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实现对离散信号数字处理的卷积滤波关键是设计期望的滤波器频谱。理论上理想低通滤波器能抑制噪声,改善系统传递信号的信噪比,但它对应的时间函数是一无限长的卷积因子序列,为方便实践必须做截断处理,这将产生吉布斯现象而导致频谱变坏,不能有效地抑制噪声,增强有用信号。本文给出了一种在做截断处理后具有最小吉布斯现象的滤波器频谱。并对选择不同截取时窗长度的截取误差进行了分析,对该滤波器的噪声抑制能力也进行了讨论。最后通过实验对系统进行了验证,给出了系统的实现框图。
The key to implementing the convolution filtering of the discrete signal digital processing is to design the desired filter spectrum. In theory, the ideal low-pass filter can suppress the noise and improve the signal-to-noise ratio of the system. However, its corresponding time function is an infinite length of convolution factor sequence. For the sake of practicality, it must be truncated, which will result in Gibbs Phenomenon causes the spectrum to deteriorate, can not inhibit the noise effectively, enhance the useful signal. This paper presents a filter spectrum that has the least Gibbs phenomenon after truncation. The choice of different interception time window length of the interception error analysis of the noise suppression of the filter are also discussed. Finally, the system is verified through experiments, and the block diagram of the system is given.