Window Functions and Spectral Leakage - Signal Processing of Random Physiological Signals - page 183

16.2.5 Equivalent Noise Bandwidth
Equivalent noise bandwidth is the ratio of the input noise power to the noise power in
the output of an FFT filter times the input data sampling rate. Every signal contains
some noise. That noise is generally spread over the frequency spectrum of interest, and
each narrowband filter passes a certain amount of that noise through its main lobe and
sidelobes. White noise is used as the input signal and the noise power out of each
filter is compared to the noise power into the filter to determine the equivalent noise
bandwidth of each passband filter. In other words, equivalent noise bandwidth represents
how much noise would come through the filter if it had an absolutely flat passband gain
and no sidelobes. It should be noted that leakage to the side lobes not only decreases the
magnitude of the main lobe but also increases the frequency resolution (spreading) of the
main lobe. The width of the spread is compared to the rectangular window, which has a
main lobe width of 1. Table 16.1 shows the equivalent bandwidth spread to be greater
than 1 for all window functions.
16.2.6 Three-Decibel Main-Lobe Bandwidth
The standard definition of a filter's bandwidth is the frequency range over which sine
waves can pass through the filter without being attenuated more than a factor of 2 (3 dB)
relative to the gain of the filter at its center frequency. The narrower the main lobe, the
smaller the range of frequencies that can contribute to the output of any FFT filter. This
means that the accuracy of the FFT filter, in defining the frequencies in a waveform, is
improved by having a narrower main lobe.
16.3 WINDOW FUNCTIONS AND WEIGHTING
EQUATIONS
16.3.1 The Rectangle Window
In this section, some of the most used window models to reduce spectral leakage are
presented. Some terms will be used to relate the effects of the particular window function
to the rectangular window. Recall that the reduction of the side-lobe leakage introduces
leakage from the expansion of the main lobe. Also some gain is lost because of the main