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## Numerical differentiation based on wavelet transforms

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Numerical differentiation based on wavelet transforms (CWT and DWT)

Updated

Numerical differentiation is important in various applications. However, it should be taken with caution because it can greatly amplify the noise in the data, especially at high frequencies. When a wavelet function is the derivative of a smoothing function, the wavelet transform has the combined properties of smoothing and differentiation.

### Comments and Ratings (13)

Mahdi S. Hosseini

### Mahdi S. Hosseini (view profile)

A generalized framework called MaxPol has been recently published and made available here
https://www.mathworks.com/matlabcentral/fileexchange/63294-maxpol-smoothing-and-differentiation-package

MaxPol provides a framework to design variety of numerical differentiation kernels with properties like:
(1) Cutoff (lowpass) design with no side-lob artifacts (for noise-robust case)
(2) Arbitrary order of differentiation
(3) Arbitrary polynomial accuracy
(4) Derivative matrix design
(5) 2D Derivative Kernels with Steering moments
(6) Intuitive examples in Signal and Image processing

eFKa

### eFKa (view profile)

i have y=[ 1,...,n] with length of y the time in nanoseconds. Why is derivative_cwt not working?

y = [ 1,...,n];
t =1:1:length(y);
y_prime = derivative_cwt(y,'gaus1',16,dx,1));
i get the following error:
Matrix dimensions must agree.
Error in derivative_cwt (line_36)
u = u -a*x-b;

I dont know what to change? Thanks for help in advance

Oskar Elek

### Oskar Elek (view profile)

I don't have the Wavelet Toolbox, but the _dwt variant worked out-of-the-box for me, and it worked precisely as advertised. Many thanks to the author for publishing this!

Mohammed alsubhi

GreaT!

karlosgk

Yotam Stern

### Yotam Stern (view profile)

excellent work!

really helpful, i was just looking into this and stumbled upon this file through google.

James Ganong

### James Ganong (view profile)

Your method worked to solve a problem that stumped me for years! I work with tracking data from ocean animals. These data can be very noisy, but I was able to extract good speed data.

Marc Cote

### Marc Cote (view profile)

Thank you, exactly what I needed.

Gianluca

### Gianluca (view profile)

Do you think the same can be applied also for integration?

Gianluca

### Gianluca (view profile)

Zika Zivic

Really very nice. Thanks.

Z. Haiyun

Excellent. It may be perfect by adding more spline wavelet.

someone used this

superbly done!!

##### MATLAB Release
MATLAB 7.1.0 (R14SP3)
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