Smoothing and filtering a comparison

Filtering and smoothing are related and are in fact complementary. Filtering is more complicated because it involves a forward and a backward Fourier transform. However, in the frequency domain the noise and signal frequencies are distinguished, allowing the design of a filter that is tailor-made for these frequency characteristics. 

Another feature of polynomial smoothing is that smoothing and differentiation (first and second derivative) can be combined in single step, which is explained in Section 40.5.5. 

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