Suppose we wish to create a vector of zeros using a variable sampling rate Fs.
i) If we want the vector to have a duration of 5 seconds (starting at time t = 0), what is the formula for the number of samples nz we need in terms of Fs?
ii) At what index in that vector should we insert a 1 in order to implement δ(t)? That is, what is the formula for the index in terms of Fs?
iii) How about for δ(t - 3)? That is, what is the formula for the index in terms of Fs at which we should insert a 1?
iv) Where should we insert a 2 for 2δ(t - 4)?