t = 



Figure A3. Example of aliasing (the short wave is not aliased) 



symbol YLAG . By Equation A5 , phase differences between equally spaced 

 sensors in a well-behaved wave field are the same. This would lead to three 

 independent but redundant estimates of 6 from Equation A9 . However, the 

 most serious need is not redundancy but measurement of nonaliased, well- 

 resolved phase differences for all wind wave frequencies. 



19. With four, equally spaced sensors, it can be seen that phase 

 differences between the end sensors, whose separation is 3 -YLAG , can also be 

 detected. While this may give an aliased phase measurement for high-frequency 

 waves, it would provide not only a nonaliased phase for low-frequency waves 

 but also a more effective sensor separation for directional resolution of low- 

 frequency waves. This suggests that better use of the four sensors can be 

 made by trying to make all sensor separations unique. Such an arrangement 

 avoids redundant measurements and provides a variety of spacings which lead to 

 nonaliased, better-resolved phase measurements for a variety of wave frequen- 

 cies. A good design might be what is referred to as a 1-2-4 array. In this 

 design, the first and second sensors are separated by YLAG , the second and 

 third are separated by 2 -YLAG , and the third and fourth are separated by 



4 -YLAG . The total possible combinations of sensor pairs would allow phase 

 estimates from sensors separated by (1, 2, 3, 4, 6, and 7) -YLAG . This 

 arrangement increases the range of wind wave frequencies at which good 

 direction resolution can be obtained. 



20. The above discussion introduces the concept of lag- space , which is 

 a convenient way to discuss and design linear arrays. Instead of thinking 

 about linear arrays in terms of absolute (x,y) sensor locations, arrays can 



A8 



