RU2229725C1 - Technique of spectral analysis of periodic multifrequency signals - Google Patents

Abstract

FIELD: measurement technology, information processing systems, determination of spectral composition of periodic signal. SUBSTANCE: reference sinusoidal signal b₀(t_j) shifted many times by phase with reference to analyzed periodic multifrequency signal a(t_j) is formed in compliance with invention. Both signals are presented in the form of readings of momentary values for same time moments t_j = t₁,t₂,...,t_N, where N is number of divisions in period T. Then points a(b₀) of joint decision under various angular frequencies ω₀ of reference signal and phases φ₀ of reference signal are found, volt-ampere characteristics are constructed and their area F_BAXmin is established. Conclusion on presence of harmonic component with angular frequency ω_K and phase φ_K in analyzed signal a(t_j) is drawn proceeding from condition F_BAX = 0. Thereafter maximal area of volt-ampere characteristic F_BAXmaxK with φ_K±90^° is determined and amplitude of K-th spectral component is found by formula

and judgment on spectral composition of analyzed signal a(t_j). is made by values ω_K,φ_K and A_mk. EFFECT: improved efficiency of determination of spectral composition of periodic multifrequency signal carrying components of any frequency. 1 dwg, 1 tbl

Description

The invention relates to the field of information processing systems and measuring equipment and can be used to determine the spectral composition of a periodic multi-frequency signal when solving various problems of transmitting information at a distance, monitoring the operability of electrical and electromechanical devices.

In the measuring technique, various methods are known for determining the spectral composition of a periodic signal.

A known method of spectral analysis of a signal [RF Patent 2039359, July 9, 1995], which consists in comparing the signal under study with a reference sinusoidal signal with a frequency of the first harmonic, repeatedly shifting one signal in phase relative to another, determining the instantaneous values of the signals at certain times, determining the modules of the ratio of the corresponding instantaneous values of the signals and from the values of the deviations of these modules between themselves determine the relative content of higher spectral components in the signal under study .

The disadvantage of this method is that the signal under study is compared only with the reference signal with the frequency of the first harmonic, leaving unaccounted for the influence of higher harmonics.

A known method of spectral analysis of the signal [RF Patent 2086991, 08/10/1997], selected as a prototype, which consists in the fact that they form a reference sinusoidal signal with a frequency of the first harmonic, repeatedly shift the phase of one signal relative to the other, for each phase shift determine the root modules the square corresponding pairs of instantaneous values of the input signal and the absolute values of the deviations of the modules between themselves determine the relative content of the higher harmonic components in the input signal.

The disadvantage of this method is that the signal under study is compared only with the reference signal with the frequency of the first harmonic, and because of this, it is not possible to accurately determine the relative content of higher harmonics in the signal under investigation, especially if it is not certain that all frequencies of higher harmonics are multiples of the fundamental frequency.

The objective of the invention is to develop a universal method for determining the spectral composition of a periodic multi-frequency signal containing spectral components of any frequency.

This is achieved by the fact that in the method of spectral analysis, including the formation of a reference sinusoidal signal, which is repeatedly phase shifted one signal relative to another, according to the invention for the analyzed periodic multi-frequency signal a (t _j ) and reference b ₀ (t _j ) = B _m sin (ω ₀ t _j + φ ₀ ) of a signal with amplitude B _m represented by samples of instantaneous values for the same time instants

t _j = t ₁ , t ₂ , t _N ,

where N is the number of partitions on the period T,

find the joint solution points α (b ₀ ) at various circular frequencies of the reference signal ω ₀ and phases of the reference signal φ ₀ , build current-voltage characteristics and determine their area F _{BAX min} , and the conclusion about the presence of a harmonic component with a circular frequency ω _K and phase φ _K in the analyzed signal a (t _j ) is done based on the condition F _BAX = 0, then the maximum area of the current-voltage characteristic F _{BAX max K} is determined and at φ _K ± 90 ° and the amplitude of the K-th spectral component is found by the formula

Where

ω ₁ - the main circular frequency,

further on the values of ω _K , φ _K and A _mk judge the spectral composition of the analyzed signal a (t _j ).

Thus, the method of spectral analysis of a periodic multi-frequency signal has several advantages, which are expressed in that it provides speed, versatility of the method and high accuracy of calculations.

The drawing shows a hardware diagram of a device that implements the considered method of spectral analysis.

The table shows the results of a test of the proposed method of spectral analysis using a complex example.

The method can be implemented using a circuit (see drawing) containing a sensor of the analyzed signal 1 (DAS), the output of which is connected to the input of the programmer of the area of the current-voltage characteristic 2 (P), the sensor of the reference signal 3 (DOS), one output of which is connected with the input of the programmer of the area of the current-voltage characteristic 2 (P), and the second with the input of the database memory unit 4 (DB). The output of the programmer of the area of the current-voltage characteristic 2 (P) and the output of the database memory unit 4 (DB) are connected to the input of the divider 5 (D).

As a sensor of the analyzed signal 1 (DAS) and a reference signal sensor 3 (DOS), a current sensor - an industrial device KEI-0.1 or a voltage sensor - a voltage transformer (220/5 V) can be used. The programmer of the area of the current-voltage 2 (P) and divider 5 (D) can be performed on the microcontroller of the 51 series atmel AT89S53. For temporary storage of values (database memory block 4 (DB)), an AT25L256 external data memory block (32 kbytes) can be used. For the user’s work, a FT008 button keyboard can be provided, which has 8 buttons designed to turn on the power, start measurement, save the reference value, and a segment indicator SCD55100 for diagnosing the presence of a harmonic component in its analyzed signal, its circular frequency ω _K , phase φ _K and amplitudes A _mk if the harmonic component in the analyzed signal is really present.

From the output of the sensor of the analyzed signal 1 (DAS) the analyzed signal, for example,

a (t _j ) = i (t _j ) = 7.553 sin (ωt _j + 13.339 °) +2.232 sin (2ωt _j -6.856 °) + 2.605 sin (3ωt _j + 111.734 °) +2.422 sin (4ωt _j + 13.852 ° ) +1.71 sin (5ωt _j -20.578 °),

where i (t _j ) is the current multi-frequency signal,

tj = t ₁ , t ₂ , t _N;

- the number of partitions on the period T;

Δt = 1 · 10 ^-4 - discreteness of the array of signal values a (t _j ),

the reference signal of the form arrives at the input of the programmer of the area of the I – V characteristic 2 (P), simultaneously with the analyzed signal from the output of the reference signal sensor 3 (DOS)

b ₀ (t _j ) = B _m sin (ω ₀ t _j + ω ₀ ),

for example, b ₀ (t _j ) = 10 sin (314t _j + 13.339 °), with the same discreteness of the array of Δt values as the analyzed signal, the input of the programmer of the area of the current-voltage characteristic 2 (P) is supplied, and the value of the amplitude of the reference signal B _m = 10 from the output of the reference signal sensor 3 (DOS) is fed to the input of the database memory block 4 (DB). In the programmer of the area of the volt-ampere characteristic 2 (P), the volt-ampere characteristic for these signals is built, its area F _{VAC min is found} by the formula for finding the polygon area

[Bronstein I.N., Semendyaev K.A. Handbook of mathematics for engineers and students of technical schools. - M .: Nauka, 1980, p. 381] and it is checked whether condition F _BAX = 0 is met. In this case, F _{BАX min} = -6.2 · 10 ^-7 , which is close to 0, i.e. the condition is met. The circular frequency of the reference signal ω ₀ = ω _K = 314 $\genfrac{}{}{0ex}{}{\text{-1}}{\text{FROM}}$ and the phase φ ₀ = 13.339 ° are fixed by the programmer 2 (П), and the phase of the Kth spectral component φ _{K is found} from the condition φ _K ± 90 ° = 13.339 ± 90 °, i.e. φ _K = -79.661 °, based on the found phase of the K-th spectral component, F _{BAX max K} = 237.46 is calculated using the same formula to find the polygon area. From the output of the programmer of the area of the current-voltage characteristic 2 (P), the values of F _{BAX max K} , the found value of the circular frequency ω _K and the phases φ _K are fed to the input of the divider 4 (D), and the amplitude value from the output of the database memory unit 4 (DB) the reference signal B _m = 10 is fed to the input of the divider 5 (D). In the divider 5 (D), the amplitude of the Kth spectral component is calculated by the formula

From the output of the divider 5 (D), the values of the circular frequency ω _K , phase φ _K and the amplitude of the K-th spectral component A _{mk are taken.} For the remaining components of the analyzed signal, the results are summarized in the table.

Claims (1)

The method of spectral analysis of a periodic signal, including the formation of a reference sinusoidal signal, which is repeatedly shifted in phase from one signal relative to another, characterized in that for the analyzed periodic multi-frequency signal α (t _j ) and reference b ₀ (t _j ) = B _m sin (ω ₀ t _j + φ ₀ ) of a signal with amplitude B _m represented by samples of instantaneous values for the same time instants t _j = t ₁ , t ₂ , ..., t _N , where N is the number of partitions in period T, find joint decision point α (b ₀₎ at different angular frequencies with the reference drove ω ₀ and the reference signal phase φ _0, construct the current-voltage characteristics and determine their area F _BAXmin, wherein the output of the presence of the harmonic component with angular frequency ω _R and phase φ _K in the analyzed signal α (t _j) made starting from the condition f _BAX = 0, then determine the maximum area of the current-voltage characteristic F _BAXmaxK at φ _K ± 90 ° and find the amplitude of the _Kth spectral component according to the formula

Where

ω ₁ - the main circular frequency, further on the values of ω _K , φ _K and A _mk judge the spectral composition of the analyzed signal α (t _j ).