Discretization issue with AMS591f_0100_DB sensor

We have been trying to measure pressure signals in small animals in an enclosed chamber. We are trying to calculate total volume changes in the animal when they are spontaneously breathing. Now an average breathing rate of a small animal is around 3 ~3.5 breaths per second. So I am trying to capture a pressure sample at 1 or 2 ms on average. the problem I am running into is a discretization error as shown below in figure 2.

figure 1, is spontaneous breathing measured by the sensor. Figure 2 shows the breathing rate of the animal after filtering. As you can observe there are flat regions that appear between each sample.So wondering what kind of an amplifier came along with the pressure sensor and can we get a more amplification with a customized amplifier to resolve this vertical resolution issue ? Any suggestions or help would be useful.