Page 381 - Fundamentals of Radar Signal Processing

center frequencies will be equally spaced, equal to the DFT sample frequencies;

and all the passband filter frequency response shapes will be identical,
determined by the window used and differing only in center frequency. The
advantages to this approach are simplicity and speed with reasonable
flexibility. The FFT provides a computationally efficient implementation of the
filterbank: the number of filters can be changed by changing the DFT size; the
filter shape can be changed by choosing a different window; and the filter

optimizes the output SNR for targets coinciding with a DFT filter center
frequency in a noise-limited interference environment.

5.3.6 Fine Doppler Estimation
Peaks in the DFT output that are sufficiently above the noise level to cross an
appropriate detection threshold are interpreted as responses to moving targets,
i.e., as samples of the peak of an asinc component of the form of Eq. (5.74). As
has been emphasized, there is no guarantee that a DFT sample will fall exactly

on the asinc function peak. Consequently, the amplitude and frequency of the
DFT sample giving rise to a detection are only approximations to the actual
amplitude and frequency of the asinc peak. In particular, the estimated Doppler
frequency of the peak can be off by as much as one-half Doppler bin, equal to
PRF/2K Hz.
If the DFT size K is significantly larger than the slow-time data sequence

length M, several DFT samples will be taken on the asinc mainlobe and the
largest may well be a good estimate of the amplitude and frequency of the asinc
peak. Frequently, however, K = M and sometimes, with the use of data turning,
it is even true that K < M. In these cases, the Doppler samples are far apart and
a half-bin error may be intolerable. One way to improve the estimate of the true
Doppler frequency F is to interpolate the DFT in the vicinity of the detected
D
peak.

The most obvious way to interpolate the DFT is to zero pad the data and
compute a larger DFT. In the absence of noise the interpolated values are exact.
However, this approach is computationally expensive and interpolates all of the
spectrum. If finer sampling is needed only over a small portion of the spectrum
around a detected peak the zero padding approach is inefficient.
Computing a larger DFT is tantamount to interpolation using an asinc

interpolation kernel. To see this, consider evaluating the DTFT at an arbitrary
value of ω using only the available DFT samples. This can be done by
computing the inverse DFT to recover the original time-domain data and then
computing the DTFT from those samples: