# Frequency-Based Adaptive Interpolation Filter in Intra Prediction
## 3 Proposed Method
### Design of 8-Tap Interpolation Filter
The energy percentage of the high-frequency coefficients, _high_freq_ratio_, is calculated in Equation (13). \[high\_freq\_ratio=\frac{\sum_{k=N*\frac{3}{2}}^{N-1}X[k]*X[k]}{\sum_{k=0}^{N-1}X[ k]*X[k]}*100 \tag{13}\]  
Table 6 shows the proposed interpolation filter selection method by the threshold _THR_ of _high_freq_ratio_ and the interpolation filters applied to the selected method. The proposed method is only used when _nTbS_ = 2 and _nTbS_ > 4. Otherwise, the existing VVC method is used when _nTbS_ = 3, 4. The proposed method uses an 8-tap DCT-IF/SIF and a 4-tap DCT-IF/SIF according to _nTbS_ and _high_freq_ratio_. The threshold (_THR_) _of high_freq_ratio_ in Table 6 was determined experimentally. To select the threshold, CIF sequences with 352 \(\times\) 288 resolution and FHD sequences with 1920 \(\times\) 1080 resolution were used. The CIF sequences used are Akiyo, Bridge-far, Highway, News, and Paris, and the FHD sequences used are IceRock, Market3, Netflix_BarScene, Netflix_Crosswalk, and Netflix_FoodMarket. Figure 6 shows the Bjontegaard Delta (BD) rate [35; 36] reductions applying the proposed reference sample interpolations for each threshold, THR1, THR2,..., THR7, according to _nTbS_. Figure 6a,b are the result of _nTbS_ = 2 and _nTbS_ = 5, respectively. \begin{table}
\begin{tabular}{c c c c c c} \hline _nTbS_ & **2** & **3** & **4** & **5** & **6** \\ \hline _Filter Selection Method_ & _high_freq_ratio_ & **VVC Method** & **VVC Method** & _high_freq_ratio_ & _high_freq_ratio_ \\ \hline _high_freq_ratio_ \(<\)_THR_ & _4-tap SIF_ & - & - & _8-tap SIF_ & _8-tap SIF_ \\ _high_freq_ratio_\(\geq\)_THR_ & _8-tap DCT-IF_ & - & - & _4-tap DCT-IF_ & _4-tap DCT-IF_ \\ \hline \end{tabular}
\end{table} 
Table 6: Proposed interpolation filter selection method and interpolation filters applied to the selected method. In Figure 5(a), since _high_freq_ratio_ is less than the given threshold, a 4-tap SIF is used. Otherwise, the 8-tap DCT-IF is used. In Figure 5(a), the most efficient BD rate reductions occurred with THR5 and THR6. Therefore, THR5 is selected as the _THR_ of _high_freq_ratio_ in this proposed method. In Figure 5(b), when experimenting with _high_freq_ratio_ at \(nTbS=5\), better coding efficiency was obtained with THR4 and a similar result was obtained when \(nTbS\) is 6. Therefore, when \(nTbS\) is 5 and 6, THR4 is selected as _THR_ of _high_freq_ratio_ in the proposed method. For CU with \(nTbS>4\), when _high_freq_ratio_ < _THR_, the 8-tap SIF is used. Otherwise, the 4-tap DCT-IF is used. Correlation and filter have a close relationship. Small blocks have low correlation values with high-frequency characteristics. So, small blocks need to highlight high-frequency samples using strong HPF (8-tap DCT-IF). Since their average correlation value is relatively lower than large blocks, weak LPF (4-tap SIF) is better interpolation than strong LPF (8-tap SIF) when the block has low-frequency characteristics. Similarly, large blocks have high correlation values with low-frequency characteristics. So, large blocks need to highlight low-frequency samples using strong LPF (8-tap SIF). Since their average correlation value is relatively higher than small blocks, weak HPF (4-tap DCT-IF) has better interpolation than strong HPF (8-tap DCT-IF) when the block has high-frequency characteristics. For example, if the CU is 4 \(\times\) 4, the \(nTbS\) value becomes 2. The 8-tap DCT-IF is used when _high_freq_ratio_\(\geq\) THR5 in Figure 5(a). Otherwise, 4-tap SIF is used for the CU. The proposed method depends on \(nTbS\) and _high_freq_ratio_. In the case where the CU has \(nTbS\) size of 2, if _high_freq_ratio_\(<\) _THR_, a 4-tap SIF with a weak LPF characteristic, as shown in Figure 4, is applied for the reference samples, because the correlation at \(nTbS\) = 2 is relatively less than that at \(nTbS\) \(>\) 4 as shown in Figure 5. Otherwise, if _high_freq_ratio_\(\geq\) _THR_, the 8-tap DCT-IF with strong HPF characteristic as shown in Figure 4 is applied for the reference samples.