band-limited function

简明释义

1. 有限带宽函数; 2. 带限函数; 3. 截频函数;

英英释义

例句

1.To avoid aliasing, we must use a band-limited function 带限函数 when sampling signals.

为了避免混叠，我们在采样信号时必须使用一个带限函数 band-limited function。

2.When designing filters, engineers often aim for a band-limited function 带限函数 to ensure smooth transitions.

在设计滤波器时，工程师通常会寻求一个带限函数 band-limited function 以确保平滑过渡。

3.The Fourier transform of a band-limited function 带限函数 is non-zero only within a specific frequency range.

一个带限函数 band-limited function 的傅里叶变换仅在特定频率范围内非零。

4.In data compression, using a band-limited function 带限函数 helps to reduce the amount of data without losing quality.

在数据压缩中，使用带限函数 band-limited function 有助于减少数据量而不损失质量。

5.In signal processing, a band-limited function 带限函数 is crucial for ensuring that no high-frequency noise interferes with the desired signal.

在信号处理中，带限函数 band-limited function 对于确保没有高频噪声干扰所需信号至关重要。

作文

In the field of signal processing, the concept of a band-limited function plays a crucial role in understanding how signals can be represented and manipulated. A band-limited function is defined as a function whose Fourier transform is non-zero only within a finite range of frequencies. This means that the function does not contain any frequency components outside this specified bandwidth. The significance of band-limited functions lies in their ability to be perfectly reconstructed from a finite set of samples, according to the Nyquist-Shannon sampling theorem. To illustrate, consider a simple audio signal. If we have a sound wave that can be represented as a band-limited function, we can sample this wave at a rate that is twice the highest frequency present in the signal. For example, if our audio signal contains frequencies up to 20 kHz, we can sample it at 40 kHz. This sampling rate will allow us to accurately capture the essence of the sound without losing any information. One of the key applications of band-limited functions is in digital audio processing. When recording music or speech, the analog signals are converted into digital form through sampling. If the original signals are band-limited, the resulting digital representation will faithfully reproduce the sound when played back. This principle is not only applicable in audio but also extends to image processing, where images can be treated as two-dimensional band-limited functions. Moreover, the concept of band-limited functions is essential in telecommunications. In modern communication systems, it is often necessary to transmit data over limited bandwidth channels. By utilizing band-limited functions, engineers can design modulation schemes that efficiently use the available bandwidth while minimizing interference and maximizing data integrity. However, it is important to note that not all functions are band-limited. Functions that contain high-frequency components cannot be perfectly reconstructed if sampled below the Nyquist rate. These functions are referred to as non-band-limited functions, and they pose challenges in various applications, such as in the transmission of video signals where high fidelity is required. In conclusion, the understanding of band-limited functions is fundamental in the realm of signal processing. They enable accurate representation and reconstruction of signals, which is vital for numerous applications across different industries. As technology continues to advance, the importance of band-limited functions will only grow, highlighting the need for ongoing research and development in this area. By mastering the principles surrounding band-limited functions, professionals in fields such as audio engineering, telecommunications, and digital media can ensure that they are equipped to handle the complexities of modern signal processing challenges.

在信号处理领域，带限函数的概念在理解信号如何被表示和操作方面起着至关重要的作用。带限函数被定义为其傅里叶变换仅在有限频率范围内非零的函数。这意味着该函数不包含超出指定带宽的任何频率成分。带限函数的重要性在于它们能够根据奈奎斯特-香农采样定理从有限的一组样本中完美重建。举例来说，考虑一个简单的音频信号。如果我们有一个可以表示为带限函数的声波，我们可以以高于信号中最高频率两倍的速率对该波进行采样。例如，如果我们的音频信号包含高达20 kHz的频率，我们可以以40 kHz的速率进行采样。这个采样率将使我们能够准确捕捉声音的本质，而不会丢失任何信息。带限函数的一个关键应用是在数字音频处理中。当录制音乐或语音时，模拟信号通过采样转换为数字形式。如果原始信号是带限的，那么生成的数字表示在播放时将忠实再现声音。这个原则不仅适用于音频，还扩展到图像处理，其中图像可以被视为二维带限函数。此外，带限函数的概念在电信中至关重要。在现代通信系统中，通常需要通过带宽有限的通道传输数据。通过利用带限函数，工程师可以设计有效利用可用带宽的调制方案，同时最小化干扰并最大化数据完整性。然而，重要的是要注意，并非所有函数都是带限的。包含高频成分的函数如果在奈奎斯特率以下采样，将无法完美重建。这些函数被称为非带限函数，并且在许多应用中，如视频信号传输等高保真度要求的场合，它们会带来挑战。总之，理解带限函数在信号处理领域是基础。它们使信号的准确表示和重建成为可能，这对于各行各业的众多应用至关重要。随着技术的不断进步，带限函数的重要性只会增加，突显出在这一领域持续研究和发展的必要性。通过掌握围绕带限函数的原则，音频工程、电信和数字媒体等领域的专业人士可以确保他们具备应对现代信号处理挑战的复杂性的能力。