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Learning Wavelet Transform by MATLAB Toolbox

Learning Wavelet Transform by MATLAB Toolbox. Professor : R.J. Chang Student : Tsung -Lin Wu Date :2012/12/14. Outline. 1. Wavelet evolution 2. Wavelet transform toolbox in MATLAB 3. Wavelet function in MATLAB 4. Wavelet packet transform toolbox in MATLAB

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Learning Wavelet Transform by MATLAB Toolbox

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  1. Learning Wavelet Transform by MATLAB Toolbox Professor:R.J. Chang Student : Tsung-Lin Wu Date :2012/12/14

  2. Outline 1. Wavelet evolution 2. Wavelet transform toolbox in MATLAB 3. Wavelet function in MATLAB 4. Wavelet packettransform toolbox in MATLAB 5. Wavelet packet function in MATLAB 6. Definition of SNR

  3. 1. Wavelet evolution • Fourier transform: • Time-frequency tile for Fourier transform: • Poor time-localization f t

  4. 1. Wavelet evolution(count.) • Short-time Fourier transform: • Time-frequency tile for STFT: • w(t-τ) is the window function. f f t t

  5. 1. Wavelet evolution(count.) • Wavelet transform: • Time-frequency tile for wavelet transform: Translations and Scaling of a Wavelet f t

  6. 1. Wavelet evolution(count.) • Compare these three methods:

  7. 2. Wavelet transform toolbox in MATLAB • Decomposition and reconstruction : • This structure contains for J = 3 the terminal nodes of the following tree. Input signal Level1 Level2 Level3

  8. 2. Wavelet transform toolbox in MATLAB(count.) • Step 1: Type command “wavemenu” at command windowand hit the Wavelet 1-D button. • Step 2: Load signal from “*.mat files” or “workspace”. • Step 3: Select the mother wavelet and levels, for example: db7, level 5. • Step 4: Push “Analyze” button.

  9. 2. Wavelet transform toolbox in MATLAB(count.) • The signals include approximations(a) and Details(d): s＝a5+d5+d4+d3+d2+d1 d1 d2 d3 d4 a5 d5

  10. Wavelet transform toolbox in MATLAB(count.) • Step 6: Push “Statistics” button to show the statistics of signal of each levels.

  11. Wavelet transform toolbox in MATLAB(count.) • Step 7: Push “De-noise” button to remove the detail parts.

  12. Wavelet transform toolbox in MATLAB(count.)

  13. 3. Wavelet function in MATLAB • 1. Single-level discrete 1-D wavelet transform: [cA,cD] = dwt(X,'wname') Example: load noissin s = noissin(1:1000); [ca1,cd1] = dwt(s,'haar'); plot(s) subplot(121),plot(ca1) subplot(122),plot(cd1) s ca1 cd1

  14. 3. Wavelet function in MATLAB(count.) • 2. Single-level inverse discrete 1-D wavelet transform: X = idwt(cA,cD,'wname') Example: load noissin s = noissin(1:1000); [ca1,cd1] = dwt(s,'haar'); X = idwt(ca1,cd1,'haar'); plot(X) ca1 + s X cd1

  15. 3. Wavelet function in MATLAB(count.) • 3.Multilevel 1-D wavelet decomposition: [C,L] = wavedec(X,N,'wname') Example: load sumsin s = sumsin; [c,l] = wavedec(s,3, 'db1');

  16. 3. Wavelet function in MATLAB(count.) • 4. Reconstruct single branch from 1-D wavelet coefficients: X = wrcoef('type',C,L,'wname',N) Example: load sumsin s = sumsin; [c,l] = wavedec(s,5, 'sym4'); a5 = wrcoef('a',c,l, 'sym4',5);

  17. 4. Waveletpacket transform toolbox in MATLAB • Step 1: Type command “wavemenu” at command windowand hit the Wavelet Packet 1-D button. • Step 2: Load signal from “*.mat files” or “workspace”. • Step 3: Select the mother wavelet and levels, for example: db7, level 5, shannon. • Step 4: Push “Analyze” button.

  18. 4. Waveletpacket transform toolbox in MATLAB

  19. 5. Waveletpacket function in MATLAB 1. Single-level discrete 1-D wavelet packet transform: [T,D] = wpdec(X,N,'wname',E) Example: load noissin s = noissin(1:1000); wpt = wpdec(s,3,'haar','shannon'); plot(wpt)

  20. 5. Waveletpacket function in MATLAB 2. Single-level denoise discrete 1-D wavelet packet transform: [XD,TREED,PERF0,PERFL2]=wpdencmp(X,SORH,N,'wname',CRIT,PAR,KEEPAPP) Example: load noissin s = noissin(1:1000); n = length(s); thr = sqrt(2*log(n*log(n)/log(2))); xwpd = wpdencmp(s,'s',3,'haar','sure',thr,1); plot(t,xx,'r',t,xwpd)

  21. 6. Definition of SNR • 第一種方法為時域計量，為信噪比最基本的定義，信號的平均功率除以雜訊平均功率，以下稱為Time Domain 1 。 • 第二種方法也是為時域計量，為 Mitaim與Kosko所使用之定義，以下稱為Time Domain 2。 • 第三種方法為頻域計量，其定義為信號頻譜在信號頻率下的平均功率除以雜訊頻譜在信號頻率下的平均功率，以下稱為Narrow Band 1 。

  22. 6. Definition of SNR • 第四種方法也是為頻域計量，其定義為信號和雜訊頻譜在信號頻率下的平均功率除以雜訊頻譜在信號頻率下的平均功率，以下稱為Narrow Band 2。 • 第五種方法也是為頻域計量，以下稱為Wide Band，其定義為總信號頻譜的平均功率除以總雜訊頻譜的平均功率，以下稱為Wide Band 。

  23. 6. Definition of SNR 以此範例來觀察上述信噪比定義的不同，模擬方法為使用Monte Carlo法。 資料規格表 Time Domain 1，Time Domain 2和Wide Band 會重合在一起。 Narrow Band 1和Narrow Band 2會重合在一起。

  24. Thank you for your attention.

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