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Table 5 The approximations of DCT generated by the proposed procedure in the case of the asymmetric scenario of type II

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

Name Adds Shifts χ2(U) \(\epsilon _{A}^{(II)}(U)\) { a, b, c, d, e, f, g } Orthogonality
APRXII.1 14 0 0.940633 0.475113 { 1, 1, 0, 0, 0, 0, 1 } +
APRXII.2 16 2 0.910697 0.445176 { 1, 2, 1, 0, 0, 0, 1 } +
APRXII.3 18 0 0.632148 0.166628 { 1, 1, 0, 0, 0, 1, 1 } -
APRXII.4 20 2 0.602212 0.136691 { 1, 1, \( \kern0.3em \frac{1}{2} \), 0, 0, 1, 1 } -
APRXII.5 22 0 0.543922 0.078402 { 1, 1, 0, 0, 1, 1, 1 } +
APRXII.6 22 4 0.517743 0.052222 { 1, 1, 0, 0, \( \kern0.3em \frac{1}{2} \), 1, 1 } -
APRXII.7 24 2 0.513986 0.048465 { 1, 1, \( \kern0.3em \frac{1}{2} \), 0, 1, 1, 1 } +
APRXII.8 24 6 0.487806 0.022286 { 1, 2, 1, 0, \( \kern0.3em \frac{1}{2} \), 1, 1 } -
APRXII.9 28 10 0.474493 0.008973 { 1, 2, 1, \( \kern0.3em \frac{1}{4},\kern0.3em \frac{1}{2} \), 1, 1 } -