V.M. Davydochkin – Ph. D. (Eng.), Head of Department of Microwave Oven of Devices and Aerials, Open Company enterprise «KONTAKT-1» (Ryazan). E-mail: email@example.com
S.V. Davydochkina – Ph. D. (Eng.), Associate Professor, Department of Higher Mathematics,
Ryazan State Agrotechnological University. E-mail: firstname.lastname@example.org
V.V. Ezersky – Dr. Sc. (Eng.), Professor, Department of Radio Management and Communication,
Ryazan State Radio Engineering University. E-mail: email@example.com
The classical problem of an estimation of frequency of a signal with the unknown initial phase, accepted against hindrances by means of the algorithm based on a method of the maximum credibility is considered. For elimination of an error of measurement of frequency against resolved hindrances adapted weight function (AWF) is used. The form of such function can be set so that on frequency of a measured signal spectra of stirring signals (hindrances) were equal to zero together with the set quantity of their derivatives. And, as well as usual weight function (WF), AWF should be symmetrized concerning signal edges.
It is shown that at usually used record of a discrete signal in shape when indexes begin with zero, there is an asymmetry of an arrangement of readout AWF concerning readout of a discrete signal. This asymmetry strongly increases an error of measurement of frequency of a signal.
For asymmetry elimination bending around readout AWF it is offered to shift to the left on an axis нормированных frequencies on size 0,5 bin.
For this case results of quantitative influence of the specified asymmetry on the form of a spectrum of the signal weighed AWF are resulted.
It is offered to carry out a choice of kind AWF with the account of possibility of reception of a zero methodical error and minimisation of the noise making error arising under the influence of noise. Expressions for an equivalent noise strip (ENS) AWF are received and quantitative research of behaviour ENS at change of size of the set zero AWF is conducted.
Possibility of simultaneous minimisation of a methodical error and noise error is considered. Analytical expressions for one parametre AWF minimising ENS at simultaneous minimisation of a methodical error are received. Analytical expressions for size ENS are thus received.
Because prior to the beginning of frequency measurement it is impossible to set correctly parametres AWF minimising methodical and noise errors, the iterative numerical algorithm of an estimation of frequency by means of AWF is offered. The algorithm consists in consecutive performance of measurements with correction on each iteration of parametres AWF with the account of the frequency of a signal measured on the previous step. Performance of these actions proceeds until again received value of frequency will differ from the previous value no more than on in advance set size.
The quantitative estimation of an error of measurement of frequency by the offered algorithm with use symmetric AWF is executed. It is received that thus received error of measurement of frequency is less, than at use of known WF Dolfa Chebysheva (DC). The prize at small measured frequencies reaches sizes of several tens and aspires in a limit at frequency increase to value 1,15−2.
At asymmetrical AWF an error it becomes ready above, than for WF DC.