951579) (0.360253) (1.000000)   
BAS2010 24 4 0.522419 0.000000 1.000000 0.147058 +
PMCBR2012 24 6 0.520192 0.000000 1.000000 0.146431 +
  1. *Values in parentheses describe results obtained with \(\overline {U}=U^{T}\); otherwise we have \(\overline {U}=U^{-1}\).