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$u[n]$ is the unit step function in discrete form. I want to know which one of the following two is the correct waveshape for $u[2-n]$, where $k$ is a constant. What's the answer? The top one is $u[n]$, the unit step function. So, what's the graph for $u[2-n]$, middle or bottom?
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HINT: For which value of $n$ does the argument of $u[2-n]$ become zero? That's where the step occurs. For which values of $n$ is the argument non-negative? That's where your unit step equals $1$. If you think about it for a minute, it should become really easy. |
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Basically, discrete unit step signal may be defined as: $$u[n] = \begin{cases} \begin{align} &1 &\scriptstyle{\text{for n > 0}}\\ &0 &\scriptstyle{\text{for n < 0}}\\ \end{align} \end{cases}$$ Doing time reversing (inverse) $$u[-n] = \begin{cases} \begin{align} &1 &\scriptstyle{\text{for -n > 0}}\\ &0 &\scriptstyle{\text{for -n < 0}}\\ \end{align} \end{cases}$$ $$u[-n] = \begin{cases} \begin{align} &1 &\scriptstyle{\text{for n < 0}}\\ &0 &\scriptstyle{\text{for n > 0}}\\ \end{align} \end{cases}$$ Now doing shifting by (+2) $$u[-n+2]=u[2-n] = \begin{cases} \begin{align} &1 &\scriptstyle{\text{for n < 2}}\\ &0 &\scriptstyle{\text{for n > 2}}\\ \end{align} \end{cases}$$ $Which\ gives\ you\ the\ second\ signal\ you\ stated\ in\ your\ question$ |
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