My sloppy terminology is confusing some people.
First, I use the term "ideal" or "true" low pass filter to mean a filter whose
attenuation is zero outside of its passband and one inside of its passband.
Second, saying "squaring" the filter kernel in 2B and 2C is not well defined.
By squaring, I mean applying the filter to the signal twice, or applying the
filter to itself (and then to the signal).
This means convolving the kernel with itself in the time domain, or multiplying
it by itself in the frequency domain.
Third, in my notes in the reader, there are some minor arithmetic mistakes in
the pictures that have the convolution examples. I also play a little fast and
lose with some of the notation of convolution. Specifically, the signals
get flipped around, and I don't really say where the results "start."
For the purposes of the assignment, it doesn't matter much - if you reverse
the order of the convolution kernels, you'll get a different answer thats OK,
and we aren't too specific about where the short signals begin and end.
To clarify some of the questions about convolution, I fixed some of my signal
processing notes. Pages
14-16 have been redone. Hopefully these will help.