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Transform, as one of the most important modules of mainstream video coding systems, seems very stable over the past several decades. However, recent developments indicate that bringing more options for transform can lead to coding efficiency benefits. In this paper, we go further to investigate how the coding efficiency can be improved over the state-of-the-art method by adapting a transform for each block. We present a variable block-sized signal-dependent transforms (SDTs) design based on the High Efficiency Video Coding (HEVC) framework. For a coding block ranged from $4\times4$ to $32\times32$ , we collect a quantity of similar blocks from the reconstructed area and use them to derive the Karhunen–Loève transform. We avoid sending overhead bits to denote the transform by performing the same procedure at the decoder. In this way, the transform for every block is tailored according to its statistics, to be signal-dependent. To make the large block-sized SDTs feasible, we present a fast algorithm for transform derivation. Experimental results show the effectiveness of the SDTs for different block sizes, which leads to up to 23.3% bit-saving. On average, we achieve BD-rate saving of 2.2%, 2.4%, 3.3%, and 7.1% under AI-Main10, RA-Main10, RA-Main10, and LP-Main10 configurations, respectively, compared with the test model HM-12 of HEVC. The proposed scheme has also been adopted into the joint exploration test model for the exploration of potential future video coding standard. [ABSTRACT FROM AUTHOR]