Page 382 - Fundamentals of Radar Signal Processing

(5.93)

The term in braces is the interpolating kernel. It can be expressed in closed form
as

(5.94)

Combining these gives

(5.95)

Equations (5.94) and (5.95) can be used to compute the DTFT at any single
value of ω from the DFT samples. It can be applied to interpolate the values of
the DFT over localized regions with any desired sample spacing and the result
is exact in the absence of noise. However, it remains relatively computationally
expensive.

A simpler but very serviceable technique for interpolating local peaks is
illustrated in Fig. 5.20. For each detected peak in the magnitude of the DFT
output, a second-order polynomial is fit through that peak and the two adjacent
magnitude data samples. Once the polynomial coefficients are known, the
amplitude and frequency of its peak are easily found by differentiating the
formula for the polynomial and setting the result to zero. It can be shown that the

second-order polynomial passing through the three samples can be expressed as