Biomedical Engineering Reference
In-Depth Information
FIGURE 2.5: The illustration of assumptions of DFT. a) The assumed signal. b)
Observation window (equation (2.33)) c) The observed fragment of signal. d) The
signal from observation window (marked with gray rectangle) is periodically re-
peated to infinity. The discontinuities of the signal at the window edge introduce
additional components to the frequency spectrum.
domain corresponds to convolution in the frequency domain (see equation 1.31).
Therefore the transform we obtain can be considered as the convolution of the trans-
form of idealized infinite signal X
(
)
f
with the transform of the window function
W T / 2
. This property deteriorates the spectral estimate; especially disturbing are
the side lobes of function W
(
f
)
(
f
)
.
2.3.2.1.1 Choice of windowing function A commonly used technique to reduce
the spectral leakage is the choice of the proper function w T / 2 (
. Usually one wants
the window w to smoothly approach zero at both edges. In order to improve estima-
tion of spectral power, windows of different shapes were introduced. Good windows
are characterized by a highly concentrated central lobe with very low or quickly di-
minishing side lobes of their transforms. In MATLAB Signal Processing Toolbox
there is a very convenient tool for studying windows properties: wintool .Itdis-
plays the time and frequency representation of the selected window and evaluates its
important characteristics:
t
)
Leakage factor—ratio of power in the side lobes to the total window power
Relative side lobe attenuation—difference in height from the main lobe peak
to the highest side lobe peak
Width of the main lobe at 3 dB below the main lobe peak
 
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