Window Functions and Spectral Leakage - Signal Processing of Random Physiological Signals - page 179

rectangular window has a decreasing rate of − 6 dB/octave. This means that the next side

lobe will be encountered at 19 dB. If the side lobes reduce rapidly, then the

main lobe of the FFT bands will lose less energy into the sidelobes and the spectra will
be less erroneous. Side lobe fall-off performance measure is important for applications
with multiple signals that are close in frequency.

− 13 − 6 =−

16.2.3 Frequency Straddle Loss
Frequency straddle loss is the reduced output of a DFT filter caused by the input sig-
nal not being at the filter's center frequency. Frequencies seldom fall at the center of
any filter's passband. When a frequency is halfway between two filters, the response of
the FFT has its lowest amplitude. For a rectangular weighting function, the frequency
response halfway between two filters is 4 dB lower than if the frequency were in the
center of a filter. Each of the other weighting functions in this chapter has less fre-
quency straddle loss than the rectangular one. This performance measure is important
in applications where maximum filter response is needed to detect the frequencies of
interest.

16.2.4 Coherent Integration Gain
Coherent integration gain (often referred to as Coherent Gain or Processing Loss )isthe
ratio of amplitude of the DFT filter output to the amplitude of the input frequency.
N -point FFTs have a coherent gain of N for frequencies at the centers of the filter
passbands. Since most weighting function coefficients are less than l, the coherent gain
of a weighted FFT is less than N . While weighting functions reduce the coherent
integration gain, the combination of this reduction and the improved straddle loss results
in an overall signal response improvement halfway between two filters. Like frequency
straddle loss, this performance measure is important in applications where maximum
filter response is needed to detect the frequencies of interest. To restore the main lobes
to their original magnitudes, the FFT coefficients may be multiplied by the inverse of
the coherent gain. Window coherent gains are compared as shown in Table 16.1 to the
rectangular window gain, which is 1 or 0 dB.