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Numerical differentiation based on wavelet transforms

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Numerical differentiation based on wavelet transforms (CWT and DWT)

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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 (11)

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!

GreaT!

karlosgk

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.

Gianluca

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

Gianluca

Zika Zivic

Really very nice. Thanks.

Z. Haiyun

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

someone used this

superbly done!!

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