Understanding an Exercise on LTI Systems with Unit Sample Response

[will225]

Hello,
am having an understanding problem, about an exercice on LTI systems with unit sample response.
i've been given the graphical depicted output y[n], and the following output x[n]= u[n]-u[n-2]
the system is as follow
x[n]----> h₁[n]----->h₂[n]------>y[n]
with h₂[n]= s[n] - s[n-1];
and i am suppose to find h₁ ,
i used the the associativity of the convolution to have another form of the problem but
what i don't understand is the information given by the equation h2 [n]
how am i suppos to use it.
the i will make the aatempt to a solution and post it.

 

[lippyka]

Since h2[n] = s[n] - s[n-1], we can use this to solve for h1[n]. To do this, we can first calculate the convolution of x[n] and h2[n], which will give us y[n]. Then, we can use the inverse convolution to calculate the convolution of y[n] and h2[n], which will give us h1[n]. So, to solve for h1[n], we can use the following equation: h1[n] = y[n]*h2[n].In this equation, y[n] is the given output of x[n] and h2[n] is the given unit sample response of h2[n]. By calculating the convolution of these two functions, we can find h1[n].