I will try to provide you with some hints based on what I understood from your post.
The ADC is supposed to sample the analogue signal generated at a defined frequency in order to yield a digital signal. In your case, you need two information to trace your curve:
- Data:
data to be traced (samples) which represents the amplitude of the signal all along sampling time (at each sampling instant).
- Time:
you need to know the period in time at which ADC is sampling the signal then associate each data with its corresponding instant in time. Period can be deduced from the frequency at which ADC samples signal T = 1/f.
ADC stores each sampled data in a register and an interrupt would be generated to notify processor about a new coming data. Your interrupt service routine (in case you are proceeding with interrupts) must be able to extract that data before it will be replaced by the next sample. As a suggestion, you may create a buffer within your application where your interrupt routine could store data in it. Then, your application can extract data from buffer and use it to draw the curve if your system has a display output or send it to a desktop application that will do the job.
You don't need to stick to the equation in your post; it is for analogue. Rather you can think of the digitized curve as f(t) = Data(t).
As you are using linux, if you don't want to deal with interrupts you may proceed with reading data using /sysfs interface. Note that opening a file to read data for every single sample could be slow depending on your application requirements.