How to find psi function in Haar continuous wavlelet transform:CWT
1 Ansicht (letzte 30 Tage)
Ältere Kommentare anzeigen
Hai Tran
am 18 Apr. 2016
Kommentiert: Hai Tran
am 10 Mai 2016
Dear all, I has a problem when i try to use Haar wavelet to reconstruct an impact force-F if I know response (strain-e). Lets me describe:
I have impact force (F is a matrix 1x1024) and response (strain e: matrix 1x1024). After using CWT in matlab with scale m=2,4,8,16,32,64,128,256,512,1024, i got a matrix of coefficient (1024x10). And I know that CWT is actually a convolution between F and Psi(Haar wavelet function).
I would like to ask How can i get Psi(Haar wavelet func...) which corresponds to each scale of m?
Thank you so much for your help
0 Kommentare
Akzeptierte Antwort
Wayne King
am 18 Apr. 2016
Hi Hai Tran, If you are using dyadic scales as you do above, I think you would be better to use the MODWT (introduced in R2015b, rather than the CWT). With the MODWT, you do not lose time resolution just like with the CWT but if you are willing to restrict yourself to the dyadic scales, the MODWT has a lot of advantages (energy preservation -- perfect reconstruction just to name a couple important ones).
That said, here is a way to get an idea what the "daughter" wavelets look like at each scale.
scales = 2.^(1:10);
delta = zeros(1024,1);
% Only provides daughter wavelets at one translation
delta(500) = 1;
dwaves = cwt(delta,scales,'haar');
Now each row of dwaves will actually be the time-reverse of the Haar wavelet at that scale.
For scale 32 (2^5)
w5 = fliplr(dwaves(5,:));
Weitere Antworten (1)
Wayne King
am 19 Apr. 2016
Hi Hai, For the CWT you will get 10 rows. For the MODWT, the final row is the scaling coefficients as you guessed.
Yes, when the scale is equal to 2^1 or 2, the Haar wavelet will have magnitude 1/2 or 1/sqrt(4).
Because the impulse was only at one translation, 500, in the case above, you only get the Haar wavelet centered at that position.
2 Kommentare
Siehe auch
Kategorien
Mehr zu Continuous Wavelet Transforms finden Sie in Help Center und File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!