Window function: Difference between revisions

Revision as of 16:55, 20 December 2023

Revision as of 17:03, 20 December 2023

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== Applications ==

Window functions are used in spectral [[frequency spectrum#spectral analysis|analysis]]/modification/[[Overlap–add method#resynthesis|resynthesis]],<ref name=OLA/> the design of [[finite impulse response]] filters, merging multiscale and multidimensional datasets<ref>{{Cite web |last=Ajala |first=R. |last2=Persaud |first2=P. |title=Ground‐Motion Evaluation of Hybrid Seismic Velocity Models |url=https://doi.org/10.1785/0320220022 |access-date=2023-12-20 |website=pubs.geoscienceworld.org}}</ref><ref>{{Cite journal |last=Ajala |first=R. |last2=Persaud |first2=P. |date=2021-10 |title=Effect of Merging Multiscale Models on Seismic Wavefield Predictions Near the Southern San Andreas Fault |url=https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2021JB021915 |journal=Journal of Geophysical Research: Solid Earth |language=en |volume=126 |issue=10 |doi=10.1029/2021JB021915 |issn=2169-9313}}</ref>, as well as [[beamforming]] and [[Antenna (radio)|antenna]] design.

[[File:Spectral_leakage_caused_by_%22windowing%22.svg|thumb|351px|Figure 2: Windowing a sinusoid causes spectral leakage. The same amount of leakage occurs whether there are an integer (blue) or non-integer (red) number of cycles within the window (rows 1 and 2). When the sinusoid is sampled and windowed, its [[discrete-time Fourier transform]] (DTFT) also exhibits the same leakage pattern (rows 3 and 4). But when the DTFT is only sparsely sampled, at a certain interval, it is possible (depending on your point of view) to: (1) avoid the leakage, or (2) create the illusion of no leakage. For the case of the blue DTFT, those samples are the outputs of the [[discrete Fourier transform]] (DFT). The red DTFT has the same interval of zero-crossings, but the DFT samples fall in-between them, and the leakage is revealed.]]