RU2533629C1 - Method of determining valid signal frequency limits and bandwidth of digital frequency filters - Google Patents

Abstract

FIELD: radio engineering, communication.

SUBSTANCE: method involves the stages, where two analogue signals are measured and discretised, the direct Fourier transform is performed and complex conjugate values of one of the signal's direct transformation results are found. Then the obtained complex signals of the direct Fourier transform are pairwise multiplied with the second signal's direct Fourier transform complex conjugate values. Next, m signals are formed to be subjected to the inverse Fourier transform, which results are used to define a mutual time-and-frequency correlation function. After that, the curve of the latter is built, which is used to determine a valid signal, its limits and bandwidth limits of digital frequency filters.

EFFECT: determination of the valid signal frequency limits and the digital frequency filter bandwidth limits.

2 dwg, 1 tbl

Description

The invention relates to the field of digital signal processing and can be used to determine the frequency boundaries of the useful signal and the passband of digital frequency filters for non-destructive testing and equipment diagnostics based on correlation analysis.

There is a method of determining the frequency boundaries of the useful signal and the passband of digital frequency filters, used in solving problems of leak detection in pipelines, selected as a prototype [A.L. Ovchinnikov, B.M. Lapshin, A.S. Chekalin, A.S. Evsikov. The experience of using the leak detector TAK-2005 in the city pipeline industry // Bulletin of the Tomsk Polytechnic University. - 2008. -T. 312. - No. 2. - S. 196-202], which consists in measuring and sampling two analog signals coming from the sensors, and calculating the coherence function of these signals, which are used to find the frequency boundaries of the useful signal in which the analyzed signals are coherent, i.e. the values of the coherence function take unit and / or pronounced maximum values. Based on the found ranges, the bandwidth limits of the digital frequency filters are set.

This method has a significant drawback. In the presence of broadband noise and a low signal-to-noise ratio in the analyzed signals, the studied signals can be coherent in almost the entire frequency range.

The objective of the invention is to determine the frequency boundaries of the useful signal and the passband of digital frequency filters.

This is achieved by the fact that in the method for determining the frequency boundaries of the useful signal and the passband of the digital frequency filters, as in the prototype, the measurement and sampling of two analog signals are carried out.

, определяют комплексно-сопряженные значения результатов прямого преобразования одного из сигналов, попарно умножают полученные комплексные сигналы прямого преобразования Фурье с комплексно-сопряженными значениями прямого преобразования Фурье второго сигнала, из полученного произведения $$P_j$$

выбирают значения и формируют $$m$$

сигналов $$M^k$$

,According to the invention, a direct Fourier transform is performed in the form of a fast Fourier transform of input sampled signals of dimension $$2^n$$

, determine the complex conjugate values of the results of the direct conversion of one of the signals, pairwise multiply the resulting complex signals of the direct Fourier transform with the complex conjugate values of the direct Fourier transform of the second signal, from the obtained product $$P_j$$

select values and form $$m$$

signals $$M^k$$

,

;Where $$j=0\mathrm{one,}\mathrm{...},2^{n-\mathrm{one}}+\mathrm{one}$$

;

; $$m=23\mathrm{...,}{2}^{n-\mathrm{one}}+\mathrm{one}$$

;

, $$k=0\mathrm{one},...,m-\mathrm{one}$$

,

according to the expression

(1) $$M_j^k=\{\begin{array}{l}{P}_j,\frac{k}{m}<\frac{j}{2^{n-\mathrm{one}}+\mathrm{one}}\le \frac{k+\mathrm{one}}{m},\\ 0\mathrm{and}n\mathrm{but}he.\end{array}$$

(one)

подвергают обратному преобразованию ФурьеReceived signals $$M^k$$

inverse Fourier transform

, $$Z^k=F^{-\mathrm{one}}\left[M^k\right]$$

,

According to the results of the inverse Fourier transform, the mutual time-frequency correlation function is determined

,(2) $$r_{12}(f_k,t_i)=Z_i^k$$

, (2)

Where $$t_i\in \left[t_{\min },t_{\max }\right];$$

$$\begin{array}{l}{f}_k\in \left[f_{\min },f_{\max }\right];\\ t_i=i\cdot \frac{\mathrm{one}}{f_d};\\ f_k=\frac{k\cdot f_{\max }}{m-\mathrm{one}};\\ t_{\min }=-\frac{2^{n-\mathrm{one}}}{f_d};\\ t_{\max }=\frac{2^{n-\mathrm{one}}-\mathrm{one}}{f_d};\\ f_{\min }=\frac{f_d}{2^n};\\ f_{\max }=\frac{f_{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="00000044.png,00000045.png"\; state="\{\{state\}\}">d</figure-callout>}}}{2};\end{array}$$

- частота дискретизации сигнала. $$f_d$$

- signal sampling rate.

, по которому судят о наличии полезного сигнала и его частотных границах. По найденным границам полезного сигнала определяют границы полос пропускания цифровых частотных фильтров.Based on the results obtained, a graph of the mutual time-frequency correlation function $$r_{12}(f,t)$$

which judges the presence of a useful signal and its frequency boundaries. The boundaries of the passband of the digital frequency filters are determined from the found boundaries of the useful signal.

The mutual frequency-time correlation function in the proposed method allows to determine the presence of a useful signal and its frequency boundaries for setting the bandwidth limits of digital frequency filters. The use of fast Fourier transform provides high speed and versatility of the method.

In FIG. 1 shows a hardware diagram of a device that implements the considered method for determining the frequency boundaries of the useful signal and the passband of digital frequency filters.

Table 1 shows the initial data and the results of the analysis of the test case.

In FIG. Figure 2 shows a graph of the mutual time-frequency correlation function of the result of the analysis of a test example.

A method for determining the frequency boundaries of the useful signal and the passband of digital frequency filters can be implemented using the device (Fig. 1), containing the first sensor for receiving the analyzed signal 1 (DAS1), connected to the first block of analog-to-digital conversion 2 (ADC1), output which is connected to the input of the first block of direct Fourier transform 3 (BF1), the second sensor of the analyzed signal 4 (DAS2), to which the second block of analog-to-digital conversion 5 (ADC2), the second block of direct conversion Fourier 6 (BF2) and the complex conjugate 7 (BOC) determination unit. The outputs of the first direct Fourier transform unit 3 (BF1) and the complex conjugate value determination unit 7 (BOC) are connected to the input of the multiplication unit 8 (BC), to which the signal generation unit 9 (BFS), the inverse Fourier transform unit 10 (BOF) are connected in series ) and interpretation block 11 (BI).

As sensors of the analyzed signal 1 (DAS1) and 4 (DAS2), current sensors can be used, for example, industrial devices KEI-0.1 or voltage sensors - voltage transformers (220/5 V). Blocks of analog-to-digital conversion 2 (ADC1) and 5 (ADC2) can be implemented on the basis of analog-to-digital converters ADS7827. Direct Fourier transform blocks 3 (BF1) and 6 (BF2), complex conjugate value determination unit 7 (BOK), multiplication unit 8 (BU), signal generation unit 9 (BFS), inverse Fourier transform unit 10 (BOF), block Interpretations 11 (BI) can be performed on an ATmel AT32AP7000 series AVR32 microcontroller.

From the output of sensors 1 (DAS1) and 4 (DAS2), the analyzed complex signals, for example,

, $$y_{\mathrm{one}}(t)=y_2(t)=u(t)$$

,

- многочастотный сигнал напряжения (таблица 1),Where $$u(t)$$

- multi-frequency voltage signal (table 1),

arrive at the inputs of analog-to-digital converters 2 (ADC1) and 5 (ADC2), from the output of which discretized signals

, $$y_{\mathrm{one}}(t_i)=y_2(t_i)=u(t_i)$$

,

$$\Delta t\cdot i$$

,Where $$t_i=$$

$$\Delta t\cdot i$$

,

, $$i=\mathrm{one,}2...,N$$

,

- размер выборки для быстрого преобразования Фурье;Where $$N=2^n=2^{\mathrm{fifteen}}=\text{32768}$$

- sample size for fast Fourier transform;

- шаг дискретизации сигнала $$u(t_i)$$

, $$\Delta t=\frac{\mathrm{one}}{44100}$$

- signal sampling step $$u(t_i)$$

,

поступают на вход блока определения комплексно-сопряженного значения 7 (БОК), где определяют комплексно-сопряженные значения для каждого элемента сигнала. Результаты прямого преобразования Фурье БПФ 3 (БФ1) и блока определения комплексно-сопряженного значения 7 (БОК) поступают на вход блока умножения 8 (БУ), где выполняют попарное умножение двух комплексных сигналов. С выхода блока умножения 8 (БУ) результаты умножения в виде комплексного сигнала размерностью $$2^{n-1}+1=\text{1638}5$$

поступают на вход блока формирования сигналов 9 (БФС), где формируют $$m=\text{421}$$

комплексных сигналов размерностью $$2^{n-1}+1=\text{1638}5$$

согласно выражению (1). С выхода блока формирования сигналов 9 (БФС) полученные комплексные сигналы поступают на вход блока вычисления обратного преобразования Фурье 10 (БОФ), где выполняют обратное преобразование Фурье над каждым комплексным сигналом. С выхода блока вычисления обратного преобразования Фурье 10 (БОФ) результаты обратного преобразования Фурье в виде действительных $$m=\text{421}$$

сигналов размерностьюarrive at the inputs of the direct Fourier transform blocks (in the form of an FFT) 3 (BF1) and 6 (BF2), where they perform a direct Fourier transform of the input signals. From the output of the direct Fourier transform block 6 (BF2), the results of the direct Fourier transform in the form of a complex signal of dimension $$2^{n-\mathrm{one}}+\mathrm{one}=\text{1638}5$$

arrive at the input of the complex conjugate value determination unit 7 (BOC), where the complex conjugate values for each signal element are determined. The results of the direct Fourier transform of the BPF 3 (BF1) and the complex conjugate value determination unit 7 (BOC) are input to the multiplication unit 8 (BC), where pairwise multiplication of two complex signals is performed. From the output of the multiplication block 8 (BU), the results of multiplication in the form of a complex signal of dimension $$2^{n-\mathrm{one}}+\mathrm{one}=\text{1638}5$$

arrive at the input of the signal conditioning unit 9 (BFS), where they form $$m=\text{421}$$

complex signals of dimension $$2^{n-\mathrm{one}}+\mathrm{one}=\text{1638}5$$

according to the expression (1). From the output of the signal generation unit 9 (BFS), the obtained complex signals are fed to the input of the inverse Fourier transform calculation unit 10 (BOF), where the inverse Fourier transform is performed on each complex signal. From the output of the inverse Fourier transform calculation unit 10 (BOF), the results of the inverse Fourier transform in the form of real $$m=\text{421}$$

signals of dimension

$$N=2^n=2^{\mathrm{fifteen}}=\text{32768}$$

и $$k=76$$

, получили $$f_k=f_{76}=\text{3990}$$

Гц,arrive at the input of the interpretation block 11 (BI), where according to expression (2) determine the mutual frequency-time correlation function. For $$m=\text{421}$$

and $$k=76$$

, got $$f_k=f_{76}=\text{3990}$$

Hz

получаем $$f_k=f_{153}=\text{8032}\text{.5}$$

Гц,at $$k=153$$

we get $$f_k=f_{153}=\text{8032}\text{.5}$$

Hz

получили $$f_k=f_{228}=\text{11970}$$

Гц,at $$k=228$$

got $$f_k=f_{228}=\text{11970}$$

Hz

получили $$f_k=f_{305}=\text{16012}\text{.5}$$

Гц.at $$k=305$$

got $$f_k=f_{305}=\text{16012}\text{.5}$$

Hz

The obtained mutual time-frequency correlation function (Fig. 2) has two pronounced vertical bands on two frequency ranges, the boundary values of which are close to those specified in the test example. Based on the found boundaries of the useful signal, the bandwidth limits of the digital frequency filters are set.

Claims (1)

A method for determining the frequency boundaries of the useful signal and the passband of digital frequency filters, including measuring and sampling two analog signals, characterized in that the sampled signals are subjected to direct Fourier transform in the form of a fast Fourier transform of dimension $$2^n$$

, determine the complex conjugate values of the results of the direct conversion of one of the signals, pairwise multiply the resulting complex signals of the direct Fourier transform with the complex conjugate values of the direct Fourier transform of the second signal, from the obtained product $$P_j$$

, the results of the direct Fourier transform of the first signal with complex conjugate values of the direct Fourier transform of the second signal, select the values and form $$m$$

signals $$M^k$$

,
Where $$j=0\mathrm{one,}\mathrm{...},2^{n-\mathrm{one}}+\mathrm{one}$$

;
$$m=23\mathrm{...,}{2}^{n-\mathrm{one}}+\mathrm{one}$$

;
$$k=0\mathrm{one},...,m-\mathrm{one}$$

,
according to the expression
$$M_j^k=\{\begin{array}{l}{P}_j,\frac{k}{m}<\frac{j}{2^{n-\mathrm{one}}+\mathrm{one}}\le \frac{k+\mathrm{one}}{m},\\ 0\mathrm{and}n\mathrm{but}he.\end{array}$$

received signals $$M^k$$

inverse Fourier transform $$Z^k=F^{-\mathrm{one}}\left[M^k\right]$$

,
determine the mutual time-frequency correlation function
$$r_{12}(f_k,t_i)=Z_i^k$$

,
Where $$t_i\in \left[t_{\min },t_{\max }\right];$$

$$\begin{array}{l}{f}_k\in \left[f_{\min },f_{\max }\right];\\ t_i=i\cdot \frac{\mathrm{one}}{f_d};\\ f_k=\frac{k\cdot f_{\max }}{m-\mathrm{one}};\\ t_{\min }=-\frac{2^{n-\mathrm{one}}}{f_d};\\ t_{\max }=\frac{2^{n-\mathrm{one}}-\mathrm{one}}{f_d};\\ f_{\min }=\frac{f_d}{2^n};\\ f_{\max }=\frac{f_d}{2};\end{array}$$

$$f_d$$

- signal sampling rate,
then, based on the results obtained, a graph of the mutual time-frequency correlation function $$r_{12}(f,t)$$

which judges the availability of a useful signal, its frequency boundaries, which determine the boundaries of the passband of digital frequency filters.

Images