Translation of a time signal in space by FFT and IFFT

Dear all,

Currently i am looking to translate my time signal, which has been taken at point 'X' to point 'X+1.875'. The way i am doing this is as follows:

• Applying a FFT to get each individual wave
• For each individual wave, determine the wave number 'k'
• Determine the phase per fase
• determine the phase shift (length x k)
• determine the new waves at the new point
• inverse fft of new waves

But by doing this, the amplitude decreases significantly of my wave crests and increases in my wave through. Can anyone spot a mistake?

if true
S=fft(wle);
T=length(wle)/Fs;
f=[0:1/T:1/2*Fs 1/2*Fs-(1/T):-1/T:1/T];
figure, plot(f,sqrt(S.*conj(S)));
hold on; plot(f,abs(S));
kd = 0:0.001:10000;
w2d=g*kd.*tanh(kd*h);
w=2*pi*f;
k=interp1(w2d,kd,w.^2);
figure, plot(k,sqrt(S.*conj(S)))
hold on; plot(k, abs(S))
Z = angle(S);
L = -1.875 ;% (somehow it translated 1.875m forward when L is set negative....)
da = L.*k';
amp2 = abs(S);
S_sh2 = amp2.*cos(Z+da) + i*amp2.*sin(Z+da);
S_sh2 = [S_sh2(1:561);conj(S_sh2(560:-1:2))];
wle_sh2 = ifft(S_sh2,'symmetric');
plot(t,wle,'r',t,wle_sh2,'k')
end

Blue is the original signal, black the newly translated signal to 1.875 meter forward