Fast convolution algorithms, including Winograd and FFT, can efficiently accelerate convolution operations in deep neural networks. However, these algorithms depend on high-precision arithmetic to maintain inference accuracy, which conflicts with the model quantization. To resolve this conflict, this paper proposes a new algebra transform for fast convolution by extending the Discrete Fourier Transform (DFT) with symbolic computing, in which only additions are required to perform the transformation at specific DFT points, avoiding the calculation of irrational number and reducing the requirement for precision.Additionally, we enhance convolution efficiency by introducing correction terms to convert invalid circular convolution outputs of the Fourier method into effective ones. We also analyze the numerical error generated by convolution algorithms, and proved that our algorithms can achieve 3.86× reduction in arithmetic complexity while the Winograd algorithm only achieves 2.25× reduction at equivalent numerical accuracy. Experiments carried out on Imagenet and FPGA demonstrate the effectiveness of combining our algorithms with model quantization, which can further improve the computation efficiency while maintaining model accuracy at the same level as quantization-alone or existing works on fast convolution quantization.