#### jagsee1972

##### Newbie level 5

I am a bit puzzled on what may be a simple question (only simple if you know).

To determine the impulse response for a system the input signal is replaced by the delta function.

e.g. the impulse response for the following function (system) is:

\[y[n] = \sum_{k = -\infty}^\infty..x[k]\]

\[h[n] = \sum_{k = -\infty}^\infty\delta[k]\]

The impulse response for the accumulator is the discrete step function u[n].

However I have seen this version of the accumulator which has its impulse response bieng u[n].

\[y[n] = \sum_{k = -\infty}^\infty..x[n-k]\]

\[h[n] = \sum_{k = -\infty}^\infty\delta[n-k]\]

I agree with the impulse function but can not see how it equals the discrete unit step function: u[n].

for example if n=-1, then this clearly should equal 0, however one of the deltas in the whole summation will equal 0 i.e. \[\delta[-1-(-1)]\] this will give an amplitude of 1 when n=-1. Which can not be true if the function is equal to u[n].

I would really appreciate some advice on where I am going wrong.