Window function: Difference between revisions

Revision as of 08:39, 18 March 2024

Revision as of 05:43, 28 March 2024

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This function is a member of both the [[#Cosine-sum windows|cosine-sum]] and [[#Power-of-sine/cosine_windows|power-of-sine]] families. Unlike the [[#Hann and Hamming windows|Hamming window]], the end points of the Hann window just touch zero. The resulting [[Spectral leakage|side-lobes]] roll off at about 18&nbsp;dB per octave.<ref name=JOShann/>

Setting &nbsp;<math>a_0</math>&nbsp; to approximately 0.54, or more precisely 25/46, produces the '''Hamming window,''', proposed by [[Richard W. Hamming]]. That choice places a zero-crossing at frequency 5{{pi}}/(''N''&nbsp;−&nbsp;1), which cancels the first sidelobe of the Hann window, giving it a height of about one-fifth that of the Hann window.<ref name=Harris/><ref name=Enochson/><ref name=JOSHamming/>

The Hamming window is often called the '''Hamming blip''' when used for [[pulse shaping]].<ref name=sunar/><ref name=sunar2/><ref name=SRD/>