What will be the convolution of u(t) with itself?Group of answer choicesy(t)=t.u(t-1)y(t)=t^2.u(t)y(t)=t.u(t)y(t)=u(t)

The convolution of a function with itself, in this case u(t), is given by the integral from negative infinity to positive infinity of the function at one point multiplied by the function at another point, with one of the functions reversed and shifted.

For the unit step function u(t), the convolution of u(t) with itself is given by:

∫ from 0 to t (u(τ) * u(t-τ)) dτ

Since u(t) is 1 for t >= 0 and 0 for t < 0, the integral simplifies to:

∫ from 0 to t dτ = [τ] from 0 to t = t

So, the convolution of u(t) with itself is t.u(t), which corresponds to the third option: y(t)=t.u(t).