Howtosignalprocessing
Explanation: The z-transform of the x(n) whose definition exists in the range n=-∞ to +∞ is known as bilateral or two sided z-transform. But in the given question the value of n=0 to +∞. So, such a z-transform is known as Unilateral or one sided z-transform.
- Why is the one sided z-transform Z+ used here instead of the two sided z-transform?
- What is two sided z-transform?
- What are the two types of z-transform?
- What is the inverse transform of the z-transform?
Why is the one sided z-transform Z+ used here instead of the two sided z-transform?
Because the two–sided (bilateral) z-transform is defined for all time , i.e. −∞<n<∞, it can not be applied to a nonrelaxed system which is described by a difference equation accompanied with initial conditions. In such situations the one-side z- transform is used . We denote X+(z) for this.
What is two sided z-transform?
z transform is to discrete-time systems what the Laplace transform is to continuous-time systems. z is a complex variable. This is sometimes referred to as the two-sided z transform, with the one-sided z transform being the same except for a summation from n = 0 to infinity.
What are the two types of z-transform?
The Z-transform may be of two types viz. unilateral (or one-sided) and bilateral (or two-sided).
What is the inverse transform of the z-transform?
The Inverse Z-Transform
(4) represents the integration around the circle of radius |z|=r in the counter clockwise direction. This is the direct method of finding inverse Z-transform. The direct method is quite tedious.
