This paper proposes a real-time denoising algorithm for fiber optic gyroscopes based on redundant second-generation wavelet transforms. The algorithm directly utilizes predictors and updaters with zero-padding interpolation to decompose and reconstruct signals. This approach ensures that the lengths of the approximation and detail signals are the same as that of the original signal, thus preventing signal distortion after reconstruction. The results of experiments on both simulated and actual output signals from fiber optic gyroscopes demonstrated that the algorithm effectively preserved the temporal characteristics of the signals, ensuring that their integrity and accuracy were not compromised by the denoising process. Moreover, it decreased the quantization noise by approximately 50.23%, decreased angular random walking by approximately 19.14%, and mitigated bias instability by approximately 53.02%. Thus, it provides an effective method for signal processing in fiber optic gyroscopes.