Biomedical Engineering Reference
In-Depth Information
FIGURE 2.6:
First column—window in time domain, second column—window
in frequency domain, third column—spectra of signal e) obtained by application of
respective window function and Fourier transform. e) signal composed of autoregres-
sive time series with spectral peak around 0.375 and sinusoid with frequency 0.42.
The windows are: a) rectangular b) Tukey with 10% round off c) Hann window d)
Blackmann-Harris. Note the spectrum leakage effects in form of spurious peaks in
case of rectangular and Tukey windows.
The avaliable windows are:
barthannwin
,
bartlett
,
blackman
,
blackmanharris
,
bohmanwin
,
chebwin
,
flattopwin
,
gausswin
,
hamming
,
hann
,
kaiser
,
nuttallwin
,
parzenwin
,
rectwin
,
triang
,
tukeywin
.
For a signal consisting of multiple frequencies the applied window has consider-
able influence on the detectability of individual spectral components [Harris, 1978].
Examples of windows and their properties are shown in Figure 2.6.
2.3.2.1.2
Errors of Fourier spectral estimate
Fourier transform
X
(
f
)
is a com-
plex number whose real
X
R
parts can be considered as un-
correlated random values of zero mean and equal variance. Since Fourier transform
is a linear operation, components
X
R
(
f
)
and imaginary
X
I
(
f
)
(
f
)
and
X
I
(
f
)
have a normal distribution, if
x
(
t
)
has normal distribution. Therefore value:
2
X
R
(
X
I
(
|
X
(
f
)
|
=
f
)+
f
)
(2.34)
Search WWH ::
Custom Search