Page 380 - Fundamentals of Radar Signal Processing

FIGURE 5.19 Relationship between data sequence x[m] and M-point sliding
analysis window w[m].

(5.92)

Equation (5.92) shows that, aside from a phase factor, the DTFT at a particular
frequency is equivalent to the convolution of the input sequence and a modulated
window function, evaluated at time m. Furthermore, if W(F) is the discrete-time

Fourier transform of w[m] (converted to an analog frequency scale), the DTFT
of w[p]exp(+ j2π F pT) is W(F + F ), which is simply the Fourier transform of
D
D
the window shifted so that it is centered at Doppler frequency –F Hz. This
D
means that measuring the DTFT at a frequency F is equivalent to passing the
D
signal through a bandpass filter centered at –F and having a passband shape
D
equal to the Fourier transform of the window function. Since the DFT evaluates
the DTFT at K distinct frequencies at once, it follows that pulse Doppler
spectral analysis using the DFT is equivalent to passing the data through a bank

of bandpass filters.
Of course, it is possible to build a literal bank of bandpass filters, each one
perhaps individually designed, and some systems are constructed in this way.
For example, the zero-Doppler filter in the filterbank can be optimized to match
the expected clutter spectrum or even made adaptive to account for changing

clutter conditions. Most commonly, however, the DFT is used for Doppler
spectrum analysis. This places several restrictions on the effective filterbank
design. There will be K filters in the bank, where K is the DFT size; the filter