. The directional analysis of ocean waves : an introductory discussion. Ocean waves. and / Q(X,Y,f) = Qoi(f) = / Roi(T) Sin(2^fT)dT. () We also have (see Equations () and ()) CoQ(f) = Cuif) = ^qqCO = Pll(f). Qoo(f) = Qii(f) = 0; P8i(f) = coi(f) - 1 Qoi(f)- (^-10) The phase of Pq,(f) is given by Qoi(f) = Arctan -^^^J^ • (^-H) This is the expected phase lead of the signal at (x , y ) over the signal at (xj^, y^) for f where - » < f . For an array of N detectors located at (x]^, y^) , (x2, y2)» (xo, yo) ...(xj^, y^j) we can find N spectra [Pj^-s] i = l,N,j=l,N. This gives a unique spe
. The directional analysis of ocean waves : an introductory discussion. Ocean waves. and / Q(X,Y,f) = Qoi(f) = / Roi(T) Sin(2^fT)dT. () We also have (see Equations () and ()) CoQ(f) = Cuif) = ^qqCO = Pll(f). Qoo(f) = Qii(f) = 0; P8i(f) = coi(f) - 1 Qoi(f)- (^-10) The phase of Pq,(f) is given by Qoi(f) = Arctan -^^^J^ • (^-H) This is the expected phase lead of the signal at (x , y ) over the signal at (xj^, y^) for f where - » < f . For an array of N detectors located at (x]^, y^) , (x2, y2)» (xo, yo) ...(xj^, y^j) we can find N spectra [Pj^-s] i = l,N,j=l,N. This gives a unique spectrum P^^ (Pn = ... = P^jvj; and since P^^ = 'P^, (see Equation () and )) J Ji we have NOhl) (4,12) 2 unique cross spectra or a total of [N(N-l) + 2]/2 unique spectra. Thus, for real n(x,y,t) we have Pi^(f) = P=^j,(f) and P^.(f) = P* (-f) allowing us to define the information about PXA,Y,f) obtainable from an array by a cross spectral matrix •. () 16. Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original Bennett, Carl M; Naval Coastal Systems Laboratory (U. S. ). Panama City, Fla. : Naval Coastal Systems Laboratory
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