FMCW Radar – Vital signs Measurements
4
4
4
()
bb
BR
j t R
j f t
cT
b t e e
Note that for a single object, the beat signal b(t) is a sinusoidal and has both frequency 𝑓
𝑏
and phase ∅
𝑏
To measure small scale vibrations, we measure the change in phase of the FMCW signal with time at the
object range bin. If an object moves a distance ∆R then the change in phase between consecutive
measurements is given by
Phase can be measured by taking the FFT of the beat signal b(t) and computing the phase at the object
range-bin.
Suppose we take the FFT and the object is at range-bin m, then the vibration signal x(t) can be extracted by
measuring the phase at range-bin m at time indices nT
s
, where n is the chirp index and T
s
is the time
between consecutive measurements
Note that we are assuming that the vibrations x(t) are
small so that the object remains in the same range-bin
during the duration of the measurements
As an example at λ=4 mm when we have displacements as
small as ∆R = 1mm, the corresponding phase change is
( , ) ( , )
4
s b s
x m nT m nT
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