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Table 3 The approximations of DCT generated by the proposed procedure in the case of the asymmetric scenario of type I

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

Name Adds Bit-shifts χ1(U) \(\epsilon _{A}^{(I)}(U)\) π(U) { a, b, c, d, e, f, g } Orthogonality
APRXI.1 14 0 1.131665 0.475113 0.184816 { 1, 1, 0, 0, 0, 0, 1 } +
APRXI.2 16 0 1.131547 0.475113 0.184783 { 1, 1, 1, 0, 0, 0, 1 } +
APRXI.3 16 2 1.071089 0.445176 0.176191 { 1, 1, \( \kern0.3em \frac{1}{2} \), 0, 0, 0, 1 } +
APRXI.4 18 0 0.755224 0.166628 0.165687 { 1, 1, 0, 0, 0, 1, 1 } -
APRXI.5 20 0 0.755118 0.166628 0.165657 { 1, 1, 1, 0, 0, 1, 1 } -
APRXI.6 20 2 0.697819 0.136691 0.157954 { 1, 2, 1, 0, 0, 1, 1 } -
APRXI.7 22 0 0.618240 0.078402 0.151962 { 1, 1, 0, 0, 1, 1, 1 } +
APRXI.8 22 4 0.554463 0.052222 0.141378 { 1, 1, 0, 0, \( \kern0.3em \frac{1}{2} \), 1, 1 } -
APRXI.9 24 2 0.554373 0.052222 0.141353 { 1, 1, 1, 0, \( \kern0.3em \frac{1}{2} \), 1, 1 } -
APRXI.10 24 6 0.501088 0.022286 0.134780 { 1, 1, \( \kern0.3em \frac{1}{2} \), 0, \( \kern0.3em \frac{1}{2} \), 1, 1 } -
APRXI.11 28 10 0.482868 0.010708 0.132910 { 1, 1, \( \kern0.3em \frac{1}{2},\kern0.3em \frac{1}{8},\kern0.3em \frac{1}{2} \), 1, 1 } -