Professor teaching us about convolution

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DmytriE
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I'm in class watching my professor teaching us about convolution. However, he keeps doing this by creating graphs and stuff. Is there a method through which I can solve convolution problems without having to draw the graphs?
 
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A more general question is how do I treat unit step functions in a convolution problem?
 
Solve the equations, which is generally a point by point multiplication and summing process. I assume that is what the professor is doing, trying to illustrate the steps.

Or, use MATLAB :)

I don't understand your second question.