harmonic analysis

简明释义

谐波分析;调和分析

英英释义

例句

1.The professor explained how harmonic analysis can be applied to signal processing to extract meaningful information from sound waves.

教授解释了如何将 和声分析 应用于信号处理，以从声波中提取有意义的信息。

2.The software uses harmonic analysis to improve audio quality in recordings.

该软件使用 和声分析 来提高录音的音频质量。

3.Using harmonic analysis, the composer was able to create a richer texture in his symphony.

通过使用 和声分析，作曲家能够在他的交响曲中创造出更丰富的音色。

4.In engineering, harmonic analysis is essential for designing systems that can withstand vibrations.

在工程学中，和声分析 对于设计能够承受振动的系统至关重要。

5.In music theory, harmonic analysis helps us understand the structure of a piece by identifying its chords and progressions.

在音乐理论中，和声分析 帮助我们通过识别和弦及进程来理解一段作品的结构。

作文

In the realm of mathematics and engineering, the term harmonic analysis refers to a branch that studies the representation of functions or signals as the superposition of basic waves, known as harmonics. This powerful analytical tool is essential in various fields, including signal processing, acoustics, and even quantum mechanics. By decomposing complex signals into simpler components, harmonic analysis allows us to understand and manipulate these signals more effectively. One of the fundamental concepts in harmonic analysis is the Fourier series, which expresses a periodic function as a sum of sine and cosine functions. This approach reveals how different frequencies contribute to the overall shape of the waveform. For instance, when analyzing sound waves, a musician can use harmonic analysis to identify the distinct pitches and tones in a musical piece. By breaking down the sound into its harmonic components, they can adjust the music to achieve a desired effect. Moreover, harmonic analysis extends beyond mere wave decomposition. It plays a crucial role in modern technology, particularly in digital signal processing (DSP). Engineers utilize harmonic analysis to design filters that enhance or suppress specific frequencies in audio signals. This application is vital in telecommunications, where clear transmission of voice and data is paramount. Without the tools provided by harmonic analysis, our ability to communicate through technology would be severely limited. Additionally, harmonic analysis finds applications in image processing. Techniques such as the Fast Fourier Transform (FFT) allow for the efficient analysis of images by transforming spatial data into frequency data. This transformation aids in tasks such as image compression and enhancement, making it easier to store and transmit visual information. In this context, harmonic analysis not only improves the quality of images but also optimizes storage space, which is increasingly important in our digital age. Furthermore, the implications of harmonic analysis stretch into the realms of physics and engineering. In structural engineering, for example, understanding the vibrational modes of structures is crucial for ensuring their stability and safety. harmonic analysis enables engineers to predict how buildings will respond to forces such as wind and earthquakes. By analyzing the harmonic frequencies of a structure, engineers can design safer buildings that withstand environmental stressors. In conclusion, harmonic analysis is an indispensable tool across various disciplines. Its ability to decompose complex signals into simpler forms enhances our understanding and manipulation of waves, whether in sound, images, or physical structures. As technology continues to advance, the relevance of harmonic analysis will only grow, paving the way for innovations that rely on the fundamental principles of wave behavior. Embracing this analytical approach opens up a world of possibilities, allowing us to explore and harness the power of harmonics in our everyday lives.

在数学和工程领域，术语harmonic analysis指的是一个研究函数或信号作为基本波（称为谐波）的叠加表示的分支。这种强大的分析工具在信号处理、声学甚至量子力学等多个领域中至关重要。通过将复杂信号分解为更简单的组成部分，harmonic analysis使我们能够更有效地理解和操作这些信号。harmonic analysis中的一个基本概念是傅里叶级数，它将周期函数表示为正弦和余弦函数的总和。这种方法揭示了不同频率如何对波形的整体形状做出贡献。例如，在分析声波时，音乐家可以使用harmonic analysis来识别音乐作品中的不同音高和音调。通过将声音分解为其谐波成分，他们可以调整音乐以达到所需的效果。此外，harmonic analysis不仅限于波的分解。它在现代技术中发挥着至关重要的作用，特别是在数字信号处理（DSP）中。工程师利用harmonic analysis设计滤波器，以增强或抑制音频信号中的特定频率。这种应用在电信中至关重要，因为清晰的语音和数据传输至关重要。如果没有harmonic analysis提供的工具，我们通过技术进行交流的能力将受到严重限制。此外，harmonic analysis在图像处理中的应用也很广泛。快速傅里叶变换（FFT）等技术允许通过将空间数据转换为频率数据来高效分析图像。这种转化有助于图像压缩和增强等任务，使得存储和传输视觉信息变得更加容易。在这种情况下，harmonic analysis不仅提高了图像的质量，还优化了存储空间，这在我们数字时代日益重要。此外，harmonic analysis的影响还延伸到物理和工程领域。例如，在结构工程中，了解结构的振动模式对于确保其稳定性和安全性至关重要。harmonic analysis使工程师能够预测建筑物如何应对风和地震等力量。通过分析结构的谐波频率，工程师可以设计出能够抵御环境压力的更安全的建筑物。总之，harmonic analysis是各个学科中不可或缺的工具。它将复杂信号分解为更简单的形式的能力增强了我们对波的理解和操作，无论是在声音、图像还是物理结构中。随着技术的不断进步，harmonic analysis的相关性只会增加，为依赖波动行为基本原理的创新铺平道路。接受这种分析方法为我们打开了一个可能性的新世界，使我们能够在日常生活中探索和利用谐波的力量。