File Exchange

image thumbnail

Numerical differentiation based on wavelet transforms

version 1.0 (966 KB) by

Numerical differentiation based on wavelet transforms (CWT and DWT)



No License

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)

A generalized framework called MaxPol has been recently published and made available here

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 (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

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!



karlosgk (view profile)

Yotam Stern

excellent work!

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

James Ganong

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

Thank you, exactly what I needed.


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


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)

Download apps, toolboxes, and other File Exchange content using Add-On Explorer in MATLAB.

» Watch video

Win prizes and improve your MATLAB skills

Play today