I am currently working with some data-sets that represents the movements of a beating heart and breathing lungs.
The data-sets are represented as a collection of floats that range from 47 to 51. We sample approximatly 70-100 of these values pr. second and they represent the change in movement of the organs.
Below is a sample of the respiratory rate. It shows how the lung expand and contract durning a period of 29 seconds.
I have a strong fundament in Informatics and Techology - but a weak fundament in Mathematics. I know how I can achieve my goals by writing computer algorithms - but I want to go deeper and explore the domain of mathematics. Simply to challenge myself - and to learn something new.
Based on the image above and with the knowledge that this should be done in real-time, I am interested in achieving the following goals:
A. I want to clean up the signal. It would be of benefit to remove some of the unwanted noise - on the fly - in real time - and maybe with some continious adaptation.
B. I wonder how i can detect if the curve is going upwards, downwards or if it is flat (person is holding his breath).
C. I wonder how much time it took for the person to perform a full inhalation and exhalation cycle
It would be of great help if I could get some input/directions towards the subjects i should study in order to achieve some - or all of these goals. I am sorry if this issue seems elementary. I am simply a late bloomer when it comes to math.