A fast filtering method for digital signals of electronic measuring instruments in the laboratory based on Fourier transform

In response to a series of problems such as high computational complexity, slow processing speed, poor denoising effect, signal loss, energy attenuation, and decreased transmission performance that traditional filtering methods face when filtering digital signals from electronic measuring instruments in the laboratory, a fast filtering method for digital signals of electronic measuring instruments in the laboratory on the basis of the Fourier transform is studied. Based on the Fourier transform, an adaptive time–frequency filtering method based on the fractional Fourier transform is proposed. By utilizing the important characteristic that this transform is equivalent to rotating the signal in the time–frequency plane, mixed noisy signals are subjected to a fractional Fourier transform at a specific rotation angle to minimize the overlap between the signal and noise in the transform domain. The linear frequency modulation (LFM) signal is filtered and extracted through fractional Fourier transform method. Most of the noise energy is removed, and the original LFM signal is recovered by fractional Fourier inverse transform to realize the rapid filtering of high-quality digital signals of electronic measuring instruments in the laboratory. Experiments have shown that using this filtering method to denoise digital signals from laboratory electronic measuring instruments can not only reduce computational complexity, improve filtering speed, but also enhance filtering effectiveness. The filtered signal has low noise content, high restoration, good transmission performance, reduced attenuation, and strong anti-interference ability. At the same time, it can effectively remove various types of noise, with an average improvement percentage of 15.68% in signal-to-noise ratio. It also maintains the integrity of data sampling and the accuracy of statistical results, which is conducive to further analysis and research.