The theory developed in the preceding paper is applied to a number of questions about timelimited and bandlimited signals. In particular, if a finite‐energy signal is given, the possible proportions of its energy in a finite time interval and a finite frequency band are found, as well as the signals which do the best job of simultaneous time and frequency concentration.

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The purpose of this paper is to examine the mathematical truth in the engineering intuition that there are approximately 2WT independent signalsV'i of bandwidth W conceturated in an interval of length T. Roughly speaking, the result is true for the best choice of the V'i (prolate spheroidal wave functions), but not for sampling functions (of the form sin tit). Some typical conclusions are: Let f( t), of total energy 1, be band-limited to bandwidth W, and let +N 12 anV'n dt < CE(

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