The semi-tensor product of vectors generalizes the conventional inner product, enabling algebraic operations between vectors of different dimensions. Building upon this foundation, we introduce a domain-based convolutional product and integrate it with the STP to formulate a padding-free convolutional operation. This new operation inherently avoids zero or other artificial padding, thereby eliminating redundant information and boundary artifacts commonly present in conventional convolutional neural networks. Based on this operation, we further develop an STP-based CNN framework that extends convolutional computation to irregular and cross-dimensional data domains. Applications to image processing and third-order signal identification demonstrate the proposed method's effectiveness in handling irregular, incomplete, and high-dimensional data without the distortions caused by padding.