Window function: Difference between revisions

Revision as of 08:22, 7 June 2025

Latest revision as of 04:16, 11 August 2025

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\begin{align}

w_0(n)\ &= w\left[ n+\tfrac{N}{2}\right]\\

&= a_0 -+ (1-a_0)\cdot \cos \left ( \tfrac{2\pi n}{N} \right),\quad -\tfrac{N}{2} \le n \le \tfrac{N}{2}.

\end{align}

</math>

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==== DPSS or Slepian window ====

The DPSS (discrete prolate spheroidal sequence) or [[Slepian function]], taper, or window [[Spectral concentration problem|maximizes the energy concentration in the main lobe]],<ref name=Slepian/> and is used in [[multitaper]] spectral analysis, which averages out noise in the spectrum and reduces information loss at the edges of the window.

The main lobe ends at a frequency bin given by the parameter ''α''.<ref name=KaiserDPSS/>

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where <math>C^{\mu}_{N}</math> is the [[Ultraspherical polynomial]] of degree N, and <math>x_0</math> and <math>\mu</math> control the side-lobe patterns.<ref name=Deczky/>

Certain specific values of <math>\mu</math> yield other well-known windows: <math>\mu=0</math> and <math>\mu=1</math> give the Dolph–Chebyshev and [[Tapio Saramäki|Saramäki]] windows respectively.<ref name=Kabal/> See [httphttps://octave.sourceforge.net/signal/function/ultrwin.html here] for illustration of Ultraspherical windows with varied parametrization.

{{clear}}