Sampling at 6 Hz cannot distinguish these 1 Hz and 7 Hz sinusoids: they differ by a whole cycle between adjacent samples. Without a suitable band limit before sampling, distinct continuous signals can produce identical sample sequences.以 6 Hz 采样时，图中的 1 Hz 与 7 Hz 正弦波无法区分：它们在相邻采样点之间相差一个完整周期。采样前若没有适当的带限，不同连续信号就可能得到完全相同的样本序列。
The slowly varying green wave and rapidly varying cyan wave meet at every gold sample. The moving marker visits times , not the unobserved points between them.缓慢变化的绿色波与快速变化的青色波经过每一个金色采样点。移动标记依次经过 时刻，不经过样本之间未观测的位置。