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The concept of "bandwidth" is commonly used as a measure of the range of frequencies over which a network has an approximately constant gain. In this note the notion of bandwidth is extended to networks with arbitrary transfer characteristics. Specifically, it is defined in terms of the maximum allowable variance of the output of a network (to within a multiplicative constant) from that of an "ideal" network, the input being a band-limited signal. The maxum bandwidth of such an input signal is termed the bandwidth of the network under consideration.