Contents: Fourier-Transform, Wavelet-Transform, τp Transform, Hilbert—Huang Transform

• Programs about Discrete Fourier Transform(DFT), Inverse Transform(IDFT) and Convolution(Matlab+Python)

Tips:

• DFT needs to read external .txt file, and the .txt file has only one requirement: Consistent number of data per line
• 2D Convolution has only one requirement: 2D data matrix size > Convolution kernel size(the sides have to be odd)

• Convolution(by myself) —— convolution.m
• Example1: a 1D discrete signal is processed by DFT —— cx1.m and cx1_sx.m
• Example2: another 1D discrete signal is processed by DFT and IDFT —— cx2.m and cx2_sx.m
• Example3: doing DFT for a time-domain signal, then it's converted to frequency-domain signal. Then the frequency-domain signal is filtered —— cx3.m and cx3_sx.m
• Cyclic convolution for a signal —— cyclic_convolution.m
• Frequency-Amplitude diagram centralization after 2D DFT —— center_fft2.m
• Butterworth low-pass filtering —— origin_lowpass_fft2.m

• 2D Convolution(by myself), then tested with a simple 2D matrix —— juanji1_2d.m and juanji2_2d.m
• Image processing by 2D convolution, using various convolution kernels to realize different image processing effects —— juanji3_2d.m
• Image filtering by 2D convolution, Median-filtering and Mean-filtering for Gaussian noise and salt noise —— noise_mean.m and noise_midval.m
• 2D Deconvolution(by myself), then tested with a simple 2D matrix processed by 2D convolution —— fjuanji1_2d.m and kz1.m
• 2D Discrete Fourier transform and Inverse Fourier transform(by myself) —— mydft2.m and myidft2.m
• Filtering in frequency domain for the image with noise —— noise_lowpass_fft2.m and noise_compare.m

Tips:

• Mang programs use the picture named zxc.jpg
• You can see more detailed interpretation from my blog: https://www.jianshu.com/nb/35397386

• 1D signal multistage decomposition, reconstruction and recover by wavelet —— xb1d_basic.m and xb1d_recover.m
• Using Matlab own wavelet toolbox functions —— oned_process1.m and oned_process2.m
• Example1: identify the discontinuities in the signal by multistage wavelet decomposition —— Identify_breakpoint.m
• Example2: time-frequency analysis by wavelet and short-time Fourier transform, studying the variation of frequency with time in time-varying signal —— tfrstft.m and time_freq_analy.m
• Example3: denoising by wavelet —— wden_qz.m and wdencmp_qz.m
• Example4: time-frequency analysis of actual seismic data, and drawing contour map, mesh2D and mesh3D pictures —— shiji.m, Data: shuju.xlsx
• You can see more detailed interpretation from my blog: https://www.jianshu.com/nb/35397386

Tips:

• When you want to use the time-frequency analysis function, you have to use the tfrstft.m function. So remember to include this file!

• Geophysical-specific τp transform —— τp.m
• You can see more detailed interpretation from my blog: https://www.jianshu.com/p/4439a1cb5c35

• 1D Discrete Hilbert Transform(DHT) —— Hilbert.m
• DHT is applied to the real signal to obtain its '3I' property: Instantaneous-frequency, Instantaneous-phase and Instantaneous-amplitude —— HT3S.m
• You can see more detailed interpretation from my blog: https://www.jianshu.com/p/b591d95ae80b

• Time-frequency analysis by Hilbert—Huang Transform(HHT) —— HHT1 folder
• Time-frequency analysis by HHT with advanced ceemdan decomposition —— HHT2 folder —— Recommand!!
• You can see more detailed interpretation from my blog: https://www.jianshu.com/p/3363abb64f32

Tips:

• HHT is currently the best method for time-frequency analysis. The new improvements simply change its empirical mode decomposition process, but the idea remains the same! So when you want to conduct time-frequency analysis, I recommend you use HHT instead of wavelet!

• 主要为"离散傅里叶变换(DFT)与卷积(conv)"相关matlab和python程序

说明：

• DFT程序中读取外部txt数据文件，格式只有一个要求：每行数据个数一致。
• 二维卷积只有一个要求：二维数据矩阵尺寸 > 卷积核尺寸(边长最好为奇数)。

新增程序如下：

• 卷积的手动实现(文件名：convolution.m)
• 例题1——离散函数信号的DFT处理，用matlab自带程序和手动实现各一个(文件名：cx1.m与cx1_sx.m);
• 例题2——原始时域信号与DFT+IDFT变换后的时域信号对比，用matlab自带程序和手动实现各一个(文件名：cx2.m与cx2_sx.m);
• 例题3——频率域的滤波操作，并在频域滤波后转换回时域，用matlab自带程序和手动实现各一个(文件名：cx3.m与cx3_sx.m);
• 对原始的循环卷积程序(cyclic_convolution.m)稍微修改，加上用matlab自动语句直接实现的功能;
• 相关说明参考：一维卷积与一维离散傅里叶变换。

新增程序如下：

• 二维卷积的手动实现，并用简单的二维矩阵进行测试(文件名：juanji1_2d.m与juanji2_2d.m);
• 二维卷积对图像的处理：用多种卷积核实现不同的图像处理效果(文件名：juanji3_2d.m);
• 二维卷积对图像做滤波：针对"高斯噪声和椒盐噪声"做"中值滤波和均值滤波"(文件名：noise_mean.m与noise_midval.m);
• 二维反卷积实现(文件名：fjuanji1_2d.m与kz1.m);
• 二维离散傅里叶正变换与逆变换的手动实现(文件名：mydft2.m与myidft2.m);
• 二维离散傅里叶变换后"频振图中心化"的手动实现(文件名：center_fft2.m);
• 在二维离散傅里叶变换后的"频域"内做"巴特沃斯低通滤波"效果(文件名：origin_lowpass_fft2.m);
• 对加了"高斯噪声/椒盐噪声"的二维图像矩阵进行频域滤波(文件名：noise_lowpass_fft2.m与noise_compare.m)。
• 另外，上面很多程序中用到了"zxc.jpg"图片，也放了进去方便直接测试程序(文件名：zxc.jpg);
• 相关说明参考：二维卷积与二维离散傅里叶变换。

新增程序如下：

• 一维信号小波多级分解与重构/恢复原始信号的手动实现(文件名：xb1d_basic.m与xb1d_recover.m)；
• 一维信号相关matlab自带函数的使用(文件名：oned_process1.m与oned_process2.m)；
• 小波应用1：利用小波多级分解辨识信号中的间断点(文件名：Identify_breakpoint.m)；
• 小波应用2：利用小波和短时傅里叶变换做时频分析，研究时变信号中频率随时间的变化情况(文件名：tfrstft.m与time_freq_analy.m)；
• 小波应用3：小波变换去噪(文件名：wden_qz.m与wdencmp_qz.m)；
• 小波应用4：实际地震数据的时频分析，并绘制等值线图、mesh2d、mesh3d图像(文件名：shiji.m；数据名：shuju.xlsx)；
• 相关参考说明：小波变换。
  注意：时频分析应用时，各个函数都要配上tfrstft.m函数(放在一起)，它里面有一些时频变换的基础功能。

新增程序如下：

• 地球物理专用的τp变换程序(文件名：tp.m)；
• 相关说明参考：τp变换。

新增程序如下：

• 一维离散希尔伯特变换手动实现(文件名：Hilbert.m)；
• 根据离散希尔伯特变换得到信号的3瞬属性：瞬时振幅/包络、瞬时相位、瞬时频率(文件名：HT3S.m)；
• 相关说明参考：离散希尔伯特变换。

新增程序如下：

• 说明：希尔伯特-黄变换是目前时频分析最好的方法。新的改进都只不过改变它的经验模态分解过程，思想不变！
• 希尔伯特-黄变换手动实现以及时频分析(文件夹名：HHT1);
• 用自带工具包的函数完成希尔伯特-黄变换与时频分析，并配备更高级的ceemdan分解方式(文件夹名：HHT2)；(推荐)
• 相关说明参考：希尔伯特-黄变换。