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m clean up spacing around commas and other punctuation, replaced: ,B → , B (2), ,J → , J, ,P → , P, ,R → , R (3), ,S → , S, ,T → , T (2), ,n → , n (2), ,p → , p |
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|Some authors limit their attention to this important subset and to even values of N.<ref name=Harris/><ref name=Heinzel2002/> But the window coefficient formulas are still the ones presented here.}}
*The parameter '''B''' displayed on each spectral plot is the function's [[
**See {{Slink|spectral leakage|Discrete-time signals|Some window metrics}} and [[
The sparse sampling of a [[discrete-time Fourier transform]] (DTFT) such as the DFTs in Fig 2 only reveals the leakage into the DFT bins from a sinusoid whose frequency is also an integer DFT bin. The unseen sidelobes reveal the leakage to expect from sinusoids at other frequencies.{{efn-la
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=== Asymmetric window functions ===
The <math>w_0(x)</math> form, according to the convention above, is symmetric around <math>x = 0</math>. However, there are window functions that are asymmetric, such as the [[Gamma distribution]] used in FIR implementations of [[Gammatone filter]]s. These asymmetries are used to reduce the delay when using large window sizes, or to emphasize the initial transient of a decaying pulse.{{
Any [[bounded function]] with [[compact support]], including asymmetric ones, can be readily used as a window function. Additionally, there are ways to transform symmetric windows into asymmetric windows by transforming the time coordinate, such as with the below formula
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{{cite patent
|title=Wideband communication intercept and direction finding device using hyperchannelization
|invent1=Carlin, Joe
|invent2=Collins, Terry
|invent3=Hays, Peter
|invent4=Hemmerdinger, Barry E. Kellogg, Robert L. Kettig, Robert L. Lemmon, Bradley K. Murdock, Thomas E. Tamaru, Robert S. Ware, Stuart M.
|pubdate=1999-12-10
|fdate=1999-12-10
| |||