D. G. Tucker 3] 
Fig. 2.1. Multiplicative and additive 
directional patterns for the same 
array of eight elements; (a) multi- 
plicative (b) additive. 
(b) 
to rectify this for display. Thus all the lobes in the directional pattern become 
of the same polarity (say positive). But in the multiplicative array, the output 
is de and the largest secondary lobes of the directional pattern are of negative 
polarity as is shown in Fig. 2.1. Thus, response from signals arriving from 
directions corresponding to these lobes can be eliminated by the use of a rec- 
tifier following the multiplier and its low-pass filter; or with an intensity-modu- 
lated display ona cathode-ray tube, signals from these directions will not brighten 
the screen. 
There are, of course, complications and disadvantages. One complication is 
that the doubled directionality strictly applies only to the directional variation 
of output from a single source as the array is rotated; it is not the same 
thing as directional discrimination. Whereas in the linear additive system direc- 
tional response and directional discrimination are essentially the same thing, in 
the multiplicative (and nonlinear) system they are not. Welsby has shown, how- 
ever, at least for some important practical situations, that resolution of two 
targets at the same range is approximately doubled [3]. The limited experi- 
mental experience we have so far had of within-pulse scanning sonar using the 
multiplicative system (see below, Section 2.3) adequately confirms this. The 
reduced secondary response of the multiplicative system has also been shown 
to be genuinely realized in a multitarget situation. One of the disadvantages 
referred to is the fact that signal-noise discrimination is 3 db worse than in 
the additive system. 
Welsby has recently discovered that some use can be made of the double- 
frequency output of the multiplier when the signals are of coherent type [4]. If 
this output is rectified and added tothe dc discussed above, then the signal-noise 
discrimination at the peak of directional response can be partially restored—to 
the extent of 1.6 db; and if subtracted instead of added, it can lead to a further 
narrowing of the main beam. 
The use of multiplicative reception has been known for a long time in con- 
