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''of an estimator of the spectral density''

A function of an angular frequency  $  \lambda $
defining a weight function used in the non-parametric estimation of the [[Spectral density|spectral density]]  $  f ( \lambda ) $
of a [[Stationary stochastic process|stationary stochastic process]]  $  X ( t) $
by smoothing the [[Periodogram|periodogram]] constructed from the observed data of the process. As an estimator of the value of the spectral density at a point  $  \lambda _ {0} $
one usually takes the integral with respect to  $  d \lambda $
of the product of the periodogram at  $  \lambda $
and an expression of the form  $  B _ {N} A ( B _ {N} ( \lambda - \lambda _ {0} ) ) $. 
Here  $  B _ {N} $
is a real number and  $  A ( \lambda ) $
is a fixed function of the frequency which takes its greatest value at  $  \lambda = 0 $
and is such that its integral over  $  \lambda $
is equal to one. This function is usually called a spectral window generator, while the term  "spectral window"  is used for the function  $  B _ {N} A ( B _ {N} \lambda ) $. 
The width of the spectral window is  $  B _ {N}  ^ {-} 1 $, 
and depends on the size  $  N $
of the sample (that is, on the length of the observed realization of the process  $  X ( t) $) 
and tends to zero as  $  N \rightarrow \infty $(
but more slowly than  $  N  ^ {-} 1 $). 
The Fourier transform of the spectral window (and in the case of discrete time  $  t $, 
when  $  - \pi \leq  \lambda < \pi $, 
the set of its Fourier coefficients) is called the lag window of an estimator of the spectral density. It defines a weight function of a discrete or continuous argument (depending on whether  $  t $
is discrete or continuous), by which one must multiply the sample auto-correlations evaluated from the given sample to make the Fourier transform of the resulting product coincide with the desired estimator of the spectral density (cf. [[Spectral density, estimator of the|Spectral density, estimator of the]]).

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  R.B. Blackman,   J.W. Tukey,   "The measurement of power spectra: From the point of view of communications engineering" , Dover, reprint  (1959)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  G.M. Jenkins,   D.G. Watts,   "Spectral analysis and its applications" , '''1–2''' , Holden-Day  (1968)</TD></TR><TR><TD valign="top">[3]</TD> <TD valign="top">  D.R. Brillinger,   "Time series. Data analysis and theory" , Holt, Rinehart &amp; Winston  (1975)</TD></TR><TR><TD valign="top">[4]</TD> <TD valign="top">  M.B. Priestley,   "Spectral analysis and time series" , '''1–2''' , Acad. Press  (1981)</TD></TR><TR><TD valign="top">[5]</TD> <TD valign="top">  A.M. Yaglom,   "Correlation theory of stationary and related random functions" , '''1–2''' , Springer  (1987)  (Translated from Russian)</TD></TR></table>