What you will learn:

  • Software: practice with loops and operations on arrays
  • Domain: approximations and error measurements, sampling

Input: Construct a (continuous) signal of your choice – say a simple sine
wave with a particular frequency and amplitude. Plot this. Note that since you
are representing the continous signal on a computer, so you are already
sampling it.

Discretization in space:

  • For the amplitude, choose a $n$ and divide the range into $2^n$ steps. For each index of your signal, (i) round up (ii) round down and (iii) round to the nearest step value.
  • Calculate the mean squared error due to this process.
  • Repeat for different values of $n$
  • Plot the error for different values of $n$. Does this match what you think it should look like?

Discretization in time:

  • What happens if you take fewer / more samples in time for representing your signal? How would you now determine the quality of your representation?
  • What is the lowest you can go? How does this relate to the frequency of the signal? (*cough* nyquist *cough*)

Discretization in both dimensions

  • Try it out!
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