derived envelope

简明释义

导出包络

英英释义

例句

1.The research team analyzed the data to create a derived envelope that represents the maximum expected values.

研究团队分析了数据，以创建一个派生包络，表示最大预期值。

2.In signal processing, the derived envelope is crucial for understanding the modulation characteristics.

在信号处理过程中，派生包络 对于理解调制特性至关重要。

3.The derived envelope of the waveform helps engineers design better filters.

波形的派生包络帮助工程师设计更好的滤波器。

4.By applying a mathematical model, we can generate a derived envelope for the temperature fluctuations.

通过应用数学模型，我们可以生成温度波动的派生包络。

5.The derived envelope in this context refers to the range of possible outcomes based on historical data.

在这个上下文中，派生包络指的是基于历史数据的可能结果范围。

作文

In the realm of mathematics and engineering, the concept of a derived envelope is crucial for understanding various phenomena related to functions and their behaviors. The term 'envelope' generally refers to a curve that is tangent to a family of curves, and when we say 'derived envelope', we are often talking about an envelope that is obtained through a specific mathematical process or derivation. This can be particularly useful in fields such as physics, where understanding the boundaries of waveforms or signal patterns is essential.To illustrate the concept, consider the case of waveforms in signal processing. When engineers analyze signals, they may derive an envelope to represent the maximum amplitude of a varying signal over time. This derived envelope provides a visual representation of the peaks of the waveform, allowing for easier interpretation and analysis. By studying the shape and behavior of this envelope, engineers can make informed decisions about filtering, modulation, and other aspects of signal manipulation.Moreover, the derived envelope can also be applied in optimization problems. For instance, in economics, one might derive an envelope curve to represent the maximum profit obtainable at different levels of production. By plotting this curve, analysts can quickly identify the most efficient production levels that yield the highest returns. The derived envelope thus serves as a powerful tool for visualizing and optimizing complex relationships between variables.Additionally, the concept of a derived envelope extends beyond pure mathematics into practical applications in various scientific fields. In physics, for example, the derived envelope can describe the trajectory of a projectile under the influence of gravity, taking into account factors such as air resistance and initial velocity. Understanding the envelope of the projectile’s path allows scientists to predict its landing point more accurately and adjust parameters accordingly.In the field of computer graphics, the derived envelope is often used in animation and modeling. When creating realistic movements or shapes, animators derive envelopes that define the boundaries of an object’s motion. This ensures that the animations remain fluid and visually appealing, adhering to the laws of physics while still being artistically expressive.In conclusion, the derived envelope is a multifaceted concept that plays a vital role in various disciplines, from mathematics to engineering, economics, and the arts. Its ability to provide insights into the behavior of complex systems makes it an invaluable tool for professionals across numerous fields. As we continue to explore and apply the principles of derived envelopes, we unlock new potentials for innovation and understanding in both theoretical and practical contexts. Thus, grasping the significance of the derived envelope is not just an academic exercise; it is a gateway to deeper comprehension and enhanced problem-solving capabilities in our increasingly complex world.

在数学和工程的领域中，derived envelope（导出包络）的概念对于理解与函数及其行为相关的各种现象至关重要。术语“包络”通常指的是与一系列曲线相切的曲线，而当我们说“导出包络”时，我们通常是在谈论通过特定的数学过程或推导获得的包络。这在物理等领域中尤其有用，因为理解波形或信号模式的边界是至关重要的。为了说明这一概念，考虑信号处理中的波形情况。当工程师分析信号时，他们可能会导出一个包络来表示随时间变化的信号的最大幅度。这个derived envelope（导出包络）提供了波形峰值的可视化表示，使得解释和分析变得更加容易。通过研究该包络的形状和行为，工程师能够就滤波、调制和信号处理的其他方面做出明智的决策。此外，derived envelope（导出包络）也可以应用于优化问题。例如，在经济学中，可能会导出一个包络曲线来表示在不同生产水平下可获得的最大利润。通过绘制这条曲线，分析师可以快速识别出产生最高回报的最有效的生产水平。因此，derived envelope（导出包络）作为可视化和优化变量之间复杂关系的强大工具，发挥着重要作用。此外，derived envelope（导出包络）的概念超越了纯数学，扩展到各个科学领域的实际应用中。在物理学中，例如，derived envelope（导出包络）可以描述在重力影响下投射物体的轨迹，同时考虑空气阻力和初始速度等因素。理解投射物体路径的包络使科学家能够更准确地预测其着陆点，并相应调整参数。在计算机图形学领域，derived envelope（导出包络）常用于动画和建模。当创建逼真的运动或形状时，动画师导出定义对象运动边界的包络。这确保了动画保持流畅且视觉上令人愉悦，同时遵循物理法则，仍然具有艺术表现力。总之，derived envelope（导出包络）是一个多层面的概念，在各个学科中发挥着至关重要的作用，从数学到工程、经济学和艺术。它提供的对复杂系统行为的洞察能力使其成为各个领域专业人士的宝贵工具。随着我们不断探索和应用导出包络的原理，我们为创新和理解开启了新的潜力，无论是在理论还是实践的背景下。因此，掌握derived envelope（导出包络）的意义不仅仅是学术上的练习；它是深入理解和增强解决问题能力的一个入口，在我们日益复杂的世界中。