Kaiser window

The Kaiser window isnearly optimal window function w_k useddigital signal processing,is defined byformula:

where I₀ iszeroth order modified Bessel function offirst kind, αan arbitrary real number that determinesshape ofwindow, andinteger n islength ofwindow.

By construction, this function peaks at unityk = n/2, i.e. atcenter ofwindow,decays exponentially towardswindow edges.

The largervalue|α|,narrowerwindow becomes; α = 0 corresponds torectangular window. Conversely,larger |α|width ofmain lobe increases inFourier transformw_k, whileside lobes decreaseamplitude. Thus, this parameter controlstradeoff between main-lobe widthside-lobe area. For large α,shape ofKaiser window tends toGaussian curve.

Tablecontents

1 Kaiser-Bessel derived (KBD) window 2 References 3 External links

Kaiser-Bessel derived (KBD) window

A related window function isKaiser-Bessel derived (KBD) window, whichdesignedbe suitableuse withmodified discrete cosine transform (MDCT). The KBD window function d_kdefinedterms ofKaiser window w_k byformula:

This defineswindowlength 2n, where by construction d_k satisfiesPrincen-Bradley condition forMDCT (usingfact that w_n-k = w_k): d_k²+d_k+n²=1 (interpreting kk+n modulo 2n). The KBD windowalso symmetric inproper manner forMDCT: d_k = d_2n-1-k.

References

• A. V. Oppenheim, R. W. Schafer,J. R. Buck, Discrete-Time Signal Processing (Prentice-Hall, 1999).
• J. F. Kaiser, "Digital Filters," System Analysis by Digital Computer chap. 7 (Wiley: New York, 1966); F. F. KuoJ. F. Kaiser, eds.

External links

• KBD Window Page