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线性时变滤波处理通常应用许多时间不变滤波来重迭一道时间区域并且转而去内插(merging)这些不同的时间区域来实现。我们现在描述一种不同类型的线性时变滤波的设计。该类滤波的频谱作为时间的一个函数沿频率轴平移,而谱形则无明显变化。这个设计是以一个具有期望谱形的时间不变滤波为基础的。对于长的滤波长度,这个设计程序是较复杂的。而且,频移速率只能是常数。然而,对于滤波长度上的频移比滤波带宽小得多的许多实际情况,时变滤波处理可以进一步地简化,而频率误差不大。事实上,通过使用指定的时变频移算子的预前应用和相应于频率恢复算子的以后应用来修改原始的时间不变滤波的复杂信号模型而达到时变滤波。在这个短滤波近似下,可以实现频移速率不均匀的更一般的时变滤波。褶积时变滤波的性质用采样正弦信号的滤波例子来说明。
Linear time-varying filtering usually applies many time invariant filters to overlap a time region and instead merging these different time regions. We now describe a different type of linear time-varying filter design. The spectrum of this type of filtering is shifted along the frequency axis as a function of time, while there is no significant change in the shape of the spectrum. This design is based on a time invariant filter with the desired spectrum. This design procedure is complicated for long filter lengths. Moreover, the frequency shift rate can only be constant. However, for many practical cases where the frequency shift over the filter length is much smaller than the filter bandwidth, the time-varying filtering process can be further simplified without a significant frequency error. In fact, time-varying filtering is achieved by using the pre-application of the specified time-varying shift operator and the later application corresponding to the frequency recovery operator to modify the complex signal model of the original time-invariant filtering. Under this short filter approximation, more general time-varying filtering with non-uniform frequency shift rates can be achieved. The nature of the convolution time-varying filtering is illustrated by the filtering example of a sampled sinusoidal signal.