unit impulse and unit step

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Unit impulse (sample)

Unit step

You take a step, and you never go back. Always 1 afterwards.

1. the discrete-time unit impulse is the first difference of the discrete-time step or the derivative!

2. discrete-time unit step is the running sum of the unit sample. That is,

or the running integral!

3. The unit impulse sequence can be used to sample the value of a signal at n = 0. In particular, since 8[n] is nonzero (and equal to 1) only for n = 0, it follows that Or,