Use the z-transform of and the system function H(z) = 1 − z−1 to find the output of a firs...

Use the z-transform of

and the system function H(z) = 1 − z−1 to find the output of a first-difference filter when x[n] is the input. Compute your answer by using polynomial multiplication and also by using the difference equation:

What is the degree of the z-transform polynomial that represents the output y[n]?