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Explicit expressions are given for the evaluation of the Wigner distribution for the case where the signal is of finite duration (or finite bandwidth), and where the functional form of the signal is given by two different expressions. Furthermore, the case where the signal is zero for a time (or frequency band) between the two regions is considered. This general case encompasses many particular cases. We specialize to limiting cases including infinite endpoints. Similar equations are given for the evaluation for the ambiguity function, which is the characteristic function of the Wigner distribution. The cataloging of explicit formulas should be of practical utility for the calculation of the Wigner distribution for signals of the type considered.