S transform is a time-frequency transform created based on the concept of short-time Fourier transform and wavelet transform. The main property of this transform that separates it from the discrete short-time Fourier transform is the variable-frequency resolution. But in this transform, the resolution change of high frequencies to low frequencies is very significant. So another transform as a Modified S Transform(MST) was introduced to adjust a parameter that controls the rate of change in resolution. In this paper, S and MST has been first discussed.Then, on the basis of the MST transform,the Optimum S Transform (EST) was introduced with a new parameter. Next, calculating the length of the used window, the dependence of it to the proposed parameters was studied and the effect of each of the parameters on the rate of changing the length of window was illustrated in theory and simulation. Finally, with simulation, the performance of the proposed method for detection of FMCW signals was examined , and the effect of each of the parameters on the detection of above signals was shown. Then the better performance of the proposed method than two last methods was proved.
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