[mus422] HW 1 problem 2f comments

[Craig Sapp]

Hello Music 422 Class,

Here are some comments for answering question 2f on Homework 1
(hopefully I will not be confusing you too much):

This question takes the samples calculated in question 2e, and applies
sinc functions centered at these points to generate the reconstructed
signal.

A hint is that the reconstructed signal at the sample points is
identical to the original signal (unless I don't know what I am talking about).
Each sinc should only be non-zero at one sample, if you set the frequency
of the sinc properly.  At all other samples, the individual sincs should be 0.

If you use floating-point arithmetic to do the reconstruction,
there will most likely be some round-off errors; however, a purely mathematical
reconstruction will not have round-off errors.  And I interpret the question as
being that Marina wants you to look at errors which are not related to
rounding off.

So when you answer "How well does it do?", you should not be looking
only at time sampled times from question 2e (which should be zero, or have
some round-off error); rather, you should be looking between these original
sample points.  You might also want to peek a little bit before time 0 and
after time 1/2 if you are curious.

Both the original signal and the reconstruction are continuous functions.
It would be acceptable to me for you to sample the original signal and the
reconstructed signal at a different sampling rate such that you also
look at points which are not in the original set of points used to generate
the reconstruction calculated in 2e.

Another hint: when you plot both the original signal and the reconstruction,
they will appear identical because any differences are very small and are
not visible.  So instead of plotting both as part of your answer to question 2f,
it would be more illuminating to plot the difference between the two.  Zooming
in on a small region of a plot which shows both functions is also acceptable,
but remember to show some points which were not in the set calculated in
problem 2e.

A bonus HW late day if you can calculate the signal summary properties (such
as in questions 2b & 2d) for a signal which is the difference between the
original signal and the reconstructed signal.

-=+Craig