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监测设备的振动通过谱分析来判别其运行状态往往是行之有效的方法。本文根据循环圆卷积矩阵的逆阵仍然是循环圆卷积矩阵的原理，提出了利用快速付里叶变换（ＦＦＴ）快速解线性卷积和反卷积的时域反滤波计算方法，并应用此算法对气缸压力波形进行了时域恢复。该算法与传统的卷积和反卷积计算方法相比，乘法次数少，计算速度快，便于对信号实时处理。采用时域反滤波方法恢复时域波形比基于频域变换重建气缸压力波形方法，计算环节少，易于硬件实现，对源信号的实时远距离监测和故障诊断具有十分重要的意义。
Monitoring equipment vibration spectrum analysis to determine its operating status is often an effective method. Based on the principle that the inverse matrix of circular circular convolutional matrices is still a circular convolution matrix, a time-domain inverse filtering method using fast Fourier transforms (FFTs) for fast linear deconvolution and deconvolution is proposed and applied This algorithm recovers the cylinder pressure waveform in time domain. Compared with traditional methods of convolution and deconvolution, this algorithm has fewer multiplications and faster computation speed, which makes it easier to process signals in real time. Compared with the method of reconstructing the pressure waveform of the cylinder based on the frequency domain transform, the time domain inverse filtering method can recover the waveform in the time domain. The method has fewer calculation steps and is easy to be implemented in hardware. It is of great significance for real-time remote monitoring and fault diagnosis of the source signal.