Page 379 - Fundamentals of Radar Signal Processing

This summation evaluates to the asinc function of Eq. (5.74) shifted to a center
frequency of ω = –2πk/K, which is equivalent to ω = 2π (K – k)/K. The kth DFT

sample therefore corresponds to filtering the data with a bandpass filter having
a frequency response with an asinc function shape centered at the frequency of
the (K – k)th DFT sample.
If the data are windowed before processing with a window function w[m],
Eq. (5.86) becomes (again for F = k/KT)
D

(5.89)

The impulse response vector and frequency response are then

(5.90)

(5.91)

The DFT still implements a bandpass filter centered at each DFT frequency but
the filter frequency response shape now becomes that of the window function.

The relation between the DFT and a bank of filters can be made more
explicit. Consider a slow-time signal y[m] obtained with a long series of pulses
and an M-point window function w[m]. The window function can be slid along
the data sequence to select a portion of the data for spectral analysis as shown
in Fig. 5.19. The DTFT of the resulting sequence w[m – p]y[p] is, in terms of
analog frequency F,