Question

Question 3 : Signals :

How this is true? I am not getting it properly..

\[\large \color{green}{u[n] = \sum_{k \rightarrow - \infty}^{n} \delta[k]}\]

Answer 1

\(u[n]\) is Unit Step Discrete signal

\(\delta[k]\) is Unit Impulse or Sample Sequence..

Answer 2

I think I have got this.. :)

Answer 3

First case: For n < 0..

Answer 4

Second Case: \(n \ge 0\)

Answer 5

As :

It is equivalent to :

\( u[n] = \begin{cases} 1, && n \ge 0 \\ 0, && n <0\end{cases}\)

So:

\[\large \color{blue}{\sum_{k \rightarrow - \infty}^{n} \delta[k] = u[n]}\]