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As is known by the [[Uncertainty principle]], having a sharp cutoff in the frequency ___domain (cutting off the Fourier Series abruptly without adjusting coefficients) causes a wide spread of information in the time ___domain (lots of ringing).
This can also be understood as applying a [[Window function]] to the Fourier series coefficients to balance maintaining a fast rise time (analogous to a narrow transition band) and small amounts of ringing (analogous to stopband attenuation).
== See also ==
* [[Lanczos resampling]]
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