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The discrete time unit step is given by $$ u[n] = \begin{cases} 1, & n \geq 0, \\ 0, & n < 0. \end{cases} \tag{1} $$

Unit Sample sequence or Impulse sequence is defined as $$ δ[n] = \begin{cases} 1, & n = 0, \\ 0, & n ≠ 0. \end{cases} \tag{2} $$

and they are related via the sum relation by $$ u[n] = \sum_{k = -\infty}^\infty \delta[k]. \tag{3}$$

The Question is : how to verify the relation between these ? $$ u[n] = \sum_{m = 0}^\infty \delta[n-m] = \sum_{k = -\infty}^\infty \delta(k), $$ $$\delta[n]=u[n]-u[n-1].\tag{4} $$

Thank you very much.

Bean
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Krishna Himawan
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    Please enter your mathematical expressions as text instead of linking to images. Use MathJax to format the expressions; you can find a quick reference here. – amd Oct 07 '18 at 16:17
  • thank you very much for the suggestion – Krishna Himawan Oct 07 '18 at 17:30
  • HINT: $u[n] = \sum_k \delta[k]$ represents integration. So, $u[n]$ should look like a step function. For other case, i.e., $\delta [n] = u[n] - u[n-1]$ represents derivative... just think about it... – user550103 Oct 10 '18 at 10:10

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