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Measurement of the time and frequency shifting signals with discrete Fourier transforms


V.A. Ufaev - Dr.Sc. (Eng.), Senior Research Scientist, Military Educational-Scientific Center of air Forces of the «Military-Air Academy named after Professor N.E. Zhukovsky and Yu. A. Gagarin» (Voronezh) E-mail: M.F. Volobuev - Ph.D. (Eng.). Associate Professor, Military Educational-Scientific Center of air Forces of the «Military-Air Academy named after Professor N.E. Zhukovsky and Yu. A. Gagarin» (Voronezh) E-mail:

On the basis of the convolution with the use of discrete Fourier transforms are defined two-dimensional correlation function. Reference signal outside the time limits proposed to redefine the way the cyclic shift to pre-cutoff. With the use of statistical simulation tools investigated the accuracy of one-parameter measurement frequency and the delay in the absence of information about the second parameter. Established the following laws. Instrumental errors are in-dependent of the sample size; in the presence of local fluctuations are no regular changes of levels of error from the true value of the measured parameters; Errors delay estimation and the frequency shift is directly proportional to the value of the nuisance parameter, and return are directly proportional to the modulation frequency and frequency deviation. The formulas for calculating the errors. The joint two-parameter measurement eliminates errors of single-parameter measurements, but because of the two-dimensional space requires a substantial increase in the number of computational operations. An alternative way to measure the joint, which consists of sequential estimation of the frequency of the maximum of the correlation function of the power spectra and the delay at the frequency of assessment. The level of measurement error in the noise close to the potential limit, and instrumental errors are reduced by more than 2 orders of magnitude relative to single-parameter estimation have a threshold character and is much higher when the monitoring interval has at least 1-2 periods of a sinusoidal modulation or 10 cycles of manipulation random code sequence.


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