same as in Figure A2a. The wave In Figure A2b, however, has a different k^ 

 in the direction along the array. The signal detected by the sensor at 

 y = Yz is different from that in Figure A2a. To distinguish between the d-^ 

 and ^2 propagation directions, the pressure sensors need to be sensitive 

 enough to distinguish the two amplitudes at J = Jz • One obvious solution 

 may be to place the sensors farther apart. However, there is a risk of 

 another problem, called aliasing. 



13. Aliasing occurs when the sensors are separated by more than half 

 the wavelength of the shortest wave that may be encountered. If this occurs, 

 a short wave cannot be distinguished from a longer wave through the phase 

 information available; both give the same phase difference for a given sensor 

 separation. It is impossible to determine which one is present (Figure A3) . 



14. At a given frequency, the longshore component of an incident wave 

 is shortest when its direction is 90 deg off the normal. To avoid aliasing, 

 it is necessary to make sure that the sensors are not separated any farther 

 than one -half of this wavelength. The trade-off is that this separation may 

 not be large enough to give the desired directional resolution. 



15. Actually, the problem is more severe than that. In a real ocean 

 environment, it is desirable to measure waves at all wind wave frequencies. 

 Resolution of high frequency (short wavelength) waves requires a small sensor 

 separation. Lower frequency (long wavelength) waves will, therefore, be 

 sorely deficient of any directional resolution because, for them, the separa- 

 tion is too small. 



16. This situation can be improved by using more than two sensors. The 

 number of sensors required will depend both on the range of wind wave frequen- 

 cies covered and the degree of directional resolution desired. 



Linear Array with Four Sensors 



17. This section explains the advantages of using more than two sensors 

 to improve resolution and avoid aliasing. The concept of coincident and 

 quadrature (Co and Quad) computations is introduced for analyzing data from 

 multielement linear arrays. An array of four sensors is considered. 



18 . The problem becomes one of determining sensor placement so that 

 gage response is optimized. A set of four sensors could be placed so they are 

 separated by equal distances with spacing between adjacent sensors given the 



A7 



