# Calculate the Output of Linear Time Invariant System Given it Impulse Response [closed]

A filter is defined as $h \left[ n \right] = \delta \left[ n \right] - \delta \left[ n - 1 \right]$.

Given a signal $h \left[ n \right]$ defined as:

$$x \left [ n \right ] = \begin{cases} 1 & \text{ if } x \geq 0 \\ 0 & \text{ if } x < 0 \end{cases}$$

Let $y \left[ n \right] = \left( x \ast h \right) \left[ n \right]$.
What is the value of $y \left[ -1 \right], \, y \left[ 0 \right], \, y \left[ 1 \right], \, y \left[ 2 \right]$?

## closed as off-topic by Marcus Müller, Stanley Pawlukiewicz, lennon310, Dilip Sarwate, Matt L.Jul 17 '18 at 14:41

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• Where are you stuck? – Olli Niemitalo Jul 5 '18 at 9:23
• Please use LaTeX for writing the questions. – Royi Jul 5 '18 at 9:56
• Sorry sir, I dont know how to use latex so I am putting a screenshots so that I wont miss any data – praneeth bharath Jul 5 '18 at 12:59
• I'm voting to close this question as off-topic because no effort shown – Stanley Pawlukiewicz Jul 5 '18 at 13:24

The Discrete Delta Function, $\delta \left[ n \right]$ is the identity operator of Linear Time Invariant Systems.
So the first element of the filter, $\delta \left[ n \right]$, just outputs the signal itself.
The other element $\delta \left[ n - 1 \right]$ just shifts the input signal.
Since the input is 1 for any $n \geq 0$ we subtract 1 from 1 unless it is $n = 0$ then we subtract zero from 1.