Page 383 - Fundamentals of Radar Signal Processing

FIGURE 5.20 Refining the estimated target amplitude and Doppler shift by
quadratic interpolation around the DFT peak.

(5.96)

where Δk is the location of the interpolated peak relative to the index k of the
0
apparent peak so that the estimated peak location becomes k′ = k + Δk (see Fig.
0
5.20). Differentiating this equation with respect to Δk, setting the result to zero,
and solving for Δk gives the estimated location of the polynomial peak relative

to k as
0

(5.97)

The amplitude of the estimated peak A′ = |Y [k + Δk]| is found by
0
computing Δk and then using that result in Eq. (5.96). Note that the formula for
Δk behaves in intuitively satisfying ways. If the first and third DFT magnitude
samples are equal, Δk = 0; the middle sample is the estimated peak. If the
second and third samples are equal, Δk = 1/2, indicating the estimated peak is

halfway between the two samples; a similar result applies if the first and second
DFT magnitude samples are equal.
This interpolation technique is less effective when the width of the
presumed mainlobe response that is to be interpolated is so narrow that the
apparent peak and its two neighbors are not on the same lobe of the response.