My solution to Problem of the Week #1 can be found outside Dr. Bovik's door (ENS 540). Please feel free to photocopy it but REMEMBER TO PUT IT BACK! Remember that others need to see it too.

Nearly everyone was able to reach the solution, but very few actually wrote down at each step (a) exactly what they were doing, and (b) which assumptions were being applied. My main beef was with folks using L or T to describe a linear system without explaining exactly what they meant by it. Don't assume that the class notes are universally accepted as the way of doing things. When I see

I do not immediately realize that this means that y = h * x, where h is the impulse reponse of the linear system L. You must state that this is what you mean. Drawing a diagram is a good idea. With regard to the assumptions you are making, you must make it clear when linearity or time invariance is being applied. For instance:

The same applies to time invariance. When making a substitution of variables, state clearly what the substitution is - don't just write the next line.

I was picky with this homework because it wasn't particularly difficult, and since it was presented as a proof then I expected your answer to conform to accepted mathematical procedure. Thus I took a point off for not stating that you were assuming linearity at a certain point in the proof, for instance.

The homeworks are all graded out of 5, by the way.

Tom