小波变换及应用 要点: 小波基、尺度、尺度函数 连续小波变换 ■离散小波变换,马拉算法 小波变换压缩原理 小波变换去噪原理 ■小波变换其他应用
小波变换及应用 要点： ▪ 小波基、尺度、尺度函数 ▪ 连续小波变换 ▪ 离散小波变换，马拉算法 ▪ 小波变换压缩原理 ▪ 小波变换去噪原理 ▪ 小波变换其他应用
小波变换及应用 散开的波纹 秒后 2秒后 1秒后 石头击到 水平 空间
小波变换及应用
实例
实 例
鼠标指向图像,按右键,选“播放 Design and animation L ONIC A S 鲨鱼会小波分析
鲨鱼会小波分析？ F L A S H 鼠标指向图像，按右键，选“播放
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File Edit View Go Web Window Help 回+舀 Find in page x: Wavelets: A New Tool for Signal Analysis: What Is Wavelet Analysis? Add to F avorites Vavelet Toolbox What Is Wavelet Analysis? Now that we know some situations when wavelet analysis is useful, it is worthwhile asking"What is wavelet analysis? and even more fundamentally, What is a wavelet? A wavelet is a waveform of effectively limited duration Phat hasan average value of zero. Compare wavelets with sine waves, which are the basis of Fourier analysis, Sinusoids do not have limited duration- they extend from minus to plus infinity. And where sinusoids are smooth and predictable, wavelets tend to be irregular and asymmetric. Sine wave Wavelet(db10) reaking up a signal into sine waves of various frequenc nilarly, wavelet analysis is the breaking up of a signal into shifted and scaled versions of Just looking at pictures of wavelets and sine waves you can see intuitively that signals with sharp changes might be better analyzed with an irregular wavelet than with a smooth sinusoid, just as some foods are better handled with a fork than a spoon. It also makes sense that local features can be described better with wavelets that have local extent. What Can Wavelet Analysis Do Number of dimensions國
区 File Edit View Go Web Window Help 回◆+舀 Find in page: WaveletToolbox.Wavelets:ANew Tool for Signal Analysis: The Continuous Wavelet Transform z Add to Favorites Wavelet Toolbox The Continuous wavelet Transform Mathematically, the process of Fourier analysis is represented by the fourier transform F(o)= f(t)e dt Fourier Transform which is the sum over all time of the signal f(t multiplied by a complex exponential (Recall that a complex exponential can be broken down nto real and imaginary sinusoidal components The results of the transform are the Fourier coefficients F(o) which when mu plied by a sinusoid of frequency o. yield Id the constituent sinusoidal components of the original signal. Graphically, the process looks like Transform Signal Constituent sinusoids of different frequencies Rear
Fourier Transform
Figure 10-10 Jean Baptiste Joseph Fourier and (b) amplitud (d)reconstruction from amplitude alone: I.T. Young, Delf Uni Chase alone(Courtesy Prof rsity of Technology) Fourier 's Fourier Transform p.202
Fourier’s Fourier Transform p.202
在线有什 么了不起? 小波变换可同时得 空问城与频城信息
小波变换可同时得到 空间域与频域信息