Transient gain of antennas related to the traditional continuous-wave (CW) definition of gain

In previous papers the problem of appropriate definition of antenna gain and radiation pattern in time domain has been considered in some detail. Using time-domain reciprocity the definitions are made to apply in both transmission and reception. Since the time-domain parameters are equivalent to the related frequency-domain parameters considered over all frequencies, the time-domain parameters are not simple numbers, but in general vector convolution operators. Specifically the gain is related to an appropriately normalized effective height convolution operator. This can in turn be reduced to a scalar number by application of appropriate mathematical norms