Digital filtering is concerned with the manipulation of discrete data sequences to remove noise or extract certain desired information. Discrete or digital signals are somewhat intuitive to human beings despite their rarity in nature. That is, people tend to make and tabulate measurements of physical entities in sets of data values with limited precision, while the entities being measured vary continuously both in their functional dependence and value.
The bandwidth of a channel describes the maximum rate of change in the input to which the channel can respond. This quantity limits the signaling rate that the channel can accommodate. For a signal: the width of its amplitude spectrum in the frequency domain. For a filter, the width of its passband.
Noise refers to random distortion that the channel introduces into the transmitted signal.
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