System model of doppler shifted laser

[jmountney]

Hello all,

I am trying to model a received laser signal, x(t), reflected off a moving target. I am currently trying to model for both frequency change due to Doppler shifting as well as a time-varying phase shift, θ(t), due to the continuous change in distance from the target. My current model is as follows:

x(t) = cos(2∏(f+f0(t))t + θ(t)),

where f0(t) is the Doppler effect at time t and θ(t)=(distance at time t)/wavelength. I do not assume constant velocity so the f0(t) may change over time. It appears that trying to simulate both phase and frequency shifts simultaneously does not accurately model what I expect.

If there is a constant velocity it will introduce a constant frequency shift. However, if there is a constant velocity, this implies the target is in motion and therefore the phase constantly changes with respect to the distance from the target. In turn, the constant phase change appears to offset the frequency change.

I am not sure if this physical model is correct. Any comments or suggestions are welcome. Thank you.

 

[Valerie Park]

The model you have is correct for a moving target, however, the only thing that needs to be changed is the frequency shift due to the Doppler effect. Instead of having f0(t) as the frequency shift, it should be fd(t) = 2vf0/c, where v is the velocity of the target and c is the speed of light. This will take into account the velocity of the target in addition to the frequency shift.