# The method of determining the transfer function of the measuring system

(57) Abstract:

The invention relates to measuring equipment and Metrology and can be used for calibration and calibration of measurement systems, in particular sonar and hydrophysical converters. The method consists in the fact that at the input of the measuring system consistently serves harmonic signals of different frequencies. Then measure the output signals of the investigated system at each frequency. Then determine the transfer function by digital processing of discrete samples of the output signal. The peculiarity of the method is that the discrete samples of the output signal is selected with a frequency at which the ratio of sampling frequency to the signal frequency is a fractional number, the same for all frequencies. Duration of the analyzed signal is set equal to the whole number of periods of beating between the sampling frequency and the signal frequency. In the particular case of the ratio of sampling frequency to the frequency of the measured signal can be set as the quotient of two numbers from the Fibonacci series. The method allows to abandon the operation of the analog filtering inherent in the known methods, and thus improve the accuracy of the measurements. for calibration and calibration of various measuring systems in dynamic mode, in particular, for determining the transfer functions of hydrophysical and hydroacoustic transducers.There is a method of determining the characteristics of the transfer function of the measuring systems [1-5], which consists in the fact that at the input of the measuring system consistently serves harmonic signals of different frequencies to measure the output signals of the measuring system at each of the frequencies and determine the transfer function of the system, for example, by digital processing of discrete samples of the output signal.This method can be implemented in various fields of measurement technology: flow measurement [1], strain [2], anemometry [3], thermoanemometer [4] , in the field of hydro-acoustics [5], the characterization of two-port technology, telecommunications and radio engineering, vibrometry and others.For the prototype accepted method [5], implemented in hydrotropes to characterize the transfer function of the measuring hydroacoustic antennas in the laboratory.In the prototype to the input of the measuring system consistently serves harmonic signals of different frequencies to measure the output signals of the investigated system at each of the frequencies and determine Cretnik samples of the input signal of the measuring system (in this case, hydroacoustic antenna) is carried out using a computer with analog-to-digital Converter (ADC), input protivooskolochnye analog filters and matching units signals from the ADC input.The disadvantage of the prototype, as follows from its description, is to work at a constant sampling rate without regard to the frequency of the measured signal. In addition, in the tract of measurements includes a lowpass filter, which, in turn, can be a source of additional errors as in the measurement of the amplitude and, to a greater degree phase.It is known that analog filters introduce phase distortion, which is unacceptable in the characterization of the transfer function of the measuring hydroacoustic antennas in the laboratory. If you pay attention to the need for multi-channel measurements, the total error arising from the identical amplitude and phase - frequency characteristics of the analog components, can reach significant values. As a result, there is additional uncertainty, in particular, when determining the directivity measurement hydroacoustic antenna.The technical result obtained as a result of implementation of the invention is to increase the measurement accuracy by eliminating operational/or stability of parameters of analog circuits leads to deterioration of measurement accuracy.This technical result is achieved due to the fact that in the known method of determining the transfer function of the measuring system consists in the fact that at the input of the measuring system consistently serves harmonic signals of different frequencies, measured output signals on each frequency and determine the transfer function of the measuring system by digital processing of discrete samples of the output signal, the discrete samples of the output signal is selected with a frequency at which the ratio of sampling frequency to the signal frequency is a fractional number, the same for all frequencies. Duration of the analyzed signal is set equal to the whole number of periods of beating between the sampling frequency and the frequency of the measured signal. Thus on an integer number of samples have an integer number of periods of the signal.In the particular case of discrete samples of the measured signal is selected with a frequency at which the ratio of sampling frequency to the signal frequency is the ratio of the two numbers from the Fibonacci series.The essence of the method consists in the following. The discretization of a continuous signal, in the idealized representation can be considered as derivatives of thewhere W(t) is a periodic function with period T, k = 1, 2,...In this case, the spectral density of a discrete signal is

S() = A(n

_{c}m

_{g})

where

_{c}- frequency signal

_{g}the frequency of the first harmonic signal sampling rate, n, m = 1, 2,..., A is the amplitude of the measured signal. Thus you can see that if the frequency of signal sampling coincides with the frequencies of the harmonics of the measured signal, then transfer spectra are superimposed spurious signals on the signal being measured. When errors occur, known as the error masking frequencies. On the other hand, if the observation time of the analyzed signal does not coincide with an integer number of periods, there is a need for the use of weighting functions, which, in turn, lead to expansion of the bandwidth of the measuring system during the processing of samples of the signal. The latter circumstance can lead to the deterioration of the signal-to-noise ratio and reduce the accuracy of measurements at a fixed time of analysis.If you select the sampling rate so that the Raman signals of low frequencies orders of magnitude with relatively large amplitudes did not coincide with the measured signal is echnosti measurements by eliminating error filter. The required bandpass filtering can be performed at the stage of signal processing in a digital way. The choice of sampling frequency is determined based on the required accuracy of measurements [6].It must be borne in mind that the number of processed samples, as the number of periods of the measured signal, can only be an integer. So it is completely exclude the imposition of impossible. This is due to the fact that these attitudes cannot be an irrational number. On the other hand, if we take the number of samples and number of periods of the measured signal such that these numbers will be members of the Fibonacci sequence, defined, in turn, so that each successive member is the sum of the previous two, there is the following property. The ratio of two Fibonacci numbers are an approximation of the so-called "Golden ratio", which is irrational. I.e. in the result occurs during the processing of overlapping signals will not be affected to a higher-order combination frequencies. In addition, when the signal processing using a computer, especially with limited resources, you may experience problems related to incomplete use of the allocated memory for the signal samples. In these slucajno to choose such numbers from the Fibonacci series, when the total number of processed samples is the number of 2

^{n}[7].Thus, the claimed combination of features of the process allows to increase the accuracy of determining the transfer function of the measuring systems, thus achieving the required outcome.Sources of information

1. USSR author's certificate N 1264007, G 01 F 25/00, 1986.2. USSR author's certificate N 1413462, G 01 L 27/00, 1988.3. USSR author's certificate N 767540, G 01 M 10/00, 1978.4. USSR author's certificate N 676928, G 01 P 5/12, 1977.5. U.S. patent N 4468760, 367-13 (H 04 R 29/00), 1982.6. Max J. Methods and techniques of signal processing at the physical measurements. So 1. - M.: Mir, 1983.7. Stakhov A. P. Algorithmic theory of measurement. - M.: Nauka, 1979. 1. The method of determining the transfer function of the measuring system consists in the fact that at the input of the measuring system consistently serves harmonic signals of different frequencies to measure the output signals of the investigated system at each of the frequencies and determine the transfer function by digital processing of discrete samples of the output signal, wherein the discrete samples of the output signal vybirayem for all frequencies, duration of the analyzed harmonic signal is set equal to the whole number of periods of beating between the sampling frequency and the signal frequency.2. The method according to p. 1, characterized in that the ratio of sampling frequency to the frequency of the measured signal is defined as the quotient of two numbers from the Fibonacci series.

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