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Performance Analysis of Using Tapered Windows for Sidelobe Reduction in Chirp-Pulse Compression

*Radio Physics and Radio Astronomy*, Vol. 24, #4, pp.300-313

**(2019)**(in Russian)

### V.G. Galushko

Purpose: Analyzing the output signal structure of the optimum filter of chirp-pulse compression in order to look into causes of discrepancy between the sidelobe level, which is obtained using standard tapered windows, with the literature data.
Design/methodology/approach: To calculate the response structure of the optimum filter with a tapered window of an arbitrary form, the standard methods of mathematical physics and statistical theory of signal processing are used.
Findings: Expressions have been derived for estimating the maximum number of zeros and maxima of the response of the optimum filter of chirp-pulse compression and separation between adjacent and ?like? (with the same numbers) zeros and maxima in dependence on the signal base. Formulas have been obtained
for loss in the signal-to-noise ratio due to application of smoothing functions. The case of applying window functions in the form of cosine harmonics of the Fourier series, which describes a rather great number of the standard windows, is analyzed in detail. An analytical expression has been derived for the output signal of the chirp-pulse compression filter on the basis of such windows, and a formula for estimating the amount of loss
in the signal-to-noise ratio is presented. A comparative performance
analysis of the Hamming and Blackman windows has been made in dependence on the signal base B. It has been found that application of the Hamming window is more efficient for B ? 80. For greater values of B, the Blackman window shows a
higher efficiency. As B increases, the efficiency of both windows steadily increases asymptotically approaching the figure declared in the literature. Coefficients of window functions containing three cosine harmonics of the Fourier series have empirically been selected that made it possible to reduce the sidelobe level by approximately 0.34 dB for B ? 21 and more than by 1 dB for B ? 7 as compared with the Hamming window.
Conclusions: The obtained results allow concluding that the optimization problem for the window function parameters in the case of small signal bases should be solved individually for each specific value of B. Most likely it would be impossible to obtain the extremely low sidelobe level, however a certain improvement of the characteristics of the chirp-pulse compression
filter seems to be quite possible.
Key words: chirp-pulse, pulse compression filter, window function, sidelobe level

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