Final answer:
To determine the impulse response of a system described by a second-order difference equation, assume an input signal of x[n] = δ[n] and substitute it into the difference equation. Solve for the output, y[n], which will be the impulse response of the system.
Step-by-step explanation:
The impulse response of a system described by a second-order difference equation can be determined by assuming a particular input signal, applying the difference equation to the signal, and solving for the output. In this case, the difference equation is given as y[n] - 4y[n-1] + 4y[n-2].
To determine the impulse response, assume an input signal of x[n] = δ[n], where δ[n] is the discrete-time unit impulse. Substitute the input signal into the difference equation and solve for the output. The output, y[n], will then be the impulse response of the system.
An equation is a mathematical statement asserting that two expressions are equal. It contains an equal sign ("=") separating the left-hand side (LHS) and the right-hand side (RHS). The goal in solving an equation is to find the value(s) of the variable(s) that satisfy the equality.