Page 403 - Fundamentals of Radar Signal Processing

(5.118)

The other frequency-domain mean frequency and spectral width estimators
result from viewing the signal spectrum of Fig. 5.31 as a probability density
function. A valid PDF must be real and nonnegative, a condition met by the
power spectrum. However, a PDF must also have unit area, so the power

spectrum must be normalized to ensure this is the case. By Parseval’s theorem,
2
the integral of |Y(ω)| = 2πE , where E is the energy in y[m]; this is the required
y
y
normalization factor. For any arbitrary PDF p (z) the mean and variance are
z
given by

(5.119)

Applying the first of these definitions to the power spectrum gives an alternative
mean frequency estimator

(5.120)

Similarly, an estimator of the spectral width is

(5.121)

Generally, the time-domain estimators are preferred if the SNR is low or
the spectral width is very narrow (Doviak and Zrni , 1993). In the latter case,
the signal is closer to the pure sinusoid assumption that motivated the time-
domain estimator. In addition, the time-domain methods are more
computationally efficient because no Fourier transform calculations are
required. Conversely, the frequency-domain estimators tend to provide better

estimators at high SNR and large spectral widths. The frequency domain