Page 374 - Fundamentals of Radar Signal Processing

TABLE 5.2 Properties of Some Common Data Windows

5.3.2 Sampling the DTFT: The Discrete Fourier Transform
In practice, the DTFT is not computed because its frequency variable is

continuous. Instead, the discrete Fourier transform is computed

(5.81)

As discussed in Chap. 3, for a finite length data sequence Y[k] is just Y(F)
evaluated at F = k/KT = k (PRF/K) Hz. These samples are called Doppler bins.
Thus, the DFT computes K samples of the DTFT evenly spaced across one
period of the DTFT. The DFT is almost invariably computed using an FFT

algorithm. The appearance of a plot of the Doppler spectrum computed using a
DFT can be a strong function of the relation between the actual DTFT shape and
the number and location of the DFT frequency samples.
In some situations, the number of data samples available can be greater
than the desired DFT size, that is, M > K. This occurs when there is a need to
reduce the DFT size for computational reasons, or when the radar timeline

permits the collection of more pulses than the number of Doppler bins required
and it is desirable to use the extra pulses to improve the SNR of the Doppler
spectrum measurement. The data turning procedure described in Chap. 3 and
Fig. 3.10 allows the use of a K-point DFT while taking advantage of all of the
data.
Some caution is needed in applying a data window when the data are
modified by zero padding or turning. In either case a length M window should

be applied to the data before it is either zero padded or turned. Applying a K-
point window to the full length of a zero-padded sequence has the effect of