Apparatus for detecting hydroacoustic noise signals in form of sequence of sounds based on calculating integral wavelet spectrum

FIELD: physics.

SUBSTANCE: invention is based on calculating a continuous wavelet transform of an input process based on a combined complex analytical wavelet whose spectral function matches the spectral power density of the entire sequence of sounds comprising K discrete components (for the biggest possible scale and, consequently, with the lowest possible central frequencies for K discrete components).

EFFECT: high noise-immunity of a detector for detecting hydroacoustic noise signals in form of a sequence of sounds.

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The present invention relates to the field of hydro-acoustics, namely, devices for the detection of noise signals with spectral power density (SPM) in the form of scales (WR) (consisting of discrete components (DS) with multiples of the Central frequency) 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 about the incoming signal.

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

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

- propellers, which, although they are part of the power plant, but should be considered 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, consisting primarily of noise around the body of a ship or SUBMARINE, and noise of various parts of the equipment and structures that are created due to the percolation of various liquid is th.

The total noise of the moving sonar object contains two main types of noise different in nature. These differences manifest themselves 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 JMP noise depending on the frequency of G(f). 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 separate "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 G_DS(f).

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 avisit (or not depend on the speed, the depth of immersion noisy object and other factors.

Features DC, due to the operation of auxiliary mechanisms, usually stable and do not depend on the speed of the ship. The frequency and amplitude of DC caused propulsion and 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 a so-called scales (WR), i.e. the sets DS, whose frequencies are multiples of each other. Such DC in the literature often referred to as harmonics.

For example, shaft SP may contain DS at frequencies that are multiples of the rotational speed of shaft lines:

where k=1, 2, 3, ..., K - number of harmonics;

v - shaft rotation speed (rpm);

f_B1- shaft rotation frequency (Hz).

Paddle the LA may contain DS at frequencies that are multiples of the product of frequency of rotation of the line shaft and number of blades:

where z is the number of blades on the propeller.

Tonal components SP are highly stable and have a very narrow bandwidth [1-6]. It is worth noting that in contrast to a separate DC noise with SP, while h is about contains narrowband components, in General is a broadband noise process.

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

The main characteristic used to describe models of DC noise hydroacoustic purposes is the power spectral density. In known methods and devices for detection of narrowband signals (when the synthesis processing algorithms are traditionally used idealized models of MTA DS. These methods and implement their pickup device currently used for detection of broadband noise in the form of scales from multiple harmonics (1-2).

Most often MTA separate DC simplistically represented as absolutely narrow δ-function, shifted from the origin (zero frequency) on the value of the center frequency DC f₁[1-4]:

Accordingly, the joint mission of the scale from a To BC is represented as a series of δ-functions shifted by multiples of the frequency spacing kf₁[1-4]:

In the case of a more realistic approach (with reference to specific values of the width of the effective bandwidth Δf DS) SPM this DS can be described as a local spectral the Noah functions G ₀(f)shifted from the origin (zero frequency) on the value of the center frequency DC f₁and, respectively, localized in the region of its center frequency f₁

In most cases, to simplify models of DS, 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].

MTA scale from DC in this case is represented 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_k(f)=G₀(f-kf₁) - SPM k-th harmonic;

And_k- amplitude of k-th harmonic;

K - the number of DS in the scale.

For model G₀(f) in the form of a rectangular function, respectively, can be written

where

As the model G₀(f) can be considered and other, more complex, localized spectral function, in the form of various "spectral Windows", matched with the existing well-known "time (correlation) Windows (rectangular, Bartlett, Parzen, Henning, Hamming, etc. [by 8.22]), but also with a constant bandwidth DC: ∆ F_k=Δf=const.

In this traditional approach, i.e. using models DS and SP types (3-8), 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 shift frequency.

In accordance with the accepted models (3, 4) or (5-8), 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) apply different methods of spectral analysis (evaluation methods MTA noise)based on the Fourier transform [7, 8]. As mentioned above, these methods and implement their pickup device used for the detection of broadband noise in the form of scales, consisting of multiple harmonics (1-2).

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 floor the owl filtering (for the General frequency range), multi-channel narrow-band bandpass filter (for formation of 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 classical methods of spectral analysis, "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") narrow-band bandpass filters (PFM), with the same bandwidth and different Central frequencies (with a uniform frequency step equal to the width of the passband of one filter);

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,

which is fed to the input of a broadband bandpass filter (SPF) (block 1)influencing the overall frequency range is the azone analyzed the noise signal.

Output SPF (block 1) bandpass noise process arrives at the inputs of M-channel chasers UPF (blocks 2.1-M), where M is formed separate frequency channels.

Formed (resultrowone) narrowband noise processes in_m(t) are fed to the inputs of a quadratic detectors (units 3.1-3), with outputs which proyektirovaniye and squared narrowband signals |y_m(t)|²arrive at the inputs of the integrators (blocks 4.1-M). The time of integration (or accumulation) of 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] (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 implement what has been created using the algorithm of fast Fourier transform (FFT)of the input signal or its correlation function.

The form of response "narrow-band filters digital comb" is 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 "forward algorithm" MTAs assessment of the analyzed signal [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), compute the square of the module of the complex Fourier coefficients, averaging (in sections) and comparison with the threshold in each frequency channel).

The first three of the above tasks, 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]. And sub the full-time 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 (analog) [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 - 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 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), which is formed and with each new count is updated to the current discrete sampling (section) x(n) of length N samples. Length selection is key N (and accordingly, 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 average score MTAfed 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 methods of detection of narrowband signals and related devices (analogs) is their low real immunity, inadequate theoretical (potential) output signal-to-noise ratio (BSA), calculated on the basis of the hypothesis ideally narrow DS (3-4) or DC with constant bandwidth independent of frequency (5-8).

Resolution methods of spectral analysis used in these methods of detection of narrowband signals and related devices (analogs)is fixed for the whole considered frequency range and, in General, equal to the reciprocal of the duration of the analyzed temporal process (observation time is defined by the so-called "time window").

Lack of immunity to these methods of detection of narrowband signals is a consequence of the use of idealized models MTA narrowband noise in the form of DS, which does not take into account all known information about the detected signal.

At the same time, it is known that the solution to the problem of detecting noise signals against the background noise, in the case of the known dependency SPM 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 z1(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 Z0(t)) [1, s]:}

occurs when the unit square transfer characteristics predetection filter is:

The expression (14) determines the type of response (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 power density of the detected noise signal |(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 in the form of a separate DS (with unknown center frequency) or broadband noise in the form of scale DS (multiple frequencies) will implement the detection of DS or formed by them al 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 (3-8).

As the authors of [1 (s), 21 (p.46)], 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 0.03...0.3% of the values of f₁.

Random is distortion, make hydroacoustic channel when the signal propagation and Doppler transformation caused by the kinematics of the noisy 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 k-th harmonic in the scale is a linear function of frequency:

and the total SPM total scale from the 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 in a separate DS or broadband noise in the form of SP DS, taking into account the large-scale properties of DS [20].

The spectral function a separate DC with a center frequency f₁can be represented as:

the G ₀(f) simulating the spectral function, localized in the region of the zero frequency (defining the overall shape of the MTA DS);

α₀- the scale factor corresponding to a multiplicative transformation (compression) of the original spectral function G₀(f);

f₁- frequency shift that corresponds to a particular value of the center frequency of the DC.

The selected values of α₀and f₁clearly define the desired relative band DS β (15).

For broadband noise in the form of a scale from a To GS scale-frequency model MTAs can be described by presenting the total spectral function by the LA as the 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 k:

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), measuredto be fair record of the amplitude scaling factors under the radical sign:

for SPD separate DC

for SPD LA N DS

When modeling random temporary implementation of narrowband noise s(t), the corresponding modes is whether the SPD as a separate DS (20) or in the form of the scale (21), can be obtained by omitting the implementation of the normal white noise w(t) through a filter with transfer function of the form (20) or (21), respectively:

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

As a model of the spectral density of pressure separate DSor 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 DC at the input 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 additional the increased JMP DS.

It is worth noting that the spectral function of the form (24) 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 (20) 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.

Despite the above multiplicative properties of DS and SP, in the traditional methods of spectral analysis used in the known methods and devices for detection of narrowband signals (analogs), resolution (frequency) is constant (fixed) value for the entire frequency range. When it is configured (by choosing the size and shape of the time window) of the width of the narrowest spectrum (low-frequency) DS (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 (too wide) for lower frequency DC.

Thus, in the classical detectors noise signal from the additional DC or in the form of scales DS with multiple frequencies, 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 (18-19). I.e. in the framework of the classical spectral analysis it is impossible to implement transfer characteristics predetection filters adapted to the different frequency channels of the entire range and, therefore, it is impossible to achieve maximum PCB (13)corresponding to the filter Eckart.

Device detection of narrowband acoustic signals based on the evaluation of the integral wavelet spectrum [20] (prototype), allows you to more accurately account for the large-scale properties of MTA DS hydroacoustic noisy objects 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), the subsequent averaging over time of the square module of the result of the wavelet transform. 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 functions ψ(t) (the so-called mother wavelet):

To be a wavelet, and basic functionsshould have the required properties [14-17]. They should be quadratically integrable, alternating (to have zero mean), 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 ve is slain-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 of account operator CWP (31), compared with (27), is the requirement of analyticity for the studied signal and the applied wavelet:

supp X_A(f)⊂[0,∞); supp Ψ_A(f)⊂[0,∞),

i.e. X_A(f)=0 and Ψ_A(f)=0 if f≤0.

In the case of wavelet analysis is valid signals (which takes place during the processing of sonar 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 (31) enough to analytical was only wavelet, since convolution analysis of the generated 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, to implement the method of detection of narrowband signals [20] (prototype) effectively can be used complex analytic wavelet Morlaix (25).

The wavelet spectrum W_x(α,τ) a one-dimensional process x(t), obtained by applying the operator CWP (27) or (31), is a two-dimensional function and represents a surface in three-dimensional space.

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 is ignal |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. The scale α wavelet transform (if known (given) 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 [14-19]. 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:

Variant of basis wavelets (28) with the discretization parameters α and τ (33) can be written in the form:

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

The scale of the wavelet spectrum correspond to the frequencies of the Fourier research which has been created 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 essence of the mathematical method, forms the basis of the detection devices narrowband acoustic signals based on the evaluation of the integral wavelet spectrum [20] (prototype) is to carry out 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 (31)):

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, neoba ately).

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. The calculation of the square of the modulus of the wavelet transformthe input process x(t).

3. The averaging time of the square of the modulus of the wavelet transformthe 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 not detected in the case of not exceeding the threshold (the hypothesis H₀) in any of the channels.

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 and the calculations - be stored in ROM.

Device detection of narrowband acoustic signals based on the evaluation of the integral wavelet spectrum [20] (prototype, shown in figure 3, where

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

block 2 - recirculator;

unit 3 - the first transmitter FFT;

blocks 4.1-M - complex multiplier products;

blocks 5.1 to 5.M - scaling device with compression ratios

unit 6 - unit complex conjugation;

unit 7 is a device for zeroing 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;

block 13 - a threshold device;

block 14 - control device.

The principle of the device (prototype) [20] is the following. 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), which is formed and with each new count is updated to the current discrete sample x(n) of length N samples.

Sformirovanaya discrete sampling of the input process x(n) is fed to the input of the first transmitter FFT (block 3), since 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 frequencies) (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 6), 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 value of the discrete step size;

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 coincide 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 to 4.M), which outputs the multiplication results are received at the inputs of the inverse FFT solvers (blocks 10.1-10.M).

With outputs M computing the inverse FFT (blocks 10.1-M) the results of the wavelet transform of the current selection (in the form of a two-dimensional array of values of the wavelet coefficients of size M 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 10.1-10. M), averaging (block 12) and threshold device (block 13).

The above-described detecting device narrowband sonar is about noise signal (DS) based on the evaluation of the integral wavelet spectrum (prototype) [20] from the point of view of theory eckartsau filtering [1] noise signals is optimal (and more robust than with classical narrowband receivers that implement various methods of spectral analysis used for detection of individual DS on an unknown center frequency in the given frequency range.

This type of receiver-detector also provides a definite advantage in noise immunity in comparison with the classical detectors narrowband signals based on the traditional spectral analysis and detection of broadband noise in the form of harmonic scales (MTA representing the sequence of the To DS with multiples of the Central frequency), due to more accurate accounting of large-scale properties of MTA separate DS. But it is not the optimal detector for the entire broadband scale.

A new proposed device detection of noise signals in the form of scales is optimal (from the point of view of theory eckartsau filter) - it is to detect from the LA To DC and not for individual DS with unknown center frequency. This can improve the noise immunity of the proposed detector compared with the prototype in solving the problem of the detection of the broadband noise in the form of a scale from a To BC.

The essence of the algorithm of the signal processing in the proposed detection unit SP (as in the device discovery DS - prototype) also consists in calculating in agrarnogo wavelet spectrum of the input process, but as the original mother wavelet is proposed to use a new (special) kind of time process, the spectral function which coincides with MTA entire scale from the DS (for the largest possible scale and, accordingly, with the lowest possible centre frequencies for DC WR). The spectral function of this wavelet can be obtained by summing the individual spectra of the source wavelet after their large-scale transformations (in accordance with the scale-frequency model of the scale (21)).

The essence of the mathematical method, forms the basis of the proposed detection devices broadband noise hydroacoustic signals in the form of the LA-based calculation of the integral of the wavelet spectrum, is to perform the following operations:

1. The calculation of the wavelet transform W_x(α,τ) of the input process x(t), relative to the basis of wavelets, Fourier spectrum which corresponds to the SOP of the signal SP from a given quantity To a separate JS (in a digital implementation, the most efficient computationally, this procedure is implemented in the frequency domain using analytic wavelet, in accordance with the operator (31)):

1.1. The calculation of the basis spectra analytic wavelets corresponding to the SPD signal SP from a given number To otdelnyh JS:

1.1.1. Selecting (setting) the source wavelet ψ(t) and calculate its Fourier spectrum Ψ(f). The spectral function Ψ(f) must comply with SPD separate DC with the given relative bandwidth β and the lowest Central frequency f₁(equal to the lower frequency of the analyzed frequency range). For example, wavelet Morlaix:

the value of β is set by selecting the values of the parameter α₀.

1.1.2. 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).

1.1.3. Scaling (stretching) of the complex spectrumanalytical wavelet in a multiple number of times corresponding to a given number To a single DC in SP:

where k=1, 2, 3, ..., K.

1.1.4. The formation of the total spectrumanalytic wavelet, corresponding SPD signal SP from a given quantity To a separate JS:

1.1.5. The calculation of the basis (array) spectra analytic wavelet by scaling the parent total spec is RA wavelet

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

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

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

2. The computation of the integral of the wavelet spectrum of the input implementation:

2.1. The calculation of the square of the modulus of the wavelet transform |W_x(α,τ)|²the input process x(t).

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

3. 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 the threshold in one of the channels (hypothesis H₁), or not detected in the case of not exceeding the threshold (the hypothesis H₀) in any of the channels. The number of actuated scale-frequency channel can be measured fundamental frequency roll scale f₁and indirect estimates of the rate of movement of the detected target.

Note that the operations 1.1.1-1.1.5 are made only with Valleta is 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 device detector.

The proposed device detection scales hydroacoustic noise signals based on the evaluation of the integral wavelet spectrum shown in figure 4, where

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

block 2 - recirculator;

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

blocks 4.1-M - group complex multiplier products;

blocks 5.1-M - the first group of the scaling device with scale factors α_m=α₀^m-1;

unit 6 - adder;

unit 7.1-7.K - the second group of the scaling device with scale factors k=1, 2, 3, ..., K;

unit 8 - unit complex conjugation;

unit 9 - the device is zero for negative frequencies;

unit 10 - second transmitter FFT;

block 11 - permanent memory (ROM);

blocks 12.1 to 12.M - solvers inverse FFT;

unit 13 - the transmitter unit square;

unit 14 - the device averaging;

block 15 - threshold device;

block 16 - 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 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 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 11) discrete sampled wavelet ψ(n) is fed to the input of the second transmitter FFT (block 10), 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 frequencies) (block 9). From the output unit 9 range of analytic wavelet Ψ_A(n) is supplied to the input of the complex conjugation (block 8), the output of which is coupled spectrum analytical waveletat the same time it arrives at the inputs To the scaling device (blocks 7.1-7.K) with scale factors:

k=1, 2, 3, ..., K,

where K is the number of DS in detectable by the LA.

With output K of the scaling device (blocks 7.1-7.K) K progesterone spectra of the basic wavelet functionwill otuput to the inputs of the adder (block 6).

From the output of the adder (block 6) formed total range of the mother wavelet in the form of "scale" with the lowest Central frequency DC (or the largest time scale):

simultaneously arrives at the inputs of M scaling devices (blocks 5.1-M) with scale factors:

α_m=α₀^m-l, m=1, ..., M,

where α₀the logarithmic value of the discrete step size;

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 DC noise signal, and the number of required discrete scale values, M is the overlap of all the analyzed frequency range.

With outputs M scaling devices (blocks 5.1-M) M progesterone spectra of the basic wavelet functionarrive at the second input of the complex multiplier products (blocks 4.1 to 4.M), which outputs the multiplication results are received at the inputs of the inverse FFT solvers (blocks 12.1 to 12.M).

With outputs M computing the inverse FFT (blocks 12.1-M) the results of the wavelet transform of the current selection (in the form of a two-dimensional array of values of the wavelet coefficients of size M to the scale of the scale on N shifts W _x(m,n)) is fed to the input of the transmitter unit square (block 13). From the output of block 13 calculated the squared modules of wavelet coefficients |W_x(m,n)|²fed to the input of the averaging device (block 14), 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 15), the output of which is the output device.

The control device (block 16) performs synchronization of work: a / d Converter (unit 1), recycler (block 2), computing the fast Fourier transform (blocks 3 and 12), ROM (block 11), computing the inverse FFT (blocks 12.1-M), the averaging device (block 14) and threshold device (block 15).

The achievable gain in noise immunity of the proposed detector (and, respectively, in the range sonar system samplemovie that implements this method of detection WR) compared to the prototype (device detection of narrowband noise in the form of a separate DC) is achieved by increasing the base of the detected signal:

where Δf is the total band signal;

T - the duration of the analyzed signal (time of observation);

or rather, due to the increase in the total width of the s band of the received signal in the form of scale.

As is known [1], the output GSP receiver broadband noise signal d_ois determined by the base value of the received signal:

wherethe input PCB.

In the receiver-detector (prototype) in each individual (scale-frequency) channel, matched in frequency (scale) with the Central frequency of each of the To DS detectable by the LA, for the observation time T would be allocated to the power of one of the DS SP. Therefore, the basis of the detected signal at "triggered" channel will be equal to:

In the proposed receiver-detector of the broadband noise in the form of al in each individual (scale-frequency) channel, matched for frequency (scale) with the Central frequencies of all To DS detectable by the LA, for the observation time T will be allocated a capacity of not one, but all To DS SP. Therefore, the basis of the detected signal at "triggered" channel will be equal to:

Thus, the gain in noise immunity (output PCB) of the proposed detector (relative narrowband detector noise in the form of DS (prototype)) when the input process containing scale from a To BC, will be:

This gain in output PCB ≈ once achieved C is by increasing the bandwidth of the detected signal approximately To a time (equal to the number of DS, members of the LA).

Described detection algorithm SP corresponds to a known (predetermined) number of DS find in LA. In this case, is selected (generated) one specific total wavelet functions from a To BC. In the case of an unknown number of DS in detectable SP possible enumeration type of the mother wavelet (39), starting with K=2 and up to a specified maximum (theoretically possible) number of DS K_max. Usually in practice in the real noise of the moving sonar objects appear shaft and blade SP with the number of DS is not more than 5-10.

To check the level of effectiveness of the proposed method of detection of narrow-band noise was a special model experiment in MathCad 14.

It was a comparative analysis of noise (upon detection of noise in the form of WR 5 DC on the background interference as white noise):

device prototype, which implements the detection of DS based on the evaluation of the integral wavelet spectrum of the input process (with wavelet Morlaix);

and offer a device that implements the method of detecting the LA-based calculation of the integral of the wavelet spectrum of the input process (with a combined total wavelet, Fourier spectrum which has the form (39) with K=5).

As the signal model used the special the constraints generated temporary implementation of noise (23) in accordance with the scale-frequency model SPD of the scale (21) and with the spectral function of DS (24). The Central frequency of the first harmonic was chosen equal to f₁=2 (Hz). The value of the relative band DS was. Formed in the scale was modeled 5 DC motors of the scale with a Central frequency f_RR=2, 4, 6, 8, 10 (Hz). The input signal-to-noise (power) was chosen to be d_I=0.01.

Figure 5 illustrates the kind of output spectral processes (blue color in the presence in the input process noise; red color in the presence of a signal and interference), calculated by different algorithms and reduced to a single average spectrum of the output process in the presence of only noise (green):

a) the integral wavelet transform with wavelet Morlaix (prototype; linear frequency scale, from 1 to 25 Hz);

b) the integral wavelet transform combined wavelet (the proposed device; linear frequency scale from 1 to 5 Hz);

C) the integral wavelet transform with wavelet Morlaix (prototype; logarithmic frequency scale);

g) the integral wavelet transform combined wavelet (the proposed device; a logarithmic frequency scale).

The averaged results are repeatedly carried out experiment showed the coincidence of theoretical and experimental gain in output PCB: al of K=5 DS it was 2.2 times ≈ .

Output maximum response in the proposed device the detector is strictly corresponds to the center frequency of the first harmonic of the shaft of the scale that can serve as the basis of indirect method of measuring the velocity of the object measured by the frequency of rotation of the line shaft.

List of used sources

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3. Urik R.J. Fundamentals of hydro-acoustics. Leningrad: Sudostroenie, 1978, 446 S.

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19. Saprykin, VA, Small CENTURIES, Lopukhin W. "Method and device for rapid computation of the discrete wavelet transform of a signal with an arbitrary discretization step of scaling factors". Patent of the Russian Federation No. 2246132 from 10.02.2005 priority from 09.01.2003. (Similar).

20. Saprykin, VA, Small CENTURIES, Shatalov GV "Device detection of narrowband acoustic signals based on the evaluation of the integral of the wavelet spectrum. Patent of the Russian Federation No. 2367970 20.09.2009 with priority dated 24.12.2007. (Prototype).

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Device detection noise hydroacoustic signals in the form of scale on the basis of the calculation 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 output of which is connected with the first inputs of the M complex multiplier products whose 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 whose outputs are connected to inputs of the averaging device, the output of which is connected to the input of the threshold device whose output is the output device; 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 of the complex conjugation; M scaling devices of the first group, the outputs of which are connected with the second inputs of the M complex multiplier products; control device, the outputs of which are connected to control inputs of analog-to-digital Converter, recirculator, the first and Vtorov the solver fast Fourier transform, computing the inverse fast Fourier transform device of averaging and threshold device, characterized in that additionally introduced: the scaling of the devices of the second group, the inputs of which are connected with the output complex conjugation, and the outputs are connected To inputs of the adder, the output of which is connected to the input M of the scaling device of the first group.