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
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!