# What is the smallest sampling points that can recover the signal?

Propose that we have a signal with a model of $$f_{4at0} = v_0(1 - \epsilon + \epsilon \exp(-c_l(t_{t2d}-t_0)))$$

$f_{4at0}$ is dependent variable while $t_{t2d}$is independent variable,others are parameters.

It is a representation of the relationship of biological material concentration-time that is inside the blood serum.Since this material cannot be assayed real time in the human body, the blood samples have to be collected from patients.It's really inconvenient to obtain blood samples from human.So, my question is what's the lower limit of sampling points? And how to schedule the sampling points?

ps: here is the matlab code that I used .I want to use the "Nyquist Sampling Principle",but I don't know how.

cl=6.2;

epsilon=0.95;

t0=0.3625;

delta=0.1;

v0=1000000;

f4at0=v0*(1-epsilon+epsilon*exp(-cl*(tt2d-t0)));

syms tt2d;

f4=v0*(1-epsilon+epsilon*exp(-cl*(tt2d-t0)));

fourier(f4,tt2d)


Output:

ans =

100000*pi*dirac(-tt2d) + 950000*transform::fourier(exp((31*tt2d)/5 + 899/400), -tt2d, -tt2d)

I don't know how to understand transform::fourier(exp((31*tt2d)/5 + 899/400), -tt2d, -tt2d).

I don't know how to calculate T since there is also a Dirac function. I don't know if there are other principles apart from the "Nyquist Sampling Principle" that can be used here.

• You need to provide some more background on your signal model. In order to meet the Nyquist criterion, you need to have samples regularly enough that you have more than 2 for each component in the signal that is periodic in $t_{t2d}$ (assuming that this isn't a bandpass signal, which is probably the case). – Jason R Sep 21 '11 at 13:15