The given expression is h*(d bd), where d(t) is the delta function. Let's break down the expression and evaluate it step by step.


The delta function, denoted as d(t), is a mathematical function that is zero everywhere except at t = 0, where it becomes infinite. The integral of the delta function over any interval that contains zero is equal to 1. In other words, the delta function behaves like an impulse.


Multiplying any function f(t) with the delta function d(t) results in a shifted version of f(t) at t = 0. The multiplication acts as a sampler, picking the value of f(t) at t = 0 and zero everywhere else.


In the given expression h*(d bd), we have a multiplication between h and the result of multiplying the delta function d(t) with another function b(t).

1. Multiplying the delta function d(t) with b(t) gives a shifted version of b(t) at t = 0.
2. The multiplication h*(d bd) means multiplying the result from step 1 with h.
3. Since the delta function d(t) is zero everywhere except at t = 0, the result of the multiplication will be zero for all t ≠ 0.
4. At t = 0, the multiplication gives h times the value of b(t) at t = 0. This is the only non-zero value in the expression.


Therefore, the expression h*(d bd) evaluates to h times the value of b(t) at t = 0. In other words, the answer is option 'C'.