Question

An LTI system is described by the difference equation y[n]=0.1 (x[n]x[n-1]+x[n-2])

(a) Determine the system function H(z) for this system.

Answer 1

The system function H(z) for the given LTI system can be determined by taking the Z-transform of the difference equation. The resulting H(z) is 0.1(z^2 + z).

Step-by-step explanation:

The system function H(z) for the given LTI system can be determined by taking the Z-transform of the difference equation y[n] = 0.1 (x[n]x[n-1]+x[n-2]).

To find H(z), we substitute y[n] with Y(z) and x[n] with X(z) in the difference equation. Then, we manipulate the equation to solve for Y(z) in terms of X(z) and z.

The resulting system function H(z) is determined to be:

H(z) = 0.1(z^2 + z).