Enter the nth sample of the discrete-time signal and the complex number into the calculator to determine the Z-Transform of the signal.
Z-Transform Formula
The following formula is used to calculate the Z-Transform of a discrete-time signal.
Z = Σ x[n] * (z^-n)
Variables:
- Z is the Z-Transform of the signal
- x[n] is the nth sample of the discrete-time signal
- z is a complex number
- n is the index of the discrete-time signal
To calculate the Z-Transform, for each sample of the discrete-time signal, multiply the sample by the complex number z raised to the power of the negative index of the sample. Sum all these results to get the Z-Transform of the signal.
What is a Z-Transform?
The Z-Transform is a mathematical technique used in signal processing and control theory for analyzing and representing discrete-time signals. It is a complex-valued function that transforms a sequence of numbers into a function of a complex variable, providing a frequency domain representation of the original sequence. The Z-Transform is particularly useful for the analysis of linear, time-invariant systems and is a fundamental tool in digital signal processing.
How to Calculate Z-Transform?
The following steps outline how to calculate the Z-Transform using the given formula:
- First, determine the value of x[n] for each sample of the discrete-time signal.
- Next, raise the complex number z to the power of -n.
- Multiply each x[n] value with the corresponding (z^-n) value.
- Sum up all the products obtained in the previous step.
- The result of the summation is the Z-Transform of the signal (Z).
Example Problem:
Use the following variables as an example problem to test your knowledge:
x[n] = [1, 2, 3, 4]
z = 0.5
n = [0, 1, 2, 3]
