How to create a Continuous Fourier Series

Hi Everyone, I'm currently working on a project where I need to create a Fourier Series for an array of values from a function generator using the continuous time TFS (with ao, an, bn, and f(t)). The goal is to plot f(t) iteratively for each n to show the progression to fit to the function. I have been able to get ao working with trapz without issue but I am having extreme difficulty approaching how to find an and bn since the array isn't an actual function. I don't know whether to apply trapz or int or anything else since I know int(f(t)*g(t)) does not equal int(f(t))*int(g(t)) I have a discrete time version written with the magnitude and phases of the analysis function Dr and am able to inverse transform it to get f(k) but then I don't know how to take Dr and represent approaching the final form through a progression of summed sinusoids. Any help is greatly appreciated. Thanks

[Image Analyst]

Everything in your computer is discrete/digitized/quantized, not continuous.

[Eric Cheatwood]

Yes, I understand this and that is why I am having such a difficult time doing this. Just to clarify this though, you do not see any way to cleverly code the continuous time TFS to represent a function or array in discrete time? (I know its common sense to use the discrete transform to represent discrete information but the instructor is adamant that a discrete array can still be represented this way.)