
38 Practical Biomedical Signal Analysis Using MATLAB
R
is a sum of squares of two independent variables of normal distribution; hence each
frequency component of estimator
ˆ
S( f ) has a distribution given by:
ˆ
S( f )
S( f )
=
χ
2
2
2
(2.35)
where χ
2
2
is a chi-square statistics of two degrees of freedom (corresponding to the
real and imaginary parts of Fourier transform) [Bendat and Piersol, 1971]. Please
note that the above expression is independent of the observation time T, which means
that increasing of epoch T does not change the distribution function describing the
error of the estimator. The increase of the time of observation T increases only the
number ...