A matrix method for constructing a discrete cosine-sine transform of order N is proposed, upon which discrete and integer cosine-sine transforms of order 16 are constructed. A fast algorithm for computing an integer cosine-sine transform of order-16 with low multiplicative complexity, which is 8.25 times smaller and requires 115% more addition operations compared to the fast discrete cosine-sine transform algorithm, is presented. Additionally, a fast algorithm for computing 2D 16-point integer cosine and cosine-sine separable adaptive transforms with low multiplicative complexity for intra-prediction with 16x16 blocks has been developed. The proposed transforms are effective in the modes of 2D and separable adaptive transforms, providing high coding efficiency in terms of accuracy and compression ratio.

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L. O. Hnativ and Ya. V. Luts, "Discrete cosine-sine transform and fast 16-point integer cosine-sine transform low-complexity for video coding," Proc. SPIE 13137, Applications of Digital Image Processing XLVII, 1313715 (Presented at Optical Engineering + Applications: August 22, 2024; Published: 30 September 2024); https://doi.org/10.1117/12.3035173.