来自系列:理解小波
Kirthi Devleker,Mathworks
该介绍视频涵盖了哪些小波以及如何使用它们来探索Matlab中的数据®。该视频侧重于两个重要的小波变换概念:缩放和移位。概念可以应用于诸如图像的2D数据。
大家好。在此介绍性会话中,我将涵盖一些基本的小波概念。我将主要使用1-D示例,但是相同的概念也可以应用于图像。首先,让我们回顾一下小波是什么。现实世界数据或信号经常表现出缓慢变化的趋势或带有瞬态的振荡。另一方面,图像具有由边缘中断的平滑区域或对比度的突然变化。这些突然的变化通常是最多的IA =数据的名称,无论是感知的,也是在他们提供的信息方面。傅里叶变换是一种有关数据分析的强大工具。但是,它没有有效地表示突然的变化。原因是傅里叶变换将数据表示为正弦波的和,其在时间或空间中未本地化。 These sine waves oscillate forever. Therefore, to accurately analyze signals and images that have abrupt changes, we need to use a new class of functions that are well localized in time and frequency: This brings us to the topic of Wavelets. A wavelet is a rapidly decaying, wave-like oscillation that has zero mean. Unlike sinusoids, which extend to infinity, a wavelet exists for a finite duration. Wavelets come in different sizes and shapes. Here are some of the well-known ones. The availability of a wide range of wavelets is a key strength of wavelet analysis. To choose the right wavelet, you'll need to consider the application you'll use it for. We will discuss this in more detail in a subsequent session. For now, let's focus on two important wavelet transform concepts: scaling and shifting. Let' start with scaling. Say you have a signal PSI(t). Scaling refers to the process of stretching or shrinking the signal in time, which can be expressed using this equation [on screen]. S is the scaling factor, which is a positive value and corresponds to how much a signal is scaled in time. The scale factor is inversely proportional to frequency. For example, scaling a sine wave by 2 results in reducing its original frequency by half or by an octave. For a wavelet, there is a reciprocal relationship between scale and frequency with a constant of proportionality. This constant of proportionality is called the "center frequency" of the wavelet. This is because, unlike the sinewave, the wavelet has a band pass characteristic in the frequency domain. Mathematically, the equivalent frequency is defined using this equation [on screen], where Cf is center frequency of the wavelet, s is the wavelet scale, and delta t is the sampling interval. Therefore when you scale a wavelet by a factor of 2, it results in reducing the equivalent frequency by an octave. For instance, here is how a sym4 wavelet with center frequency 0.71 Hz corresponds to a sine wave of same frequency. A larger scale factor results in a stretched wavelet, which corresponds to a lower frequency. A smaller scale factor results in a shrunken wavelet, which corresponds to a high frequency. A stretched wavelet helps in capturing the slowly varying changes in a signal while a compressed wavelet helps in capturing abrupt changes. You can construct different scales that inversely correspond the equivalent frequencies, as mentioned earlier. Next, we'll discuss shifting. Shifting a wavelet simply means delaying or advancing the onset of the wavelet along the length of the signal. A shifted wavelet represented using this notation [on screen] means that the wavelet is shifted and centered at k. We need to shift the wavelet to align with the feature we are looking for in a signal.The two major transforms in wavelet analysis are Continuous and Discrete Wavelet Transforms. These transforms differ based on how the wavelets are scaled and shifted. More on this in the next session. But for now, you've got the basic concepts behind wavelets.
您还可以从以下列表中选择一个网站:
选择中国网站(以中文或英文)以获取最佳网站性能。其他MathWorks国家网站未优化您的位置。