time-invariant system

简明释义

时间恒定系统

英英释义

例句

1.Signal processing often deals with time-invariant systems 时不变系统 to ensure consistent output for given inputs.

信号处理通常涉及到时不变系统 time-invariant systems，以确保对于给定输入的输出是一致的。

2.Understanding time-invariant systems 时不变系统 helps engineers design more reliable control systems.

理解时不变系统 time-invariant systems 有助于工程师设计更可靠的控制系统。

3.A time-invariant system 时不变系统 can be represented mathematically using differential equations that do not include time-dependent variables.

一个时不变系统 time-invariant system 可以通过不包含时间相关变量的微分方程进行数学表示。

4.In control theory, a time-invariant system 时不变系统 is one where the system's behavior does not change over time.

在控制理论中，时不变系统 time-invariant system 是指系统的行为随时间不发生变化。

5.An example of a time-invariant system 时不变系统 is a simple electrical circuit that behaves the same regardless of when it is analyzed.

一个时不变系统 time-invariant system 的例子是一个简单的电路，无论何时分析，其行为都是相同的。

作文

In the field of engineering and systems theory, the concept of a time-invariant system is fundamental to understanding how various systems behave over time. A time-invariant system is defined as a system whose output does not change when the input is shifted in time. This means that if you apply an input signal to the system at one point in time, the output will remain the same regardless of when you apply that input. This property allows for greater predictability and simplifies the analysis of systems in various applications, such as electrical circuits, control systems, and communications. To illustrate this concept, consider a simple example of an electronic circuit that processes audio signals. If the circuit is designed to amplify a specific frequency, the gain provided by the circuit will remain constant regardless of when the audio signal is applied. In this case, the circuit can be classified as a time-invariant system because the amplification effect is consistent over time. One of the key advantages of time-invariant systems is that they can be analyzed using tools from linear algebra and calculus, such as convolution and Fourier transforms. These mathematical techniques rely on the assumption that the system's behavior does not change over time, which greatly simplifies the process of designing and analyzing systems. For instance, engineers can use these tools to predict how a time-invariant system will respond to different inputs, allowing for efficient design and troubleshooting. However, not all systems are time-invariant. There are many systems where the output changes based on the time at which the input is applied. These are known as time-variant systems. An example of a time-variant system could be a temperature control system in a building that adjusts its heating or cooling based on the time of day. In this case, the response of the system varies depending on the time, making it more complex to analyze and predict. Understanding the distinction between time-invariant and time-variant systems is crucial for engineers and scientists. It helps them determine the appropriate methods and tools to use when designing systems and analyzing their performance. When dealing with time-invariant systems, engineers can leverage the powerful mathematical techniques available, while for time-variant systems, they may need to employ more complex models and simulations. In conclusion, the concept of a time-invariant system plays a vital role in various engineering disciplines. By recognizing the properties of these systems, professionals can develop more efficient designs and solutions. The ability to predict system behavior over time without the complications introduced by time dependence allows for advancements in technology and engineering practices. As we continue to explore and innovate in the fields of engineering and systems theory, the principles surrounding time-invariant systems will remain a cornerstone of our understanding and application of system dynamics.

在工程和系统理论领域，时间不变系统的概念对于理解各种系统随时间的行为至关重要。时间不变系统被定义为当输入信号在时间上发生偏移时，其输出不会改变的系统。这意味着如果你在某个时间点向系统施加输入信号，输出将保持不变，无论何时施加该输入。这一特性使得系统的可预测性增强，并简化了在电路、控制系统和通信等各种应用中对系统的分析。为了说明这一概念，考虑一个处理音频信号的简单电子电路的例子。如果电路设计用于放大特定频率，则电路提供的增益将始终保持不变，无论何时施加音频信号。在这种情况下，该电路可以被归类为时间不变系统，因为放大效果在时间上是一致的。时间不变系统的一个主要优点是它们可以使用线性代数和微积分等工具进行分析，例如卷积和傅里叶变换。这些数学技术依赖于系统行为在时间上不变的假设，这大大简化了系统设计和分析的过程。例如，工程师可以利用这些工具预测时间不变系统对不同输入的响应，从而实现高效的设计和故障排除。然而，并非所有系统都是时间不变的。许多系统的输出会根据输入施加的时间而变化。这些被称为时间变化系统。一个时间变化系统的例子可能是建筑物中的温控系统，它根据一天中的时间调整供暖或制冷。在这种情况下，系统的响应会随着时间的变化而变化，使其分析和预测更加复杂。理解时间不变系统和时间变化系统之间的区别对于工程师和科学家来说至关重要。这帮助他们确定在设计系统和分析性能时应使用的适当方法和工具。在处理时间不变系统时，工程师可以利用可用的强大数学技术，而对于时间变化系统，他们可能需要采用更复杂的模型和仿真。总之，时间不变系统的概念在各种工程学科中发挥着重要作用。通过认识到这些系统的特性，专业人员能够开发出更高效的设计和解决方案。能够预测系统随时间的行为而不受时间依赖性引入的复杂性的影响，有助于推动技术和工程实践的发展。随着我们在工程和系统理论领域不断探索和创新，围绕时间不变系统的原则将继续成为我们理解和应用系统动态的基石。