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Solved Examples of Z-Transform | Digital Signal Processing - Electronics and Communication Engineering (ECE) PDF Download
Example 1
Find the response of the system 
when all the initial conditions are zero.
Solution − Taking Z-transform on both the sides of the above equation, we get
Taking the inverse Z-transform of the above equation, we get
Example 2
Find the system function H(z) and unit sample response h(n) of the system whose difference equation is described as under
where, y(n) and x(n) are the output and input of the system, respectively.
Solution − Taking the Z-transform of the above difference equation, we get
This system has a pole at 
Hence, taking the inverse Z-transform of the above, we get
Example 3
Determine Y(z),n≥0 in the following case −
Solution − Applying the Z-transform to the above equation, we get
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FAQs on Solved Examples of Z-Transform - Digital Signal Processing - Electronics and Communication Engineering (ECE)
| 1. What is the Z-transform in electrical engineering? |  |
Ans. The Z-transform is a mathematical tool used in electrical engineering to analyze discrete-time signals and systems. It converts a discrete-time signal into a complex frequency domain representation, allowing for analysis and manipulation using algebraic techniques.
| 2. How is the Z-transform related to the Laplace transform? | |
Ans. The Z-transform is a generalization of the Laplace transform for discrete-time systems. While the Laplace transform is used for continuous-time signals and systems, the Z-transform is specifically designed for discrete-time signals and systems. Both transforms provide a way to analyze signals and systems in the frequency domain.
| 3. What are the advantages of using the Z-transform in electrical engineering? | |
Ans. The Z-transform offers several advantages in electrical engineering. It allows for the analysis of discrete-time systems, which are commonly encountered in digital signal processing and control systems. The Z-transform also enables the use of algebraic techniques for system analysis, simplifying calculations and providing insight into system behavior.
| 4. How is the Z-transform used in digital filter design? | |
Ans. The Z-transform plays a crucial role in digital filter design. By applying the Z-transform to the difference equation of a digital filter, the transfer function of the filter can be obtained in the frequency domain. This transfer function can then be analyzed and manipulated to design filters with desired frequency response characteristics.
| 5. Can the Z-transform be used for real-time signal processing? | |
Ans. Yes, the Z-transform can be used for real-time signal processing. Since many real-world signals are discrete-time in nature, the Z-transform provides a powerful tool for analyzing and processing these signals in real-time applications. The Z-transform can be implemented efficiently using digital signal processing techniques, making it suitable for real-time systems.
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