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.
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
i have y=[ 1,...,n] with length of y the time in nanoseconds. Why is derivative_cwt not working?
y = [ 1,...,n];
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
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!
really helpful, i was just looking into this and stumbled upon this file through google.
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.
Thank you, exactly what I needed.
Do you think the same can be applied also for integration?
Really very nice. Thanks.
Excellent. It may be perfect by adding more spline wavelet.