Understanding the $\mathcal Z$-transform

1. What does the z-transform tell us?
2. How do you calculate z-transform?
3. What is z-transform and basic formula for z-transform?

What does the z-transform tell us?

In a like manner, the Z-Transform allows us to analyze the frequency and phase of sinusoidal components of a system to characterize a system's response. In short: If the Z-Transform of a system identifies exponentially increasing output values, then your system exhibits instability for that value of x[n] and z^-n.

How do you calculate z-transform?

Concept of Z-Transform and Inverse Z-Transform

X(Z)|z=ejω=F. T[x(n)].

What is z-transform and basic formula for z-transform?

The relationship between a discrete-time signal x[n] and its one-sided z-transform X(z) is expressed as follows: X(z)=∞∑n=0x[n]z−n. This summation begins as a sequence of individual values, and since we are summing from n = 0 to n = infinity, the sequence is of infinite length.