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Table 7 The approximations of DCT generated by the proposed procedure in the case of the symmetric scenario (π(V)=0.131042)

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

Name Adds Shifts \(\chi _{3}(U,\overline {U})\) \(\epsilon _{A}^{(III)}(U,\overline {U})\) \(\text {tr}(\overline {U}^{T}\overline {U})/N\) π(U) { a, b, c, d, e, f, g } Orthogonality
APRXIII.1 14 0 0.656552 0.000000 1.000000 0.184816 { 1, 0, 1, 0, 0, 0, 1 } +
APRXIII.2 16 0 0.656434 0.000000 1.000000 0.184783 { 1, 1, 1, 0, 0, 0, 1 } +
APRXIII.3 16 2 0.625912 0.000000 1.000000 0.176191 { 1, 2, 1, 0, 0, 0, 1 } +
APRXIII.4 20 2 0.620702 0.000000 1.000000 0.174724 { 1, 2, 1, 1, 0, 0, 1 } +
APRXIII.5 20 6 0.619900 0.021828 1.000000 0.168354 { 1, 2, 1, 0, 0, \( \kern0.3em \frac{1}{8} \), 1 } -
APRXIII.6 20 10 0.617859 0.005585 1.000000 0.172352 { 1, 2, 1, 0, 0, \( \kern0.3em \frac{1}{8} \), 2 } -
APRXIII.7 22 0 0.539839 0.000000 1.000000 0.151962 { 1, 1, 0, 0, 1, 1, 1 } +
APRXIII.8 24 0 0.539742 0.000000 1.000000 0.151934 { 1, 1, 1, 0, 1, 1, 1 } +
APRXIII.9 24 2 0.514646 0.000000 1.000000 0.144870 { 1, 1, \( \kern0.3em \frac{1}{2} \), 0, 1, 1, 1 } +
APRXIII.10 26 8 0.503287 0.004210 1.000000 0.140487 { 1, 0, 1, \( \kern0.3em \frac{1}{4},\kern0.3em \frac{1}{2} \), 1, 1 } -
APRXIII.11 28 6 0.503197 0.004210 1.000000 0.140462 { 1, 1, 1, \( \kern0.3em \frac{1}{4},\kern0.3em \frac{1}{2} \), 1, 1 } -
APRXIII.12 28 10 0.479996 0.004210 1.000000 0.133931 { 1, 2, 1, \( \kern0.3em \frac{1}{4},\kern0.3em \frac{1}{2} \), 1, 1 } -