Question

The Z-transform of x[n] = -0.8"u[-n - 1] is x(z) = 1/1+0.8z⁻¹ |z| < 0,8

a. true
b. false

Answer 1

The Z-transform given in the question is false because the correct Z-transform of the sequence x[n] is X(z) = z / (z + 0.8) for |z| > 0.8.

Step-by-step explanation:

The Z-transform of the sequence x[n] = -0.8^n u[-n - 1] is actually X(z) = z / (z + 0.8) for |z| > 0.8, contrary to the supplied expression in the question. This result is obtained considering that the sequence is a right-sided sequence for n ≤ -1 and applying the properties of the Z-transform dealing with time reversal and scaling in the z-domain. Therefore, the statement is false.