# Frequency-Based Adaptive Interpolation Filter in Intra Prediction
## 3 Proposed Method
### Design of 8-Tap Interpolation Filter
When the current block has many detailed areas including high frequencies, the CU size is partitioned into small blocks in the consideration of bit rate and distortion using boundary reference samples of small width and height. However, when the current block consists of a homogeneous area, the CU size is partitioned into large blocks in the consideration of bit rate and distortion using boundary reference samples of large width and height [32; 33; 34]. Figure 5 shows the correlation values of the reference samples according to the \(nTbS\) size and the video resolution shown as A1, A2, B, C, and D. The reference samples have a high correlation in the large \(nTbS\) and a low correlation in the small \(nTbS\), respectively, which means that small \(nTbS\) have high-frequency characteristics consistent with a low correlation and large \(nTbS\) have low-frequency characteristics consistent with high correlation. VVC uses two interpolation filters as explained in Section 2.1: 4-tap DCT-IF is used for all blocks when \(nTbS\) = 2, alternatively 4-tap DCT-IF or 4-tap SIF is used when \(nTbS\) = 3 or 4 depending on \(minDistVerHor\) in Equation (4) and \(intraHorVerDistThres[nTbS]\) in Table 3, and 4-tap SIF applied to all blocks when \(nTbS\) \(\geq\) 5. In this paper, in addition to the proposed interpolation filters, we also propose a selection method of the proposed interpolation filters for generating accurate fractional boundary prediction samples using the frequency information of the integer reference samples. Even if the CU reference samples have a low-frequency characteristic, DCT-IF is used for the CU reference samples with \(nTbS\) = 2 in the VVC standard. However, from Figure 4, it is more effective to use SIF than DCT-IF when the CU reference samples have the low-frequency characteristics regardless of the \(nTbS\)_size. Similarly, even if the CU reference samples have high-frequency characteristics, SIF is used for a CU with \(nTbS\) > 4 in the VVC standard. However, it is more effective to use DCT-IF than SIF in Figure 4 when the CU reference samples have high-frequency characteristics regardless of the \(nTbS\) size. To solve this problem, a method was developed that selects two different filters which consist of  
Figure 5: Correlation of reference samples according to \(nTbS\) and picture resolution A1, A2, B, C, and D.  
SIF and DCT-IF, according to the frequency characteristics of the reference samples. The reference samples are transformed using the scaled integer one-dimensional (1D) DCT-II kernel to detect the high-frequency energy of the reference samples. The scaled DCT-II coefficient \(X[k]\), \(k\) = 0, 1, 2,..., N \(-\) 1, is derived from Equation (12) as follows:  
\[X[k]=\left(2^{6+M/2}\sqrt{\frac{2}{N}}\sum_{n=0}^{N-1}c_{k}x(n)\cos\frac{(n+1/ 2)\pi k}{N}\right)\gg shift \tag{12}\]  
where \(N\) is the number of reference samples necessary for \(X[k]\) and \(M\) is \(log_{2}(N)\), and shift is \(M+1\). After 1-D transform, high-frequency energy is observed in the transform domain. As the energy is concentrated in the low-frequency components, the reference samples are composed of homogeneous samples. However, as energy exists in the high-frequency components, the reference samples contain high-frequency samples, which indicates that the samples in the CU have high-frequency components. The transform size of the reference samples is set according to the intra prediction mode of the current block. If the intra prediction mode is greater than mode 34 (diagonal mode), the upper CU reference samples are transformed with the \(N\) = _CU width_ in Equation (12). Moreover, if the intra prediction mode is less than mode 34, the left reference samples are used with the \(N\) = _CU height_ in Equation (12). \(X[k]\) is used to measure the energy ratio of the high-frequency coefficients. If there exists energy in the high-frequency data, DCT-IF is used because the reference samples are composed of high-frequency data. In contrast, SIF is used for high-energy reference samples in low-frequency data.