Z-transform of alternating sequence

1. Why do we use z-transform in DSP?
2. How do you find the z-transform of a signal?
3. What is the ROC of z-transform of a two sided infinite sequence?

Why do we use z-transform in DSP?

The Z-Transform is an important tool in DSP that is fundamental to filter design and system analysis. It will help you understand the behavior and stability conditions of a system.

How do you find the z-transform of a signal?

To find the Z Transform of this shifted function, start with the definition of the transform: Since the first three elements (k=0, 1, 2) of the transform are zero, we can start the summation at k=3. In general, a time delay of n samples, results in multiplication by z-n in the z domain.

What is the ROC of z-transform of a two sided infinite sequence?

From the above graph, we can state that the ROC of a two sided sequence will be of the form r₂ < |z| < r₁. Explanation: The entire timing sequence is divided into two parts n=0 to ∞ and n=-∞ to 0. Since the z-transform of the signal given in the questions contains both the parts, it is called as Bi-lateral z-transform.