Solved Examples - Basic System Properties | Digital Signal Processing - Electronics and Communication Engineering (ECE) PDF Download

Example 1 − Check whether y(t) = x∗(t) is linear or non-linear.

Solution − The function represents the conjugate of input. It can be verified by either first law of homogeneity and law of additivity or by the two rules. However, verifying through rules is lot easier, so we will go by that.

If the input to the system is zero, the output also tends to zero. Therefore, our first condition is satisfied. There is no non-linear operator used either at the input nor the output. Therefore, the system is Linear.

Example 2 − Check whether  Solved Examples - Basic System Properties | Digital Signal Processing - Electronics and Communication Engineering (ECE)  is linear or non linear

Solution − Clearly, we can see that when time becomes less than or equal to zero the input becomes zero. So, we can say that at zero input the output is also zero and our first condition is satisfied.

Again, there is no non-linear operator used at the input nor at the output. Therefore, the system is Linear.

Example 3 − Check whether y(t) = sint.x(t) is stable or not.

Solution − Suppose, we have taken the value of x(t) as 3. Here, sine function has been multiplied with it and maximum and minimum value of sine function varies between -1 to +1.

Therefore, the maximum and minimum value of the whole function will also vary between -3 and +3. Thus, the system is stable because here we are getting a bounded input for a bounded output.

The document Solved Examples - Basic System Properties | Digital Signal Processing - Electronics and Communication Engineering (ECE) is a part of the Electronics and Communication Engineering (ECE) Course Digital Signal Processing.
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FAQs on Solved Examples - Basic System Properties - Digital Signal Processing - Electronics and Communication Engineering (ECE)

1. What are the basic system properties in electrical engineering?
Ans. The basic system properties in electrical engineering include linearity, time invariance, causality, stability, and memorylessness. Linearity refers to the property of a system where the output is directly proportional to the input. Time invariance means that the system's response remains the same regardless of the time at which the input is applied. Causality states that the output of a system depends only on the present and past values of the input. Stability refers to the property of a system where the output remains bounded for any bounded input. Memorylessness means that the output of a system depends only on the present value of the input and not on its past values.
2. How does linearity affect the behavior of a system in electrical engineering?
Ans. Linearity is a fundamental property in electrical engineering that determines how a system responds to different inputs. A linear system follows the principle of superposition, where the output is directly proportional to the input. This means that if we apply two inputs to a linear system, the output will be the sum of the individual outputs produced by each input separately. Linearity enables engineers to analyze and design systems using mathematical techniques such as Fourier analysis, Laplace transforms, and transfer functions.
3. What is the significance of time invariance in electrical engineering systems?
Ans. Time invariance is a crucial property in electrical engineering systems as it ensures that the system's response remains consistent over time. It means that the behavior and characteristics of the system do not change with time. This property allows engineers to analyze and predict the system's behavior accurately. Time invariance simplifies the analysis and design of systems by making it possible to use techniques such as convolution, frequency response analysis, and stability analysis. It also facilitates the use of time-domain and frequency-domain representations of signals and systems.
4. How does causality impact the functionality of electrical engineering systems?
Ans. Causality is an essential property in electrical engineering systems as it determines the cause-effect relationship between the input and output of a system. A causal system implies that the output of the system depends only on the present and past values of the input, and not on future values. This property allows engineers to predict and control the system's response based on the input signal. Causality simplifies the analysis and design of systems, as it eliminates the need to consider future inputs and focuses on the present and past behavior of the system.
5. Why is stability crucial in electrical engineering systems?
Ans. Stability is a critical property in electrical engineering systems as it ensures that the system's output remains bounded for any bounded input. A stable system does not exhibit runaway or oscillatory behavior, which can lead to unpredictable and unreliable performance. Stability allows engineers to design systems that produce consistent and predictable outputs, thereby ensuring the desired functionality and performance. It is essential in various applications, including power systems, control systems, and communication systems, where stability guarantees the safe and efficient operation of the system.
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