Numerical Differentiation of Noisy, Nonsmooth Data

<table>The function <svg height="13.4875" id="M118" style="vertical-align:-2.34499pt" version="1.1" viewbox="0 0 10.675 13.4875" width="10.675" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.4875)">
<g transform="translate(72,-61.21)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑓</tspan>
</text>
</g>
</g>
</svg> is denoised, then differentiated with finite differences. The result is noisy and inaccurate.</table>

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fig3

Figure 3

Figure 3: Numerical Differentiation of Noisy, Nonsmooth Data 