I have one system with input and output

$$y[n]=x[n]x[n-1]$$

where $\sigma$ is the unit step function and $\delta$ is the unit impulse function. I know that

$$a[n]=\sum_{k=-\infty}^{\infty}h[k]\sigma [n-k]=\sum_{k=-\infty}^{n}h[k]$$

Where $a$ is the step function that I have to calculate. How do I calculate it when i have product of two inputs? I tried transforming it to Z-Transform than calculating $H(z)$ but it's too complicated.

How do I calculate this?

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  • 1
    are you sure what you want to write down is well-defined? – Marcus Müller Dec 6 at 12:41
  • i would like to know how to calculate h(n) @MarcusMüller – Alena Dec 6 at 13:06
  • I understood that, but you have to ask yourself whether that $h[n]$ even exists. Hint: it doesn't. – Marcus Müller Dec 6 at 13:07
  • why? @MarcusMüller – Alena Dec 6 at 13:12
  • Which kind of systems can be represented completely by their impulse response, Alena? – Marcus Müller Dec 6 at 13:14