Device for detection of narrow-band noise hydroacoustic signals based on calculation of integral wavelet-spectrum

FIELD: physics, acoustics.

SUBSTANCE: invention is related to the field of hydroacoustics, namely to devices for detection of narrow-band noise hydroacoustic signals (with spectral density of power in the form of separate discrete components or their scales) at the background of additive noise. Invention is based on calculation of continuous wavelet transformation of input process on the basis of complex analytical wavelet, relative band of amplitude spectrum of which matches relative band of spectral density of detected signal power. Device comprises analog-digital converter (ADC) 1, recirculator 2, the first calculator of fast Fourier transform (FFT) 3, complex multipliers 4.1 - 4.M, scaling devices 5.1 - 5.M, device of complex conjugation 6, device of negative frequencies nulling 7, the second calculator FFT 8, permanent memory (PM) 9, calculators of reverse FFT 10.1 - 10.M, calculator of module square 11, averaging device 12, threshold device 13, control device 14.

EFFECT: improved noise immunity of narrow-band noise hydroacoustic signal detector.

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The invention relates to the field of hydro-acoustics, namely, devices for the detection of narrowband signals (with the spectral power density in the form of separate discrete components or scales) on the background of additive noise.

It is known that the implementation of best practice in solving the problem of detection signals against the background noise is largely determined by the level of knowledge of the incoming signal [10-13].

The main sources of acoustic noise signal emitted by the moving water objects (surface vessels or submarines)are [1-6]:

- power plant, which includes: machine, gears, shaft, bearings, etc.;

- propellers, which, although they are part of the power plant, but are treated separately, due to the dramatically different ways in which they create acoustic noise;

- support mechanisms, which include mechanical and electrical systems, not related to power plant (such as fans, generators, pumps and the like);

- hydrodynamic effects, forming a first noise around the body of the ship, as well as noises of various pieces of equipment and structures that are created due to the flow of various liquids.

While the total the total noise radiated on iroshima in the water object, contains two main types of noise different in nature. The differences between these two types of noise are manifested primarily in the form of their spectral characteristics.

One of them is broadband noise with a continuous spectrum. Under continuous implied range, which is a continuous function of the spectral power density (MTA) noise depending on the frequency. In the technical literature this component of the MTA noise called "continuous part of the spectrum.

Another type of noise is narrowband (or tonal) noise with intermittent range. This type of noise consists of a single tone (sinusoidal) components, and its spectrum contains "bar" components appearing at discrete frequencies. In the technical literature, these sinusoidal noise components are called "discrete components" (DS) spectrum of the noise.

Thus, the noise emitted by a moving object in the water, is usually a mixture of noise the two types and can be considered as noise with a continuous spectrum containing individual superimposed discrete components [1-6].

The emergence of narrowband noise component caused by the operation of the system of motion of the ship, screws and auxiliary mechanisms. Depending on their origin different DS can depend either nezavisli speed, the depth of immersion noisy object and other factors.

Characteristics of discrete components, due to the operation of auxiliary mechanisms, usually stable and do not depend on the speed of the ship.

The frequency and amplitude discrete components caused by power plant and the propellers change together with the speed of the vehicle. The spectral function of the DS have multiplicative transformation, proportional to the change in the speed of rotation of the line shaft.

In some cases, DS, excited from the same source, are in sync with each other and form scales - i.e. the sets DS, whose frequencies are multiples of each other. DS, whose frequencies are multiples among themselves, called harmonics.

So, for example, roll scale may contain DS at frequencies that are multiples of the frequency of rotation of the line shaft. Blade scale may contain DS at frequencies that are multiples of the product of frequency of rotation of the line shaft on the number of propeller blades. Tonal components scales are highly stable and have a very narrow bandwidth [1-6].

Thus, the narrowband component of hydroacoustic noise moving in water objects can be represented in the form of separate discrete components (DS) spectral power density (MTA) liobratimim their harmonic scales.

Narrowband sonar noise (i.e. discrete components of the total noise of a moving object in the water is a useful signal to be detected against the background noise, narrowband systems samplemovie.

In known methods and devices for detection of narrowband signals currently being received and used idealized models of their MTAs.

MTA separate DS is represented as δ-functions, shifted from the origin (zero frequency) on the value of the center frequency DC f₁[1-4]:

MTA scale from N DS is represented as a series of δ-functions shifted by multiples of the frequency spacing nf₁[1-4]:

either in the form of a series of shifted narrowband spectral functions G₀(f) (other than δ-functions) with a constant bandwidth Δf DS=const:

where G₀(f) - narrowband spectral function defined in the field of zero frequency,

f₁the Central frequency of the first harmonic of the scale,

G_n(f)=G₀(f-fn₁) - MTA n-th harmonic,

A_nthe amplitude of the nth harmonic,

N is the number of DS in the scale.

Often it is assumed that the shape of the spectral function G₀(f) is a narrowband rectangular function of the form [1]:

wherestandard rectangular function [1, p.143]. Accordingly,

where

In this approach, i.e. using models (1-5), transformation of the spectral functions of individual DS and their scales (due to motion of the ship) when changing speed (shaft speed) can only be described approximately using a conventional frequency shift.

In accordance with the accepted models (1-5), in the known methods of detecting narrowband sonar signals (corresponding DS spectrum of the noise sources processed objects) and their corresponding devices (i.e. narrowband sonar systems samplemovie), using different methods of spectral analysis (or assessment methods MTA noise)based on the Fourier transform [7, 8].

There is a method of detection of narrow-band noise with discrete components MTA and delivers it to the device, in fact, are multi-energy receiver (analog) [1, s-352]. This method is a sequential execution of operations: broadband bandpass filter (for the formation of a common frequency band), multi-channel narrow-band bandpass filter (for shaped who I separate frequency channels), quadratic detection, integration and comparison with the threshold in each frequency channel).

This method can be directly applied in devices-detectors with analog design, which is easy to implement one of the classic types of spectral analysis - based "method"filtering.

Device (analog) [1, s-352]that implements the specified method for detecting narrow-band noise, is shown in figure 1, where:

unit 1 - wideband bandpass filter,

blocks 2.1-M set ("comb") narrowband bandpass filter (UPF),

blocks 3.1-3 - quadratic detectors,

blocks 4.1-M integrators,

block 5 - M - channel threshold device.

The principle of operation of this device is as follows. To the input device enters the implementation of the input process

where s(t) is detected narrowband noise signal,

n(t) is the additive interference in the form of normal white noise.

This realization x(t) is fed to the input of a broadband bandpass filter (block 1) with a center frequency f₀and the bandwidth ΔF=f_in-f_n, i.e. with the frequency response of the form:

which forms a common frequency range of the analyzed noise signal in accordance with the frequency response of the form (6).

From the output of block 1 of bandpass noise is th process arrives at the inputs of M-channel chasers UPF (blocks 2.1-M), with a fixed bandwidth Δf=ΔF/M and different Central frequencies f_m(but with a uniform frequency step equal to the width of the passband of one filter Δf), i.e. with the frequency response of the form:

where m=1,...,M - number of frequency channels,

M is the number of frequency channels,

where M is formed separate frequency channels in accordance with the frequency response of the form (7).

Formed (resultrowone) narrowband noise processes y_m(t) are fed to the inputs of a quadratic detectors (units 3.1-3), with outputs which proyektirovaniye and squared narrowband processes |y_m(t)|²arrive at the inputs of the integrators (blocks 4.1-M). Integration time (accumulation) narrowband signals is usually chosen equal to the value inversely proportional bandwidth UPF [1], and provides a potential resolution in frequency for this method of spectral analysis (filtering method).

From the outputs of the integrators selected responses z_m(t) fed to the input of the M-channel threshold device (block 5), the output of which is the output device.

Methods of detection of narrowband signals implemented in today's digital narrow-band hydrophone systems based on so-called "algorithms for estimating SPM" [7, 8] (in the Snov, which is also the Fourier transform). I.e. in modern narrowband receivers (digital realization) "narrowband comb filter is formed by computing the discrete Fourier transform (usually implemented using algorithms fast Fourier transform) of the input signal or its correlation function.

The form of response "narrow-band digital filters chasers" will be determined by the spectral function of the time window used in the processing of the input data.

The way to detect narrowband signals on the basis of "indirect" method of spectral estimation (analog) [7, s-454] is a sequential execution of operations: bleaching, the calculation of the autocorrelation function, multiplied by a function of the time window, computing a Fourier transform and comparison with the threshold in each frequency channel).

The way to detect narrowband signals based on the so-called "direct algorithm for estimating SPM analyze process [7, s-455], represents the sequential execution of operations: partitioning the input data, "weighing" (multiplying by the function "time window"), calculate the Fourier transform (in sections), the calculation of the squared modules of the complex Fourier coefficients, averaging (in sections) and comparison with the threshold in each frequency channel).

The first three lane the numerical operations in General, represent a more General operation called in the technical literature by various synonyms: windowed Fourier transform", "short-time Fourier transform" ("short-time Fourier transform (STFT), the calculation of periodogram" or "spectrum" [7-9]. Moreover, the intermediate operation "weight" of the sample (section) data (i.e. multiplying by the window function to reduce the values of time samples at the edges of the sample and, consequently, reduce the level of side lobes narrow-band spectral components) can be excluded. In this case, use the most simple - rectangular window formed automatically when you perform a partition of the original data.

Device (prototype) [7, s-457]that implements the above method of detection of narrowband signals, shown in figure 2, where:

unit 1 - analog-to-digital Converter (ADC)

block 2 - recirculator,

unit 3 - the solver fast Fourier transform (FFT),

unit 4 - the transmitter unit square,

block 5 - random access memory (RAM),

unit 6 - unit averaging,

unit 7 - the threshold device

unit 8 - control device.

The principle of operation of this device is as follows. To the input device enters the implementation of the input process x(t), which will SHS at the ADC input (block 1) with the sampling frequency, satisfying the requirements of the sampling theorem:

.

ADC output (block 1) discrete samples are sent to the input of the recirculator (block 2), which is formed and with each new count is updated to the current discrete sampling (section) h(n) of length N samples. Sample length N (and, therefore, the analysis time T=NΔt_d) is determined by the required resolution in frequency Δf (and, accordingly, the bandwidth of the elementary frequency channel) of the detector JS:

The generated current discrete sampling of the input process x(n) is fed to the input of the transmitter FFT (block 3), the output of which is integrated spectrum of X(n) of the current sample is fed to the input of the transmitter unit square (block 4), which calculated the squared modulus of the spectrum of the current selection |X(n)|²fed to the input of buffer RAM (block 5). RAM accumulates M consistently calculated current arrays |X_m(n)|². After accumulation of M calculated implementations of the squared module of the spectrum, with outputs of RAM (block 5) reads M one-dimensional arrays of length N samples, and is supplied to the averaging device (block 6), where the calculated current average score MTA input process:

From the output of the averaging device (block 6) current averaged OC the NCA MTA fed to the input of the threshold device (block 7), the output of which is the output device.

The control unit (unit 8) performs synchronization of work: a / d Converter (unit 1), recycler (block 2), evaluator Fourier transform (block 3), random access memory (block 5), the averaging device (block 6) and threshold device (block 7).

The disadvantage of the above detectors narrowband signals (analog and prototype) is their low real immunity that does not meet theoretical signal-to-noise ratio, computed on the basis of the hypothesis ideally narrow DS (1-2) or DC with constant bandwidth independent of frequency (3-5).

Resolution methods of spectral analysis used in these detectors narrowband signals (analog and prototype), is fixed for the whole considered frequency range and, in General, equal to the reciprocal of the duration of the analyzed temporal process.

The lack of robustness of these detectors narrowband signals is a consequence of the use of idealized models MTA narrow-band noise, which doesn't take into account all known information about the detected signal.

At the same time, it is known that the solution of the problem about which Eugenia noise signals against the background noise, in the case of well-known MTAs signal G_c(f) and interference G_p(f), the optimal is the energy receiver (quadratic detector and integrator), pre (predetermined) filter Eckart [1, s-351; 13, s-285].

The maximum of the generalized signal to noise ratio (cap) output power receiver with pre detectores filtering (defined as the ratio of the increment of the mathematical expectation of the output process z(t), due to the presence of the useful signal in the input process, the variance of the output process in the absence of a signal) [1, s]:

occurs when the unit square transfer characteristics predetection filter is:

The expression (12) determines the type of response (i.e., the square of the module of the transfer characteristic) optimal predetection filter, called in the technical literature by the filter Eckart [1, s-351; 13, s-285].

If the noise is not white noise, the characteristics of the optimal filter must have a decline in those spectral regions where the interference power is high.

In the presence of white noise (i.e. with a uniform spectrum interference) the square of the module of the transfer characteristic is optimal predetection filter Eckart must coincide with the spectral density improvement is using the power of the detected noise signal |H(f)| ²=G_c(f).

In the narrowband case (i.e. when the detected DC noise) crosstalk (within bandwidth JMP DS) can with great certainty be regarded as white noise with a uniform MTA G_p(f)=const. Therefore, the frequency response narrowband predetection filter in each frequency channel, ideally, should repeat the form MTA DS narrowband noise. Otherwise there will be loss of noise immunity in comparison with the optimal receiver - multi-power receiver with predeterminada filters of Eckart [1, 13] in each frequency channel.

Thus, the use of more accurate models of the detected narrow-band noise will implement the detection of DC noise with higher noise immunity.

In fact, the input process x(t) of the detector narrowband acoustic signals has a more complex structure SPM than in conventional models (1-5).

As noted by the author [1, s], the effective band width JMP DS ∆ F depends on the value of the frequency at which it occurs. Moreover, it is directly proportional to the center frequency of the DC f=f₁and is 0.3...0.03% from the values of f₁.

Random distortion, make a real hydroacoustic channel when the signal propagation and Doppler transformation caused by the kinematics of masego object and the carrier gas of samplemovie, lead to additional broadening of the bandwidth Δf up to ≈0.5% of the values of f₁. But this saves the scale-frequency properties of MTA separate DC or total SPM total scale. I.e. the relative band JMP each individual DS (or DS, forming part of the scale formed by one common source), is always constant and is of the order:

.

In other words, the effective bandwidth BC is a linear function of its center frequency:

Accordingly, the effective bandwidth of each n-th harmonic in the scale is a linear function of frequency:

and the total SPM total scale N DS has a large-scale (multiplicative) properties in the area of frequency.

These ratios can be based on more accurate (scale-frequency) model MTA narrowband noise, taking into account the large-scale properties of NS.

Scale-frequency model MTA narrowband noise component can be described as follows. The spectral function DS with a center frequency f₁can be represented in the form

where α is a scaling factor that takes into account the multiplicative transformation of the original spectral function DS.

For scale N DS scale often is tnou model MTAs can be described by presenting the total spectral function as a sum of expanding into a multiple number of times the spectral functions of the first harmonic, where the scale factor is the number of harmonics:

It is worth noting that when considering the spectral density of pressure (SPD) G_p(f)measured at(instead of the spectral power density G(f), measured inbe fair record of the amplitude scaling factors under the radical sign:

In the simulation, a random temporary implementation of narrowband noise s(t), the corresponding model SPD as a separate DS (17) or in the form of the scale (18), can be obtained by omitting the implementation of the normal white noise w(t) through a filter with transfer function of the form (17) or (18), respectively:

where F^-1{ } is the operator inverse Fourier transform.

As a model of the spectral density of pressure separateor the first DS (the first harmonic)the overall scale can be adopted spectral function in the form of compacted at α₀time and shifted by the value of f₁(Hz) is the Gaussian function:

This function, in its simplicity, describes quite well the final form of the JMP DS on in the ode of the receiver-detector taking into account:

- influence of instability of rotation of the various ship's mechanisms with Central frequency f₁,

effects according to the frequency response of the mechanical paths (ship structures) formed on the spectrum of radiated narrowband noise,

- influence of the Doppler multiplier (scaling) transformation due to the motion of the emitting object and the carrier gas of samplemovie,

- random frequency-amplitude-phase distortions due to the effect of the distribution channel, described by the convolution of the SPM signal scattering function of the channel and resulting in an additional broadening of the MTA DS.

It is worth noting that the spectral function of the form (21) is scaled by a Fourier spectrum of a known complex analytic wavelet Morlaix [14-17]:

Fourier spectrum of this type of wavelets is:

where 1₊(f) is the Heaviside function.

The frequency shift f₁(Hz) in the model SPD (21) sets the center frequency of the DS, and the selection of the values of the scaling factor α₀allows you to obtain the required value of the relative line DS.

Modelin the form of compressed and shifted in frequency of the Gaussian function (21) accurately describes the properties of SPD real DS. But since this function is what I symmetric about the center frequency, it introduces some distortion in the simulation multiplicative transformations of spectral functions DC.

As more accurate models of the spectral functions of the DS can be proposed function of the form:

The spectral function of the form (23) more rigorously takes into account the multiplicative relationship between the effective bandwidth ∆ F_nlowertopand Centralfrequencies of different DC scale or when their multiplicative transformations:

,,.

Function (23) can be viewed as a range of modernized complex analytic wavelet Morlaix:

The spectral function of the modernized wavelet Morlaix (23) equal to zero for negative values of frequencies without additional factor as a function of Heaviside 1₊(f). It is asymmetrical and, therefore, more accurately describes the multiplicative transformation of spectral functions DC.

General view of the spectral functions normal (22b) and upgraded (23) wavelets Morlaix shown in figa. The results of the multiplicative transformations of the spectral functions of the form (22b) is shown in figb and spectral is th function of the form (23) - on figv.

At the same time, the resolution in frequency of traditional methods of spectral analysis used in the known methods and devices for detection of narrowband signals (analogues and prototype), when it is configured (by choosing the size and shape of the time window) on the width of the spectrum of the low frequency AC (in the analyzed frequency range) analysis bandwidth is too narrow for the higher frequency DC scale. When it is configured on the width of the spectrum of a high frequency DC band analysis will be excessive for lower-frequency DC.

Thus, in the known detectors narrowband noise signal, using different methods of analog or digital spectral analysis (Fourier transform), it is essentially impossible to provide a variable resolution in frequency (in all the analyzed frequency range), the corresponding scale-frequency model MTA DS (15-16). I.e. it is impossible to implement a customized transfer characteristics predetection filters for different frequency channels of the entire range and, thus, to achieve maximum PCB (11), corresponding to filter Eckart.

The proposed new device detection of narrowband noise allows you to more accurately account for the large-scale properties of MTA DS hydroacoustic fussy about the projects and to improve the noise immunity of the respective receivers-detectors. This is achieved by applying to the input process instead of the conventional short-time Fourier transform ("coarse" (uniform) resolution over the entire frequency range) of a new type of transformation, namely the continuous wavelet transform (adapted resolution (analysis bandwidth) in accordance with the large-scale properties of the detected narrow-band signal), followed by averaging over time of the square module of the result of the conversion.

In scientific literature the set of operations is called a calculation of the integral of the wavelet spectrum [18] or "scalogram" (scalogram) [15] analyzed input process.

Continuous wavelet transform (CWP) can be defined as the scalar product of the investigated process x(t) and a special basis of wavelet functions ψ_ατ(t) [14-17]:

where the hell are the top denotes the complex conjugation operation.

The General principle of construction of the basis wavelet transform is to use a multiplicative transformation with scale parameter α and shifts with the shift parameter τ of the source wavelet function ψ(t) (the so-called mother wavelet):

To be a wavelet, the basis functions ψ_ατ(t)∈L²(R should have the required properties [14-17]. They should be quadratically integrable, alternating (to have lulavim middle), and must tend to zero at ±∞, and for practical purposes - the sooner the better (and the wavelet should be well localized in both time and frequency). In order to make it possible inverse wavelet transform, the spectral function of a wavelet Ψ(f) must satisfy one condition:

The formula for continuous inverse wavelet transform has the form:

For a more efficient computation (in a digital implementation) operator CWP (24) can be defined in the frequency domain [19] (analog) in the form:

where ψ(f)=F{ψ(t)} is the image of the Fourier selected source wavelet ψ (t)

X(f)=F{x(t)} is the image of Fourier analyzed process x(t).

When this is achieved a substantial improvement in the performance of digital devices that implement the CWP, by calculating convolutions using effective procedures FFT.

The only limitation to this form records the operator's GDP, compared to (24) is the requirement of analyticity for the studied signal and the applied wavelet:

ie

In the case of wavelet analysis is valid signals (which occurs when printing handling the ke hydroacoustic signals) it is easy to imagine in an analytical form, without loss of information, by zeroing negative frequencies of their complex Fourier spectra. The same goes for the used wavelets. Some widely used complex wavelets (e.g., wavelet Morlaix [14-17]) are, by denition, are the analytical signals.

In principle, to implement the operator (28) enough to analytical was only wavelet, since convolution of the analyzed signal with the analytic wavelet (which corresponds to multiplication of their Fourier spectra) in the end also gives the result of the analytical signal.

Nowadays, a large number of different families of wavelets: Haar, Daubechies, Morlaix, FHAT, MAT etc. [14-17]. The choice of the type of the analyzing wavelet, as a rule, is determined by what information you want to extract from the signal, and the degree of similarity of the wavelet and the analyzed signal. Each wavelet has its own characteristic features in the time and frequency domains. Using different types of wavelets can better identify and highlight some of the properties of the analyzed signal in scale-time domain. As mentioned above, the proposed detector narrowband signals effectively can be used complex analytic wavelet Morlaix (22) or its modification (23).

Wavelet arr is C W _x(α,τ) a one-dimensional process x(t), obtained by applying the operator CWP (24) or (28), is a two-dimensional function and represents a surface in three-dimensional space. When analyzing the results of the wavelet transform instead of the image surfaces often consider their projections on the plane (α, τ) with the contour, allowing to trace the change of the amplitudes of the wavelet image at different scales and at different points in time [15].

Note that in the analysis of complex signal or when using complex wavelet, the wavelet transform is obtained complex wavelet spectrum and, accordingly, two-dimensional arrays of values of magnitude and phase (or real and imaginary part) of wavelet coefficients:

The result of the integral averaging unit square CWP signal |W_x(α,τ)|²during the observation time for all scales α is a one-dimensional scaling functions and is called the integral of the wavelet spectrum [18] or scalogram [15]:

The integral wavelet transformsignal x(t) by its physical nature is very close to the estimate of its MTAderived from averaging the results window (short-time) Fourier transform. This α wavelet transform (if known basic mother wavelet ψ(t)) is uniquely correspond to the frequencies f Fourier spectrum.

The interest for digital signal processing is the discrete version CWP [14-17]. The necessary discretization of the values of α and τ, while maintaining the ability to recover the signal from its transform, should be as follows:

Instead of the exponential form of sampling scale factors α possible linear discretization of the form:

Discrete variant of basis wavelets (25) with the discretization parameters α and τ (30) can be written in the form:

in the mathematical literature is called "frames" [14].

The scale of the wavelet spectrum correspond to the Fourier frequencies of the signal. Therefore, the wavelet transform can be interpreted as a special kind of "time-frequency representation of signal [9]. Although more accurately it should be called "scale-temporal view.

Moreover, the linear scale (31), although more excessive in comparison with the logarithmic (30), but more convenient to compare the results of the wavelet transformation (i.e. scale-temporal representation of signals) with different types of frequency-time diagrams of signals [9].

The distinctive properties of resolution in the frequency-time domain wavelet transform and Krotkov the time (windowed) Fourier transform on a linear scale illustrate graphs, shown in figure 4.

The essence of the mathematical method, forms the basis of the proposed detection devices narrowband acoustic signals, is to perform the following operations:

1. The calculation of the wavelet transform W_x(α,τ) of the input process x(t) (the most effective this procedure is implemented in the frequency domain using analytic wavelet, in accordance with the operator 28:

1.1. The choice of the source wavelet ψ(t), compute its Fourier spectrum Ψ(f), the complex conjugationzeroing of negative frequencies (cast to analytical mind):when f>0 andif f≤0 (in the case of the choice of complex analytic wavelet, the last procedure - zeroing the negative frequencies optional).

1.2. The calculation of the basis spectra analytic wavelet by scaling the original spectrum of the mother wavelet:

1.3. The calculation of the Fourier spectrum of the input process X(f).

1.4. The multiplication of Fourier spectrum of the input process X(f) with the dual basis of the scaled spectra of analytic wavelets.

1.5. Calculating the inverse Fourier transform on the result of the last multiplication:.

2. ycycline square modulus of the wavelet transform |W _x(α,τ)|²the input process x(t).

3. The averaging time of the square of the modulus of the wavelet transform |W_x(α,τ)|²the input process x(t):

4. Comparing the integral of the wavelet spectrumwith a threshold (selectable depending on the desired false alarm probability) and the decision about the detection signal in case of exceeding a threshold in one or more channels (hypothesis H₁), or the non-detection in the case of non - exceeding of the threshold (the hypothesis H₀) in any of the channels.

Note that the operations 1.1 and 1.2 are made only with the wavelet ψ(t), and not with the test input process x(t), and thus, these operations can be carried out in advance, and the results of their calculations is stored in ROM.

Description of the device

The proposed device detection narrowband acoustic signals based on the evaluation of the integral of the wavelet spectrum is shown in figure 5, where:

unit 1 - analog-to-digital Converter (ADC)

block 2 - recirculator,

unit 3 - the first solver fast Fourier transform (FFT),

blocks 4.1-M - complex multiplier products,

blocks 5.1-M - scaling device with compression ratios α_m=α₀^m-1,

unit 6 - unit complex is about mates

unit 7 - the device is zero for negative frequencies

unit 8 - the second transmitter FFT,

unit 9 - permanent memory (ROM),

the blocks 10.1-M - solvers inverse FFT,

unit 11 - the transmitter unit square,

unit 12 - the device averaging,

unit 13 - the threshold device

block 14 - control device.

The principle of the device is as follows. To the input device enters the implementation of the input process x(t), which is fed to the input of the ADC (block 1) with a sampling rate that satisfies the requirements of the sampling theorem:

ADC output (block 1) discrete samples are sent to the input of the recirculator (block 2), where a and every Novem count is updated to the current discrete sample x(n) of length N samples.

The generated current discrete sampling of the input process x(n) is fed to the input of the first transmitter FFT (block 3), the output of which is integrated spectrum of X(n) input implementation is supplied simultaneously to the input M of the complex multiplier products (blocks 4.1-M).

From ROM (block 9) discrete sampling "mother" wavelet ψ(n) is fed to the input of the second transmitter FFT (block 8), the output of which is integrated spectrum of the wavelet Ψ(n) is supplied to the input of the shaper analytical signal (device reset negative h is the frequency) (block 7). From the output of the unit 7, the spectrum of the analytic wavelet Ψ_A(n) is supplied to the input of the complex conjugation (block b), the output of which is coupled spectrum analytical waveletsimultaneously arrives at the inputs of M scaling devices (blocks 5.1-M) with scale factors

α_m=α₀^m-1, m=1,...,M,

where α₀the logarithmic discrete step of the scale,

M - the number of discrete values of the scale (the number generated by the scale-frequency channels).

The selected value of the logarithmic pitch scale α₀specifies the relative bandwidth of the analysis of the detected narrow-band noise signal.

The number of required discrete values of the scale M is determined by the ratio of relative band General frequency range (in octaves) and the relative bandwidth of the detected DC (coinciding with a relative bandwidth of the amplitude spectrum of the selected wavelet).

M progesterone spectra of the basic wavelet functionarrive at the second input of the complex multiplier products (blocks 4.1-M), which outputs the multiplication results are received at the inputs of the inverse FFT solvers (blocks 10.1-M).

With outputs M computing the inverse FFT (blocks 10.1-M) the results of the wavelet-ol is education the current selection (in the form of a two-dimensional array of values of the wavelet coefficients of size M of N scale shifts W _x(m,n)) is fed to the input of the transmitter unit square (block 11). From the output of block 11 calculated the squared modules of wavelet coefficients |W_x(m,n)|²fed to the input of the averaging device (block 12), the output of which is averaged over time, the squared modulus of the wavelet transform of the current sample of the input process x(n)

fed to the input of the threshold device (block 13)whose output is the output device.

The control device (block 14) performs synchronization of work: a / d Converter (unit 1), recycler (block 2), computing the fast Fourier transform (blocks 3 and 8), ROM (block 9), computing the inverse FFT (blocks 10.1-M), the averaging device (block 12) and threshold device (block 13).

To check the level of effectiveness of the proposed detection devices narrowband noise was a special model experiment in MathCad 12.

It was a comparative analysis of the noise immunity of the classical detector DS (prototype) based on windowed Fourier transform (using the Hamming window) and the proposed device is based on wavelet analysis.

As a model of the narrowband signal was used specially formed temporary implementation escapemonos the noise (20) in accordance with the scale-frequency model SPD scale (18) and with the spectral function of DS (21). The Central frequency of the first harmonic was chosen equal to f₁=1 (Hz). The value of the relative band DS was

Formed in the scale was modeled 4 DC motors of the scale with the Central frequencies(Hz) and 4 DS blade scale with Central frequencies(Hz). Type SPD G_SP(f)that is implemented in MathCad 12, shown in Fig.6.

View the corresponding time implementation of narrowband noise from 8 DS shown in figa. Figure 7 (b) shows separate the time dependence for each of the 8 DS.

The obtained averaged experimental results for the proposed (a) traditional and (b) detectors narrowband noise is shown in Fig.

The computation of the integral wavelet spectrum (with analytical complex wavelet Morlaix, relative band spectrum which coincides with the relative band DS) narrowband noise signal was carried out with a uniform scale factors for the convenience of comparison with the detector based on windowed Fourier transform.

The result of the experiment revealed a significant advantage in noise immunity of the proposed detector DS. A model experiment was carried out for the same level of the useful signal, but when choosing the x values of noise variance . As can be seen from Fig, when the value of σ_p=6 detection of DS classical detector is almost impossible, while the proposed device gives good results even when the value of σ_p=10. Thus, the gain in noise immunity amounted to ≈1.6 times.

The irregularity of the spectrum of a high frequency and wideband DS with conventional SPM analysis is evident even in the absence of noise (σ_p=0), while the proposed device provides a satisfactory smooth results even at considerable variance noise σ_p=8-10.

It should be noted that an important condition for the effectiveness of the proposed detector narrowband noise is the correct choice of the form of the spectral functions used wavelet. Studies have shown the best performance when using the modernized complex analytic wavelet Morlaix with effective relative width coinciding with the relative width MTA investigated narrowband DS.

Moreover, as can be seen from Fig, in contrast to the known detectors narrowband signals (analog and prototype) and device for spectral analysis (in which the operation of partitioning in time results in the field of frequency convolution of the spectrum of DS with the spectrum of a time window, which causes the blurring of the DC power in the side lobes) in the proposed device due to selection of a particular type of wavelet (for example, wavelet Morlaix) can completely eliminate the appearance of side lobes, smooth out the irregularity of the current "spectrum" and to improve the noise immunity of the detector DS.

List of used sources

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Device detection of narrowband acoustic signals based on the evaluation of the integral of the wavelet spectrum, comprising: an analog-to-digital Converter, the input of which is applied the input signal and the output of which is connected to the input of the recirculator, the output of which is connected to the input of the first transmitter fast Fourier transform; the transmitter unit square, the output of which is connected to the input of the averaging, the output of which is connected to the input of the threshold device whose output is the output device; panel is engaged in the device, the outputs of which are connected to control inputs of analog-to-digital Converter, recirculator, the first transmitter fast Fourier transform, averaging and threshold device; characterized in that additionally introduced: M complex multiplier products, with the first inputs of which is connected to the output of the first transmitter fast Fourier transform, and the outputs are connected to inputs of M computing the inverse fast Fourier transform, the outputs of which are connected with inputs of the transmitter unit square; a persistent storage device, the output of which is connected to the input of the second transmitter fast Fourier transform, the output of which is connected to the input of the zero for negative frequencies, the output of which is connected to the input the device is complex conjugation, the output of which is connected to the input M of the scaling device, the outputs of which are connected with the second inputs of the M complex multiplier products; outputs a control device connected to control inputs of a permanent mass storage device, a second transmitter fast Fourier transform and M computing the inverse fast Fourier transform.