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Subtract the received signal from the original signal (downconvert) to find the difference if they are coherent or use a long fft to find the shift. If the new signal is shifted up in frequency, it is closing (blue Doppler). If it is down in frequency is is receding (red Doppler). Try to think...
Try running a small data set through the MATLAB profiler. This will tell you where the offending (slow) bits of code are. Often the problem is simple (not pre-allocating matrices or appending datasets in loops). MATLAB also executes datasets faster when indexing by row rather than column.
Chirp function is
x(t) = sin[2*pi(f*t*+k/2*t+phi)]
set you time vector (eg. t = 0:ts:1)
k is the chirp rate, f the carrier frequency and phi the initial phase (can set to 0).
in MATLAB should look something like this: x = sin(2*pi(f*t*+k/2*t+phi))
Have a look at this TI application note:
https://www.ti.com/lit/an/slaa274b/slaa274b.pdf
It has the details for the equation and the model used to calc the SpO2 that you are after.
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