I am reading signal processing first by Mcclellan In chap 3,last para of article 3.1.2, I came across a term "discontinuous" as shown underlined in attached photo
What is meant by it in the context of discussion in photo? Is it meaning discrete?
2026-03-27 23:13:57.1774653237
What is meant by "discontinuous" here?
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It means not continuous.
For an example, consider the following function on $[0,2],$ which can be extended to be periodic:
$$f(x)=\begin{cases}x &\text{ if } 0\le x\lt 1\\ 0& \text{ if } 1\le x\lt 2\end{cases}.$$
The graph of this function would look kind of like this:
......./_/_/_/_/_/........