envelope curve

简明释义

包络曲线

英英释义

例句

1.The sound engineer adjusted the settings to create an optimal envelope curve for the audio track.

声音工程师调整设置，以为音轨创建最佳的包络曲线。

2.In signal processing, understanding the envelope curve can help in analyzing the modulation of signals.

在信号处理中，理解包络曲线有助于分析信号的调制。

3.In music synthesis, the envelope curve controls the dynamics of a sound over time.

在音乐合成中，包络曲线控制声音随时间的动态变化。

4.The designer used an envelope curve to define the shape of the product's surface.

设计师使用包络曲线来定义产品表面的形状。

5.The envelope curve of the stock price showed a steady increase over the past year.

股票价格的包络曲线显示出过去一年的稳定增长。

作文

The concept of the envelope curve is widely used in various fields, including mathematics, physics, and engineering. An envelope curve is essentially a curve that serves as a boundary for a family of curves. It can be visualized as a smooth curve that 'envelopes' or contains other curves within it. This concept helps in understanding how different functions behave in relation to one another and allows for better visualization of complex data sets.In mathematics, the envelope curve can be derived from a set of parametric equations. For instance, consider a family of sine waves with varying amplitudes and frequencies. The envelope curve would represent the maximum and minimum bounds of these waves, providing insight into their overall behavior. By plotting the envelope curve, mathematicians can easily identify trends and patterns that may not be immediately apparent when looking at individual curves alone.In physics, the envelope curve is often used in wave mechanics. When studying sound waves or electromagnetic waves, researchers use envelope curves to analyze the modulation of wave amplitude over time. For example, in audio signal processing, the envelope curve can illustrate how the volume of a sound changes, helping engineers design better sound systems and improve audio quality.Engineering applications of the envelope curve are abundant as well. In structural engineering, the envelope curve is crucial for understanding load distributions on structures. Engineers can use this concept to determine how forces act upon a bridge or building, ensuring safety and stability. By analyzing the envelope curve, engineers can predict potential failure points and reinforce structures accordingly.Moreover, the envelope curve plays a significant role in optimization problems. In operations research, for example, decision-makers often seek to optimize resource allocation. The envelope curve can help visualize the trade-offs between different options, allowing for more informed decisions. By understanding the envelope curve, businesses can maximize profits while minimizing costs.In summary, the envelope curve is a powerful tool that aids in the analysis and interpretation of various phenomena across multiple disciplines. Its ability to summarize complex relationships into a single, comprehensible curve makes it invaluable for researchers, engineers, and mathematicians alike. As technology continues to advance and data becomes increasingly complex, the importance of understanding concepts like the envelope curve will only grow. Whether in the realm of science, engineering, or business, mastering the envelope curve will undoubtedly enhance our ability to make sense of the world around us.In conclusion, the envelope curve serves as an essential framework for analyzing relationships among different curves and functions. By encapsulating the essence of multiple data sets into a singular form, it provides clarity and insight that can lead to better decision-making and understanding across various fields. Therefore, grasping the concept of the envelope curve is vital for anyone engaged in analytical work, as it bridges the gap between complexity and simplicity, enabling clearer communication of ideas and findings.

“包络曲线”这一概念在数学、物理学和工程学等多个领域广泛应用。“包络曲线”本质上是一条为一组曲线提供边界的曲线。它可以被视为一条平滑的曲线，‘包围’或包含其他曲线在其内部。这个概念有助于理解不同函数之间的关系，并允许更好地可视化复杂的数据集。在数学中，“包络曲线”可以通过一组参数方程推导出来。例如，考虑一系列具有不同幅度和频率的正弦波。“包络曲线”将表示这些波的最大和最小边界，从而提供对其整体行为的洞察。通过绘制“包络曲线”，数学家可以轻松识别出趋势和模式，这些在单独查看各个曲线时可能并不明显。在物理学中，“包络曲线”常用于波动力学。当研究声波或电磁波时，研究人员使用“包络曲线”来分析波幅随时间的调制。例如，在音频信号处理领域，“包络曲线”可以说明声音的音量如何变化，帮助工程师设计更好的音响系统，提高音频质量。工程应用中，“包络曲线”同样丰富。在结构工程中，“包络曲线”对于理解结构上的荷载分布至关重要。工程师可以利用这一概念来确定桥梁或建筑物上力量的作用方式，从而确保安全和稳定。通过分析“包络曲线”，工程师可以预测潜在的失效点，并相应地加固结构。此外，“包络曲线”在优化问题中也发挥着重要作用。在运筹学中，例如，决策者通常寻求优化资源配置。“包络曲线”可以帮助可视化不同选项之间的权衡，从而允许做出更明智的决策。通过理解“包络曲线”，企业可以在最小化成本的同时最大化利润。总之，“包络曲线”是一个强大的工具，有助于分析和解释多个学科中的各种现象。它将复杂关系总结为单一易懂的曲线，使其对研究人员、工程师和数学家来说都具有不可或缺的价值。随着技术的不断进步和数据的日益复杂，理解像“包络曲线”这样的概念的重要性只会增加。无论是在科学、工程还是商业领域，掌握“包络曲线”无疑将增强我们理解周围世界的能力。最后，“包络曲线”作为分析不同曲线和函数之间关系的重要框架，提供了一个简单而清晰的视角来理解复杂的数据集。通过将多组数据的本质封装成单一形式，它提供了可以带来更好决策和理解的清晰度。因此，掌握“包络曲线”的概念对于任何从事分析工作的人都是至关重要的，因为它架起了复杂与简单之间的桥梁，使思想和发现的交流更加清晰。