Page 372 - Fundamentals of Radar Signal Processing

(5.75)

where the notation Y (F) is used to emphasize that the spectrum is computed
w
with a window applied to the data. This is simply the Fourier transform of the
window function itself, shifted to be centered on the target Doppler frequency

F rather than at zero. Figure 5.17b illustrates the effect of the window on the
D
DTFT for the same data used in part a of the figure. In fact, the asinc function of
Fig. 5.17a is also just the Fourier transform of the rectangular window function
(equivalent to no window). An extensive description of common window
functions and their characteristics is in Harris (1978). In general, nonrectangular
windows cause an increase in mainlobe width, a decrease in peak amplitude,
and a decrease in SNR in exchange for large reductions in peak sidelobe level.

It is straightforward to compute the reduction in peak amplitude and the
SNR loss given the window function w[n]. Consider the peak gain first. From
2
2
2
Eq. (5.74), the peak value of | Y(F)| when no window is used is A M .
Evaluating Eq. (5.75) at F = F gives the peak power when a window is used:
D

(5.76)

The ratio |Y(F)| /|Y(F )| , called the loss in processing gain (LPG), is
2
2
D

(5.77)

With this definition LPG ≥ 1, so the loss in dB is a positive number. Using Eq.
(5.77), the LPG can be computed for any window. Values of 5 to 8 dB are
common. Details depend on the specific window function, but the LPG is

typically a weak function of the window length M, higher for small M and
rapidly approaching an asymptotic value for large M (on the order of 100 or
more).
Although the window reduces the peak amplitude of the DTFT
substantially, it also reduces noise power. Processing loss (PL) is the reduction
in SNR at the peak of the DTFT for a pure sinusoidal input. Denoting the SNR
with and without the window as χ and χ , respectively, it is possible to separate
w
the effects of the window on the target and noise components of the signal