Apparatus for detecting composite broad-band frequency-modulated signals with filtration in scale-time domain based on discrete wavelet transform

FIELD: physics.

SUBSTANCE: apparatus has an analogue-to-digital converter (1) whose output is connected to the input of a recirculator (2). The output of the recirculator is connected to the first input of a discrete wavelet transform computer (3). The wavelet transform output is connected to the input of a fast Fourier transform computer (8), the output of which is connected to the first input of a complex multiplier (9), the output of which is connected to the input of an inverse fast Fourier transform computer (11), the output of which is connected to the input of a squared absolute value computer (12), the output of which is connected to the input of a threshold device (13), the output of which is the output of the apparatus; a control device (14), the outputs of which are connected to control inputs of the analogue-to-digital converter (1), the recirculator (2), the discrete wavelet transform computer (3), a multiplier (5), an inverse discrete wavelet transform computer (7), the fast Fourier transform computer (8), the complex multiplier (9), the inverse fast Fourier transform computer (11) and read-only memory (4, 6, 10).

EFFECT: reduced computational and hardware expenses when filtering a signal in a scale-time domain.

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The invention relates to the field of sonar and radar systems, namely the complex detectors broadband frequency-modulated signals of known shape 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.

For signals with unknown initial phase is optimal quadrature receiver [2-4] (analog), providing a slight loss (1-1 .2 dB) compared with a matched filter. The main disadvantage of quadrature reception is limited its application only to the class of narrow-band signals. In the case of broadband signals necessary multichannel scheme, performing quadrature filtering for each component.

If the phase spectrum of the signal is unknown, use energy methods and devices receiving [2-4] (analog), which is a sequential execution of the filtering operations, quadratic detection and integration. The drawback of such methods is the effect of the suppression of small signal", which is a consequence of the fact that the output signal-to-noise ratio (BSA) is proportional to the square of the input PCB.

If the form of the received signal s(t) is completely known is on (except for the amplitude A and the time of arrival of the signal t ₀: As(t-t₀)), the potential robustness in solving the problem of the detection signals (including broadband frequency modulation) on a background of white noise, in principle, provides a correlation receiver or coherent filter [1 (s-343), 2-4] (analog).

Moreover, the robustness of these two methods of detecting a known signal correlator and matched filter) in a theoretical sense exactly the same. The generalized signal-to-noise ratio (BSA) at the output of these detectors, defined as the ratio of the increment component of the output of the process is the mathematical expectation E[y(t)], due to the presence of the useful signal, the variance of the output process in the absence of a signal D[y₀(t)], equal to twice the signal energy E_s(taking into account the random amplitude) to the spectral density of the noise N [1]

Data discovery methods known signal implicitly assume one of the types of one-dimensional representation of signal and noise: either in the spectral region (matched filtering), or in the time domain (correlation method).

However, for the input process x(t) sonar or radar receiver includes a two-dimensional representation - scale-time domain, obtained by p is the so-called imeneniya the wavelet transform (EAP) [5-9].

Continuous EAP can be defined as the scalar product of the investigated process x(t) and the basic wavelet function ψ_ατ(t) [5]

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

The General principle of construction of the basis of the EAP is to use large-scale transformations with parameter compression ratio 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 [5-9]. They should be quadratically integrable, alternating (and have zero mean), the wavelets must tend to zero atand for practical purposes - the sooner the better (and the wavelet should be well localized in both time and frequency). So it's probably the reverse of the EAP, the spectral function of a waveletmust satisfy another condition

The formula for continuous inverse wavelet transform has the form

As can be seen from (4), the original signal x(t) can be recovered through the integral sum of the same basis functions ψ_ατ(t) with weights in view of the wavelet spectrum of the signal [W _ψx](α,τ). Here the constant C_ψ(3) acts as a normalizing factor, similar to the factor (2π)^1/2, normalizing the Fourier transform.

For better calculation operators direct (1) and reverse (4) EAP can be represented in the frequency domain [5, 9]. When this is achieved a substantial improvement in the performance of digital devices that implement the EAP, by calculating convolutions using effective procedures FFT. The operator (1) continuous direct EAP can be defined in the frequency domain [5 (p.59, 67-68), 9]

whereimage Fourier selected source wavelet ψ(t);

image Fourier analyzed process x(t).

Operator (4) continuous reverse EAP can also be defined in the frequency domain as

where- Fourier transform on the wavelet spectrum of the process x(t).

The only limitation to this form of account operators (5) and (6) continuous EAP, compared with (1) and (4), is the requirement of analyticity for the studied signal and the applied wavelet [5 (p.67-68)]

ieandif f≤0.

You know, large numbers the creation of other types of time-frequency representation of signals (Tabor, Page, Wigner, Cswa-Williams, etc.) [10], but they all (unlike EAP) have the worst confining properties in the time-frequency plane (have a false items and bad simultaneous appearance of Delta-pulse and tone) and do not always have the inverse transformation for exact recovery of the original time signal. Accordingly, these methods of time-frequency representation is usually only used for signal analysis, but not for solving problems of detection on the background noise.

The use of scale-temporal representation (based on IP) to the input process x(t) of the detector signals [11]

where s(t) is detected echoes;

n(t) is the additive interference as Gaussian white noise,

allows (up directly matched filtering) to implement preliminary "bandpass filtering the wavelet spectrum of the received signal, s(t) simultaneously in the field of time and scale (frequency) using a special filter H(α, τ)

where as a scale-time filter H(α, τ) is a two-dimensional function of a special form

wherethe wavelet spectrum of copies of the emitted signal s(t);

A₀- the level specified on the basis of the conditions ,

option is 0<B<1 is selected depending on the type of frequency modulation signal and the storage conditions specified amount of energy of the original signalattributable to the recovered signal s₁(t) after application of the reverse of the EAP to the result of the multiplication (filter)

Pre-filters (8) of the input process x(t) in the scale-time domain (for the most widely used in sonar and radar class of frequency-modulated signals) allows to achieve a significant increase in noise, compared to the classical coherent filter or correlation receiver [1-4].

Output CPEs proposed detector rightly be written in the form:output PCB classical matched filtering in the form:.

The gain in noise immunity of the proposed method of detection CMS compared with the classical coherent filtering caused by the reduction of the noise level (N₁<N) after wavelet filtering" (8) the input process, while maintaining approximately constant the energy of the received signalin the output process (when performing a hypothesis H₁).

Reducing the spectral density of the noise (as well as the e variance) and accordingly, the increase in GSP (characterizing the gain in noise immunity) is approximately equal to the ratio of "squares" scale-temporal region occupied by the wavelet spectrum of the input process to "wavelet filtering" Wx and after wavelet filtering" Wx₁

as in the case of white noise, its power (after VP) is uniformly distributed on a large scale the time domain within a conditional "rectangle", limited on the time axis τ - pulse duration of T_Sand along the axis of the scale of the α - band magnitude Δα_S=α₁α₂(clearly the corresponding spectral band of the frequency deviation of the modulated signal Δf_S=f_in-f_n). After filtration (8) remaining in the output process x₁(t) of the power interference scale-time domain is limited to the area of media filtration function (α, τ)∈supp{[H(α, τ)}, where H(α, τ)≠0.

The method of detection of frequency-modulated signals filtered scale-time domain [11] includes the following operations.

1. The calculation of the wavelet transform Wx(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 (5)):

1.1. the choice of the source wavelet, ψ(t) computation of its range For 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 (compression) of the original spectrum of the mother wavelet:;

1.3. the calculation of the Fourier spectrum of the input process;

1.4. the multiplication of Fourier spectrum of the input processwith the dual basis compressed spectra of analytic wavelets;

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

2. The calculation of the wavelet transform Ws(α,τ) of the reference probe signal s(t) (using the previously calculated of the basis spectra analytic wavelets(in accordance with clause 1.2)):

2.1 calculation of the Fourier spectrum of the reference signal;

2.2 the multiplication of Fourier spectrum of the reference signalwith the dual basis compressed spectra of analytic wavelets;

2.3 in the overall number of General inverse Fourier transform on the result of the last multiplication: .

3. The formation of two-dimensional filter function H(α,τ) scale-temporal plane, the clip region of values of (α,τ), where the magnitude of a complex wavelet spectrum of the standard probing signal Ws(α,τ) exceeds a certain level, A₀(13):

4. The multiplication of the wavelet spectrum of the input process and scale-temporal filtering functions:

.

5. The calculation of the inverse wavelet transform for the last multiplication Wx₁(α,τ) (using the previously calculated of the basis spectra analytic wavelets(in accordance with clause 1.2)):

5.1 calculation of the direct Fourier transform in τ from the two-dimensional wavelet spectrum;

5.2 multiplication of Fourier spectrumwith the dual basis of spectra analytic wavelets;

5.3 calculation of the inverse Fourier transform by f from the last multiplication:;

5.4 integrationas(dividing by the normalizing factor C_ψ(3), which is part of the operator (6)may not be made, because it does not affect the robustness of the proposed method of detection; integration multiplicate the ate least it is only necessary in the case of exponential sampling scale factors, in the case of a linear sampling is sufficient to carry out the integration over the conventional additive as

5.5 calculation of the real part of the restored process(the need for this procedure due to the analyticity of the used wavelet ψ(t) and, respectively, by analysis of the output process x₁(t).

Further processing of the process x₁(t) coincide with the classical implementation of the method detection signal of known shape-based matched filtering.

6. Matched filtering of the detected signal s(t) known form:

6.1. calculation of complex Fourier spectrumprocess x₁(t);

6.2. calculation of complex Fourier spectrumthe reference signal s(t)and its complex conjugation;

6.3. the multiplication of the complex Fourier spectrumwith the dual Fourier spectrum of the standard;

6.4. calculating the inverse Fourier transform on the result of the last multiplication:.

7. Selection (quadratic detection) of the envelope of the response of the matched filter: (calculating, key writing, the square module response SF y(t)).

8. Comparisonwith a threshold (selectable depending on the desired false alarm probability) and the decision about the detection signal in case of exceeding the threshold (the hypothesis H₁), or the non-detection in the case of non - exceeding of the threshold (the hypothesis H₀).

It should be noted that when using the envelope of the response SFit is enough to observe the amplitude at time intervals approximately equal to the effective bandwidth of the envelope [1, s].

Note also that the operations 1.1 and 1.2 are made only with the wavelet ψ(t), operation 2.1, 2.2, 2.3, 3, and 6.2 are made only with the reference signal s(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.

The device [11] (prototype)that implements a method for detecting the complex of broadband frequency-modulated signals filtered scale-time domain [11], is shown in figure 1, where:

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

block 2 - recirculator;

unit 3 - the solver fast Fourier transform (FFT) 1;

blocks 4.1-M - complex multiplier products;

block 5 - permanent memory (ROM) 1;

blocks 6.1-M - solvers inverse FFT;

unit 7 - matrix complex is the multiplier;

unit 8 - ROM 2;

blocks 9.1-M - FFT solvers;

the blocks 10.1-M - complex multiplier products;

unit 11.1-M - solvers inverse FFT;

block 12 - matrix integrator;

unit 13 - the transmitter 2 FFT;

unit 14 - the complex multiplier;

block 15 - ROM 3;

block 16 - calculator inverse FFT;

block 17 - transmitter unit square;

block 18 - threshold device;

block 19 - control device.

Thus, the detection unit complex broadband frequency-modulated signals filtered scale-temporal region (prototype) [11] includes: analog-to-digital Converter (unit 1), the input of which is applied the input signal, the ADC output is connected to the input of the recirculator (block 2), the output of which is connected to the input of the first transmitter fast Fourier transform (block 3), the output of which is connected with the first inputs of the M complex multiplier products (blocks 4.1-M)whose outputs are connected to inputs of M computing the inverse Fourier transform (units 6.1-M)the outputs are connected to first inputs of a matrix of complex multiplier (block 7), the outputs of which are connected with inputs M computing the fast Fourier transform (blocks 9.1-M), the outputs of which are connected with the first inputs of the M complex multiplier products (blocks 10.1-M)whose outputs are connected to inputs of M will calculate the MDL inverse fast Fourier transform (blocks 11.1-M), the outputs are connected to inputs of matrix integrator (block 12), the output of which is connected to the input of the second transmitter fast Fourier transform (block 13), the output of which is connected to the first input of complex multiplier (block 14), the output of which is connected to the input of the transmitter inverse fast Fourier transform (block 16), the output of which is connected to the input of the transmitter unit square (block 17), the output of which is connected to the input of the threshold device (block 18), the output of which is an output device; the first persistent storage device (block 5), the outputs of which are connected with the second the inputs of the M complex multiplier products (blocks 4.1-M) and with the second inputs of the M complex multiplier products (blocks 10.1-M); the second persistent storage device (block 8), the output of which is connected with the second input matrix complex multiplier (block 7); the third permanent storage device (block 15), the output of which is connected to a second input of the complex multiplier (block 14); control unit (unit 19), the outputs of which are connected to control inputs of analog-to-digital Converter (unit 1), recycler (block 2), calculators fast conversion Fourier (blocks 3, 9.1-M and 13), the complex multiplier products (blocks 4.1-M, 7, 10.1-M and 14), computing the inverse fast Fourier transform (block the 6.1-M, 11.1-M and 16) and permanent storage devices (blocks 5, 8, and 15).

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), which is formed and with each new count is updated to the current discrete sample x(n) of length N samples. Sample length N is determined by the duration of the emitted signal and the sampling interval:. 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 a comprehensive rangeinput implementation is supplied simultaneously to the input M of the complex multiplier products (blocks 4.1-M).

With outputs of the first read-only memory (block 5) reads M one-dimensional arrays of length N samples (pre-calculated basiscompressed spectra of analytic wavelets) and arrives 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 (units 6.1-M). The number of scale is determined by the poppy is isalnum value of the ratio of the source wavelet α _maxand step linear discretization scale.

With the output of the inverse FFT solvers (units 6.1-M) the result of the wavelet transform of the input process Wx(m, n) in the form of a two-dimensional array of size M of N scale shifts is supplied to the first inputs of the matrix complex multiplier (block 7).

From the output of the second ROM (block 8) is read pre-calculated two-dimensional array of filter function H(m, n) (scale-temporal plane) of size M N scale shifts and is supplied to the second input matrix complex multiplier (block 7), the outputs of which M one-dimensional arrays of length N samples of the multiplication (i.e. filtering scale-temporal plane) Wx₁(m, n) are fed to the inputs of the FFT solvers (blocks 9.1-M), which outputs the results of the FFTcome to the first inputs of the M complex multiplier products (blocks 10.1-M).

With outputs of the first read-only memory (block 5) reads M one-dimensional arrays of length N samples (pre-calculated basiscompressed spectra of analytic wavelets) and arrives at the second input of the complex multiplier products (blocks 10.1-M), which outputs the multiplication results are received at the inputs of the inverse FFT solvers (blocks 11.1-M), which outputs the results of the inverse FFT arrive at the inputs of matrix integrator (block 12), which is the integral summationscale m.

Output matrix integrator (block 12) temporary implementation of the filtered scale-temporal process area x₁(n) is fed to the input of the second transmitter FFT (block 13), the output of which a comprehensive rangearrives at the first input of complex multiplier (block 14).

From the third ROM (block 15) is read pre-calculated complex conjugate spectrum of the reference signaland is supplied to the second input of the complex multiplier (block 14), the output of which is the result of the multiplication is fed to the input of the transmitter inverse FFT (block 16). From the output of the transmitter inverse FFT (block 16), the response of the matched filter y(n) is fed to the input of the transmitter unit square (block 17), the output of which is allocated to envelopefed to the input of the threshold device (block 18), the output of which is the output device.

The control device (block 19) synchronizes operation: analog-to-digital Converter (unit 1), recycler (block 2), computing the fast Fourier transform (blocks 3, 9.1-M and 13), the complex multiplier products (blocks 4.1-M, 7, 10.1-M and 14), calculators reverse the th fast Fourier transform (units 6.1-M, 11.1-M and 16) and permanent storage devices (blocks 5, 8, and 15).

However, this device [11] (prototype)that implements a method for detecting the complex of broadband frequency-modulated signals with filtering, scale-time domain [11], has the following disadvantage. Digital implementation of operations the calculation of the forward and reverse continuous (redundant discrete wavelet transform with arbitrary small discretization step of scaling factors α_m=α₀^m, 1<α₀<2, which analyzes the signal with arbitrary precision measuring scale, is not effective from the point of view of the required performance and the computational and hardware costs.

So, for the numerical implementation of the forward and reverse CWP (the main components of the operation pre-filtering the useful signal to background noise in the large-time domain [11]) of the input sample length of N samples requires the following digital resources:

- in memory ROM (block 5) should be stored M the calculated pre-compressed copies of the spectrum of the source waveleteach length N times (it is worth noting that for their preliminary calculations required M scaling (compression) of the spectrum of the source wavelet and, accordingly, the same interpolation procedures);

- to implement the direct calculation of the wavelet transform with arbitrary discrete step scale in the spectral region required: one operation direct FFT (block 3) and M operations inverse FFT (units 6.1-M), or aboutcomplex multiplications (taking into account the fact that one FFT operation for a signal of length N samples requirescomplex multiplications [12 (s)]); plus MN complex multiplications in the multiplier products (blocks 4.1-M);

- to implement the multiplication of the filter function H(m, n) and the wavelet transform of the input process Wx(m, n) requires MN complex multiplications (blocks 4.1-M);

for implementation of computing the inverse wavelet transform with arbitrary discrete step scale in the spectral region required: M operations direct FFT (blocks 9.1-M) and inverse FFT operations (blocks 11.1-M), or, respectively, about MNlog₂N complex multiplications; plus MN complex multiplications in the multiplier products (blocks 10.1-M);

Total:

- memory required ROM - 2 MN;

- the required amount of computing complex multiplications.

Below is a new device that implements the method for detecting the complex of broadband frequency-modulated signals filtered scale-time domain, based on the use of calculators direct and inverse discrete wavelet transform (DWT) with a discretization step of scaling factors equal to 2, is much more effective from the point of view of performance, computing, and hardware cost than the prototype.

Thus the immunity of the proposed new detector, as was shown by the simulation environment MathCadl3, almost completely coincides with the immunity of the device-prototype [11], i.e. has the same winning (11) relative to the classical matched filter.

Theoretical foundations of the fast algorithm of discrete wavelet transform

When the discrete wavelet transform the necessary discretization of the values of the parameters α and τ, while maintaining the ability to recover the signal from its wavelet transform should be performed as follows

where m, n ∈ Z; α₀>1; τ₀≠0.

The shift parameter depends on the parameter scale. With scale increases and the step size of the shift. At step shift τ₀=1, the corresponding one odce is, the basis of wavelet functions is represented in the form

Under certain, very specific, the choice of the wavelet ψ and initial values α₀τ₀a discrete set of functions ψ_ατforms an orthonormal basis in the Hilbert space [5].

In particular, if the discrete EAP, without loss of generality, choose α₀=2 and τ₀=1

I.e. in digital form when fiberboard minimum step logarithmic scale compression option (or its base) is equal to two, and the minimum step of setting time shift - unit (i.e. one reference).

For this method the discretization parameters compression and shear developed all known efficient algorithms fast discrete wavelet transform (DWT - discrete wavelet transform) [5-8]. In this case, compression of the original signal in the 2^mtimes sufficient to produce an appropriate number of times thinning even-numbered or odd time samples. This method is implemented scaling of signals in the algorithms of fast discrete wavelet transform.

In contrast to theory of continuous EAP in theory of discrete orthogonal EAP, or rather, in theory cranemaster analysis [5], in addition to the functions of a wavelet ψ(t) introduces another important concept is the so-called scaling function (or the scale of Bermuda function) φ(t). In the literature of the scaling function φ(t) is sometimes called the "father" wavelet by analogy with the mother wavelet ψ(t).

Functions of the wavelet and scaling functions in theory of fiberboard are associated with discrete sequence g_nand h_n. Function ψ(t), φ(t) and the sequence g_nh_nlinked by the following key ratios

When calculating the fiberboard is possible iterative calculation of the discrete wavelet coefficients c_j,kand d_j,kwithout the direct use of the paternal functions φ(t) and the mother wavelet ψ(t}. For an arbitrary phase decomposition of j can be written

having thus fully discrete decomposition of the signal (direct fiberboard). Sequence h_nand g_nare essentially impulse response digital low - pass and high-pass filters. The coefficients of the approximation of c_j,kand detail of the d_j,k. have "half" length compared to c_j-1,k.

For a matrix description of the procedure fiberboard through the vector v^jdenote the sequence of finite length c_j,nfor some non scale j (or the step of calculating the DVP). At each stage fiberboard this vector is converted to a vector V^j+1which which contains the sequence c _j+1,nand d_j+1,neach of which is half-length. The transformation can be written in the form (18) matrix multiplication v^j+1=M_jv^jwhere M_j- a square matrix consisting of zeros and elements of h_nmultiplied by. Because of the properties of h_nthe matrix M_jis orthonormal and its inverse matrix is equal to the transposed.

As an illustration we can consider the following example. Take the filters g_nand h_nlength L=4, the sequence of signal c₀length N=8, and as the initial value of the scale j=0.

Then the operation of the matrix-vector multiplication can be represented in the form

The sequence g_ncan be obtained from h_naccording to the formula: g_n=(-1)ⁿh_-n+2L+1to rewrite (18) in the form

Thus, the operation (19) is one step fiberboard. Full DVP algorithm is an iterative multiplication of the upper half of the vector v^j+1for a square matrix M_j+1whose size is 2^D-j. This procedure is repeated D times until the length of the vector will be equal to one reference.

Complete decomposition of the original signal c_0,nlength N=2^Dthe wavelet coefficients d_j,nrequire D similar matrix multiplications (for j=0, ..., D-1 stages fiberboard. It should be noted that the total number of elementary multiplications in the algorithm fiberboard depends on the length L of the selected sequences of the h_n, g_ni.e. the type of the wavelet and its order. Typically, the most famous of the discrete wavelets (Haar, Daubechies - different orders of magnitude) the length L of the sequence h_nsignificantly less than the length of N samples of the analyzed signal. The most economical in this sense is the Haar wavelet length just two count.

The final result fiberboard contains N wavelet coefficients: N - 1 coefficients parts d_j,nand one factor approximation of c_J,0. Usually the result of a one-dimensional fiberboard write one string of length N coefficients (in particular, in applications of MathCad and MathLab). For the considered example, the DVP will be

[d_1,0d_1,1d_1,2d_1,3; d_2,0d_2,1; d_3,0; c_3,0].

The coefficient of the approximation of the last level c_J,0go for the start of the implementation of the iterative calculation of the inverse fiberboard.

Reverse fiberboard can be described by multiplying v^j+1return matrix

In foreign literature is considered a fast algorithm for computing fiberboard associated with the work Small (S.Mallat) [5]. The fast algorithm is Alla discrete wavelet transform of the original signal of length N samples is implemented in D=log ₂N stages and requires only 2NL multiplications.

The essence of the proposed device

The proposed device - detector complex broadband frequency-modulated signals filtered scale-temporal region-based discrete wavelet transform is shown in figure 2, where:

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

block 2 - recirculator;

unit 3 - the evaluator discrete wavelet transform (DWT);

unit 4 - permanent memory (ROM) 1;

block 5 - multiplier;

unit 6 - ROM 2;

unit 7 - calculator reverse fiberboard;

unit 8 - the transmitter 2 FFT;

unit 9 - the complex multiplier;

unit 10, ROM 3;

block 11 - calculator inverse FFT;

unit 12 - the transmitter unit square;

block 13 - a threshold device;

block 14 - control device.

Thus, the detector complex broadband frequency-modulated signals filtered scale-temporal region-based discrete wavelet transform includes: analog-to-digital Converter (unit 1), the input of which is applied the input signal, the output of the analog-to-digital Converter connected to the input of the recirculator (block 2), the output of which is connected to the first input of the transmitter fiberboard (block 3), the output of which is connected to the first input of the multiplier (block 5), you are the od of which is connected to the first input of the transmitter reverse fiberboard (block 7), the output of which is connected to the input of transmitter fast Fourier transform (block 8), the output of which is connected to the first input of complex multiplier (block 9), the output of which is connected to the input of the transmitter inverse fast Fourier transform (block 11), the output of which is connected to the input of the transmitter unit square (block 12), the output of which is connected to the input of the threshold device (block 13), the output of which is an output device; the first persistent storage device (block 4), the output of which is connected with the second inputs of the transmitter fiberboard (block 3) and evaluator feedback fiberboard (block 7); the second persistent storage device (block 6), the output of which is connected with the second input of the multiplier (block 5); the third permanent storage device (block 10), the output of which is connected to a second input of the complex multiplier (block 9); control device; (block 14), the outputs of which are connected to control inputs of analog-to-digital Converter (unit 1), recycler (block 2), evaluator fiberboard (block 3), multiplier (block 5), calculator reverse fiberboard (block 7), the solver fast Fourier transform (block 8), the complex multiplier (block 9), calculator inverse fast Fourier transform (block 11) and permanent storage devices (blocks 4, 6 and 10).

The principle of the device 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. The generated current discrete sampling of the input process x(n) arrives at the first input of the transmitter fiberboard (block 3), the output of which the discrete wavelet transform of the input process Wx(n) in the form of a one-dimensional array of size N samples is supplied to the first input of the multiplier (block 5).

With outputs of the first ROM (block 4) reads the sequence h(n) of length L samples (corresponding to the selected basis discretely wavelets) and is supplied to the second inputs of the transmitter fiberboard (block 3) and evaluator feedback fiberboard (block 7).

From the output of the second ROM (block 6) is read pre-calculated array filter function H(n) (scale-temporal plane) of size N times, and is supplied to the second input of the multiplier (block 5), which outputs a one-dimensional array of length N samples of the multiplication (i.e. filtering scale-temporal region) Wx₁(n) arrives at the first input of the transmitter reverse fiberboard (the POC 7), since the output of which temporary implementation of the filtered scale-temporal process area x₁(n) is fed to the input of the transmitter FFT (block 8), the output of which a comprehensive rangearrives at the first input of complex multiplier (block 9).

From the third ROM (block 10) is read pre-calculated complex conjugate spectrum of the reference signaland is supplied to the second input of the complex multiplier (block 9), the output of which is the result of the multiplication is fed to the input of the transmitter inverse FFT (block 11). From the output of the transmitter inverse FFT (block 11), the response of the matched filter y(n) is fed to the input of the transmitter unit square (block 12), the output of which is allocated to envelopefed 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), evaluator fiberboard (block 3), multiplier (block 5), calculator reverse fiberboard (block 7), the solver fast Fourier transform (block 8), the complex multiplier (block 9), calculator inverse fast Fourier transform (block 11) and permanent storage devices (blocks 4, 6 and 10).

Thus, h is emom device detector for digital implementation of the forward and reverse fiberboard (the main components of the operation pre-filtering the useful signal to background noise in the large-time domain input samples length N samples requires the following digital resources:

- in memory ROM (block 5) should be stored impulse response h(n) of length L samples (corresponding to the selected basis of discrete wavelets);

- in memory ROM (block 8) should be stored pre-calculated one-dimensional array of filter function H(n) (scale-time domain) of size N samples;

for realizing the calculation of direct fiberboard required 2LN operations of multiplication (block 3);

- to implement the multiplication of the filter function H(n) and the DVP input process Wx(n) requires N multiplications (block 5);

- to implement the calculation of the inverse fiberboard required 2LN operations of multiplication (block 7).

Total:

- memory required ROM - N+L;

- the required amount of computing - (4L+1)N complex multiplications.

Other operations that implement a consistent filtering (blocks 8-13), completely similar to the device prototype.

To clarify the essence of the operation of forming large-scale temporal filter function H(n), the filtering operation of the input process x(n) scale-time domain using fiberboard and illustrate the gain in noise immunity of the proposed detector signal of known form in relation to the classical matched filter figure 3-15 shows the simulation results (obtained in MathCad) of the processing, the chirp signal, discover the background of Gaussian white noise, classical coherent filter and the proposed detector.

Figure 3 shows the reference chirp signal.

Figure 4 shows the interference as Gaussian noise.

Figure 5 shows the cumulative input process of the useful signal and the interference.

Figure 6 shows the result of fiberboard reference chirp signal using discrete wavelet Daubechies 20 order).

Figure 7 shows the result fiberboard total process of the useful signal and the interference.

On Fig illustrates the kind of large-scale temporal filtering functions for the chirp signal.

Figure 9 shows the result of filtering in scale-time domain (i.e. multiplication DVP input process on the filter function).

Figure 10 shows a view of the filtered signal resulting from application of the reverse fiberboard.

Figure 11 shows a view of the envelope of the autocorrelation function of the reference chirp signal.

On Fig see the response of the detector on the basis of the classical matched filter.

On Fig see the response of the proposed detector with additional pre-filtering on the basis of DVP and subsequent coherent filtering.

On Fig shows the normalized response of the detector on the basis of the classical matched filter.

On Fig shows the normalized off the to of the proposed detector with additional pre-filtering on the basis of DVP and subsequent coherent filtering.

References

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4. Van-Tris, Theory of detection, estimation, and modulation, vol. 1, M.: Owls. radio, 1972, S. 744, v.3, M: Owls. radio, 1977, 661 S.

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7. I.M. Dremin, Ivanov O.V., V.A. Nechitailo Wavelets and their use. The success of the physical Sciences. Volume 171, No. 5, 2001, s-501.

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9. Saprykin, VA, Small CENTURIES, Lopukhin RV 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.

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11. Saprykin, VA, Small VV Method and device for detection of complex broadband frequency-modulated signals filtered scale-time domain. The patent on izaberete is the development of the Russian Federation No. 2282209 from 20.08.2006 priority from 07.12.2004 (Prototype).

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Device detection complex broadband frequency-modulated signals filtered scale-temporal region-based discrete wavelet transform, containing analog-to-digital Converter (1), the input of which is applied the input signal, the output of the analog-to-digital Converter connected to the input of the recirculator (2), characterized in that the output of the recirculator (2) connected to the first input of the transmitter discrete wavelet transform (3), the output of which is connected to the first input of the multiplier (5), the output of which is connected to the first input of the transmitter inverse discrete wavelet transform (7), the output of which is connected to the input of transmitter fast Fourier transform (8), the output of which is connected to the first input of complex multiplier (9), the output of which is connected to the input of the transmitter inverse fast Fourier transform (11), the output of which is connected to the input of the transmitter unit square (12), the output of which is connected to the input of the threshold device (13), the output of which is an output device; the first persistent storage device (4), the output of which is connected with the second inputs of the transmitter discrete wavelet transform (3) and evaluator inverse discrete Wei the years-transform (7); the second persistent storage device (6), the output of which is connected with the second input of the multiplier (5); the third permanent storage device (10), the output of which is connected to a second input of the complex multiplier (9); control device (14), the outputs of which are connected to control inputs of analog-to-digital Converter (1), recycler (2), computer fiberboard (3), multiplier (5), transmitter reverse fiberboard (7), solver fast Fourier transform (8), complex multiplier (9), calculator inverse fast conversion Fourier (11) and permanent storage devices (4, 6, 10).