Signal phase, In-phase and antiphase signals For a single spin I, one gets the following signal during acquisition with receiver reference phase x l、→>Icos(g2t)+ Iy sin(g2t) Iy>ly cos(Q2t)-I sin(S2t These two signals are 90 out of phase(also after FT), which is indicated by one Ix component having a sine. the other one a cosine modulation For a spin I, coupled to another spin I one gets the following signal during acquisition(neglecting chemical shift evolution) Ix> Ix cos(2t)+ ly sin(g2t) I cos(Ωt)cos(πJt)+2 Ily 12z cos(2tsin(πJt ly sin(Q2t)cos(t)-2 I1x I2z sin(Q2t) Sin(πJt) the detected x component corresponds to an in-phase dublet with splitting J, i.e., lines with intensity /2 at positions(Q2+12)and(Q2-12) t 2兀/2t) cos a cos B=//2 [ cos(a+B)+ cos(a-B) 2 I1x 12z>2 Iix lz cos(@2t)+ 2 Ily 12z sin(S2t)> 2 IIx lz cos(Ωt)cos(πJt)+ Ly cos( Q2t)sin(πJt) 2 lly I2z sin(Q2t)sin(TJt)-I sin( @2t) sin(TJt) this tiem the x component corresponds to an anti-phase dublet with splitting J, i.e., lines with intensities of /2 and -/2 at positions(Q2+12)and(Q2-12)34 Signal phase, In-phase and antiphase signals For a single spin I1 one gets the following signal during acquisition with receiver reference phase x: Ix ® Ix cos (Wt ) + Iy sin (Wt) Iy ® Iy cos (Wt ) - Ix sin (Wt) These two signals are 90° out of phase (also after FT), which is indicated by one Ix component having a sine, the other one a cosine modulation. For a spin I1 coupled to another spin I2 one gets the following signal during acquisition (neglecting chemical shift evolution): Ix ® Ix cos (Wt) + Iy sin (Wt) ® Ix cos (Wt) cos (pJt) + 2 I1y I2z cos (Wt) sin(pJt) + Iy sin (Wt) cos (pJt) - 2 I1x I2z sin (Wt) sin(pJt) the detected x component corresponds to an in-phase dublet with splitting J, i.e., lines with intensity 1 /2 at positions (W + J /2) and (W - J /2) ( pJt = 2p J /2 t ). cos a cos b = 1 /2 [cos (a+b) + cos (a-b)] 2 I1x I2z ® 2 I1x I2z cos (Wt) + 2 I1y I2z sin (Wt) ® 2 I1x I2z cos (Wt) cos(pJt) + Iy cos (Wt) sin (pJt) + 2 I1y I2z sin (Wt) sin(pJt) - Ix sin (Wt) sin (pJt) this tiem the x component corresponds to an anti-phase dublet with splitting J, i.e., lines with intensities of 1 /2 and -1 /2 at positions (W + J /2) and (W - J /2) :