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    <p>You could try a <code>ListConvolve</code> with a Gaussian kernel to smooth your data. One of the nice features of this is that the <em>derivative</em> of the <strong>convolution</strong> with a Gaussian kernel is equivalent to <em>convolving</em> with a <strong>derivative</strong> of the Gaussian kernel.</p> <p>Here is some sample data:</p> <pre><code>data = Table[Sin[x] + .5 RandomReal[{-1, 1}], {x, 0, 6 \[Pi], .05}]; ListLinePlot[data] </code></pre> <p><img src="https://i.stack.imgur.com/na1uS.png" alt="enter image description here"></p> <p>This is a simple convolution with a Gaussian kernel:</p> <pre><code>data2 = Block[{\[Sigma] = 2}, ListConvolve[ Table[1/(Sqrt[2 \[Pi]] \[Sigma]) E^(-x^2/(2 \[Sigma])), {x, -2 , 2, 1/10} ], data, {11, 11} ] ]; ListLinePlot[data2] </code></pre> <p><img src="https://i.stack.imgur.com/5t8cG.png" alt="enter image description here"></p> <p>Convolution with the first derivative of a Gaussian:</p> <pre><code>data3 = Block[{\[Sigma] = 1}, ListConvolve[ Table[-((E^(-(x^2/(2 \[Sigma]))) x)/(Sqrt[2 \[Pi]] \[Sigma]^2)), {x, -2 \[Sigma],2 \[Sigma], \[Sigma]/10} ], data, {11, 11} ] ]; ListLinePlot[data3] </code></pre> <p><img src="https://i.stack.imgur.com/sNgpU.png" alt="enter image description here"></p> <p>You may want to play with the sigma parameter to see what gets optimal results in your case.</p> <p>The whole theory behind this is called <a href="http://en.wikipedia.org/wiki/Scale_space" rel="nofollow noreferrer">Scale Space</a>. Note that the above statement about convolution holds for continuous space. <a href="http://en.wikipedia.org/wiki/Scale_space_implementation" rel="nofollow noreferrer">For a discrete implementation, the kernel could be chosen somewhat better.</a></p> <p>Note further that, just as MovingAverage, a convolution can move the features of your data.</p>
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    1. USAlexey Popkov
    1. USSjoerd C. de Vries
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    1. COGreat answer, thanks!
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      1. USDaniel Chisholm
    2. COA normalization constant is looking for a foster parent ...
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    3. CO@belisarius Tell me where I forgot one
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