D. G. Tucker 35 
PHASE - 
SHIFT 
) 2p 3p 4p Sp 6p FREQUENCY 
Fig, 2.4. Phase—frequency requirement of special filter in Fig. 2.3. 
each step in m, i.e., the equivalent spatial elements are less than half a wave- 
length apart and (b) reversing the polarity of alternate frequency components. 
The latter can be done by inserting the special filter in one channel, as shown 
in Fig. 2.3, having a phase shift-frequency characteristic as shown in Fig. 2.4. 
The values of E,, are then chosen to give the required directional response. For 
more complicated cases of superdirectivity, it is always possible to separate 
the various frequency components before multiplication, multiply them separately, 
and then adjust amplitudes and polarity as requiredin the separate outputs before 
they are finally added together. 
It is clear that superdirectivity obtained witha multifrequency array removes 
much of the difficulty of interelement coupling that was mentioned in Section 
2.2.2, since it is probably only at the lowest frequency that the elements are 
less than half a wavelength apart. 
The system so far described involves frequencies spread over a rather wide 
band; it may be useful at low frequencies where a full array would be too large 
for handling, but where a two-element array could have its transducers mounted, 
for example, on two different ships or ontwo different towed bodies. For narrow- 
band use at higher frequencies, the series of harmonics may be replaced by a 
series of frequencies 
(f + S8f) = nS S)Sir 
where 6 is small compared with unity. The frequency f should be transmitted 
at a relatively high level or be suitably enhanced or reinserted at the receiver 
[10]. The complex signals from the two transducers are separately envelope- 
detected before being multiplied together—see the example in Section 2.3.2. 
2.2.4. Wide-Band Arrays 
Normally, echo-ranging systems have fractional bandwidths, although it is 
well known that detection is improved as the bandwidth is widened—and properly 
utilized. We are developing a really wide-band system—9 to 1 ratio of upper to 
lower frequency—so that frequency response of the target as well as its range 
and bearing may be displayed. One of the more important problems to be solved 
