34 Lecture 2 
5 
SIGNAL = > Am cos (mpt +&m) 
m=1,2,3,.. 
ARRAY 
a 
» Em cos(mpt +x. +m) 
r i) 
» Em cos(mpt +%, - mg) 
: CUT OFF SPECIAL 
>rp FILTER 
MULTIPLIER 
r 
- DIC RES cos 2m¢ 
m=1,2,3,.. 
Fig. 2.3. Multifrequency multiplicative pair (with provision for superdirectivity). 
Now the amplitude £2 determines the "taper" of the array, and it is clear 
that, if desired, this taper (although effective at the receiver) may be imposed 
at the transmitter by giving different amplitudes to the transmitted signal com- 
ponents. But it should also be noted that if the transmission properties of the 
medium (or the target strengths in an echo-ranging system) are different at 
different frequencies, then an unwanted taper function will be imposed. 
When all harmonics are used (i.e., m=1,2,3,...), then, in the space-fre- 
quency equivalence, this corresponds toa multielement array with an odd number 
of elements but with the central element omitted. The effect of the central ele- 
ment can be obtained by adding tothe output of the multiplier a dc voltage derived 
from the square-law rectification of the output of one of the array elements. 
Superdirectivity can be obtained with this system; and if approached from 
the point of view that a particular number of frequencies (or pairs of elements 
in the corresponding "spatial," or multielement, array) is specified and that a 
superdirective response is to be obtained from it, then superdirectivity can be 
obtained easily. On this basis the problem reduces to (a) choosing p and d so 
that the number of wavelengths in d progresses by less than one wavelength for 
