Respiration (breathing) signal movement artifact removal

Situation: I have breathing data of participants who have done different things during the study which caused their breathing change; watching mindless video to which resulted in unconscious regular baseline breathing; attending to a pacer with causes slow-paced breathing in range of 5 to 9 breath per minute; performing a stressor task which cause breathing to become fast and irregular.

Goal: I need to extract breath per minute (BPM) and breathing irregularity (using FFT).

Challanges. Participants’ movement caused the signals look noisy . Note: this is a baseline data which supposed to be regular. I need to remove the artifacts related to movement but I don’t know how. Why is this important? My BPM values can be wrong and the FFT gives a large power to frequencies very close to zero.

File examples: http://stanford.edu/~parism/HPC_physio_split_undownsampled_256_example/
These are files from a person in the treatment group. The sequence of the columns in the file is as follows:
‘Time’,’BVP’, ‘EDA’, ‘Temp’,’ABD’, ‘CST’,’Label’

The treatment group received the breathing pacer intervention during pre-, stressor, and post- block2. That means the pacer created vibration patterns at frequency of 6breath per minute (for this participant) to breathe with. During the pre- and post- stressors, the participant is not experiencing any cognitive tasks. Therefore they are very likely to synchronize their breathing with the pacer. During the the stressor2 tasks, they are less likely to do so. The pre- post- and stressor 1 blocks are similar to those in block 2. The only difference is that the participant is not receiving any intervention. Therefore they are less likely to do slow-paced breathing.

During the baseline the participant is not receiving any vibrations. They are just breathing at their resting heart rate. During the meditation phase, the participant is listening to an audio to pace to practice slow-paced breathing. We derived the pace of the pacer (in this example 6) from the last 30 seconds of this file. During the Practice, the participant is breathing with the pacer for about 90 seconds to ensure that they are comfortable with the pacer’s pace.

Thank you in advance for help.