CN101931602A - Secret signal synchronized method based on fractional Fourier transform domain - Google Patents

Abstract

The invention discloses a secret signal synchronized method based on a fractional Fourier transform (FRFT) domain, which comprises the following steps: (1) carrying out the FRFT domain; (2) obtaining a spectral overlap formula based on the FRFT; (3) and synchronously analyzing secret signals of a voice information hide system. The secret information of the invention can be embedded any time and any where, and the invention has wide application prospects in the voice information hide field.

Description

A kind of secret signal synchronized method based on fractional Fourier transform domain

Technical field

The present invention relates to a kind of secret signal synchronized method, particularly a kind of voice messaging based on fractional Fourier transform domain is hidden the secret signal synchronized method in the system.

Background technology

How utilizing call voice to carry out the long-distance transmission of concealed data in recent years is focus and the difficult point that the voice manipulative communications deception becomes military security department and voice signal processing researcher extensive concern.In existing technology and the method, people utilize LSB technology audio signal is embedded on wavelet field.In addition, the subband amplitude modulation technique also has some to use in the audio frequency letter is hidden, and has obtained certain effect.But at present the certain methods that proposes mainly concentrates on the audio signal that frequency band is 20～20KHz, and is that the method hidden of the call voice of 300～3400Hz is ripe not enough to frequency band.

Voice messaging is hidden, and general flow process judges exactly whether present frame is speech frame, embeds if just carry out concealed data.This method exist bigger potential safety hazard, if the prison hearer suspects this section voice, just find the hiding-place of secret signal easily by simple analysis.Therefore must improve the embedding means, guarantee that secret information can embed at random, this just brings a problem, is exactly how the recipient knows which point has embedded secret information, and which point does not have, i.e. the secret information stationary problem.The method for synchronous that voice messaging is hidden mainly still depends on the synchronous system of digital communication system itself at present, does not also have method synchronous about secret signal and that the digital communication system separated in synchronization comes.

Summary of the invention

The present invention seeks to provides a kind of secret signal synchronized method based on fractional Fourier transform domain at the defective that prior art exists.

The present invention adopts following technical scheme for achieving the above object:

The secret signal synchronized method that the present invention is based on fractional Fourier transform domain may further comprise the steps:

(1) fractional Fourier transform domain

The a rank fractional fourier transform algorithm of input voice sequence s (t) is as follows:

S _a(u)＝F ^a(s(t))

In the formula, 0＜| p|＜2, n is an integer, j is an imaginary unit;

(2) based on the overlapping formula of the spectrum on the fractional fourier transform

The centre frequency of each waveform is u in the formula _cCsca+f _i, u _c, λ _i, f _i, (i=1 .. N) are constant, and X (u) and x (t) are respectively the frequency domain and the time domain form of output signal.

(3) secret signal of the hiding system of voice messaging is analyzed synchronously

When sending carrier signal, send one group and be lower than channel noise level, satisfy formula f _iSina+ τ _iCosa=u ₀Condition, amplitude are subjected to the signal of pseudo noise code control, and receiving terminal is u on fractional Fourier transform domain _cThe place is judged.

Advantage of the present invention and effect are:

Concealed synchronizing signal all can not effectively be found at time domain, frequency domain, under the prerequisite of known fraction rank factor a, can effectively extract concealed synchronizing signal on score field.Theoretical research and experimental analysis show that by this method, secret information can embed whenever and wherever possible, and the present invention hides in the field at voice messaging and has broad application prospects.

Description of drawings

Fig. 1 is a carrier wave voice manipulative communications deception system transmitting element.

Fig. 2 is based on the embedding grammar at random of LSB.

Fig. 3 is a carrier wave voice manipulative communications deception system receiving element.

Fig. 4 is Chebyshev mapping and the 8 bit quantization sequence characteristics of W=4.

Fig. 5 is a 2FSK carrier wave voice manipulative communications deception system model.

Fig. 6 is 2FSK modulating system output waveform and the frequency spectrum that does not embed crypto-synchronization information.

Fig. 7 is 2FSK modulating system output waveform and the frequency spectrum that embeds crypto-synchronization information.

Fig. 8 is 2FSK modulating system receiving terminal waveform and the frequency spectrum that embeds crypto-synchronization information.

Fig. 9 is a concealed synchronizing signal mark amplitude spectrum under the noise circumstance.

Figure 10 is a mark amplitude spectrum under the pink noise circumstance.

Figure 11 is the mark amplitude spectrum under the volvo automobile noise environment.

Figure 12 is a mark amplitude spectrum under the noise circumstance of factory workshop.

Embodiment

A kind of secret signal synchronized method based on fractional Fourier transform domain of the present invention is characterized in that may further comprise the steps:

(1) fractional Fourier transform domain

The a rank fractional fourier transform algorithm of input voice sequence s (t) is as follows:

S _a(u)＝F ^a(s(t))

In the formula,

0＜| p|＜2, n is an integer, j is an imaginary unit.

(2) based on the overlapping derivation of the spectrum on the fractional fourier transform

Order:

λ in the following formula _i, f _i, τ _i, (i=1 .. N) are constant.Then have:

X _a(u)＝F ^a(x(t))

Formula makes u '=u-f in (3) _iSina substitution (3), and make t '=t-τ _i, the abbreviation arrangement then has:

Make u "=u '-τ _iCosa, substitution formula (4) is further put in order:

With u "=u '-τ _iCosa, u '=u-f _iSina substitution formula (5) is also further put in order:

In the following formula:

Select one group of suitable f _i, τ _i, satisfy:

f _isina+τ _icosa＝u ₀ (8)

Make u ₀=0, then have:

f _isina+τ _icosa＝0 (9)

In formula (10),

d

Order: S _a(u)=δ (u-u _c)

Then:

Then formula (10) is:

Formula (13) (14) shows, N time domain waveform formula (8) energy height on fractional Fourier transform domain that satisfies condition concentrates on u _cPoint, only u _cThe place is non-0 value, and other is all 0.According to principle of conservation of energy, if N wave level all is lower than noise level, then, at last at fractional Fourier transform domain u _cThe place can form the level above decision threshold.Formula (15) is similar to the chirp signal, and the centre frequency of each waveform is u in the formula _cCsca+f _i

(3) secret signal of the hiding system of voice messaging is analyzed synchronously

In manipulative communications deception, according to the characteristic of some communication channels, exist characteristics such as multipath transmisstion and frequency dispersal as wireless channels such as short wave channels, if adopt FSK modulation and non-coherent demodulation mode, can utilize carrier signal to carry the secret information synchronizing signal.That is to say, when sending carrier signal, can send one group be lower than channel noise level, signal that (8) condition that satisfies formula, amplitude are subjected to pseudo noise code control, receiving terminal can be on fractional Fourier transform domain u _cThe place is judged.

Below in conjunction with drawings and Examples, technical solutions according to the invention are further elaborated.

In order to analyze a kind of superior function of hiding the secret signal synchronized method of system based on the voice messaging of fractional Fourier transform domain set forth above, at first we have provided the carrier wave voice manipulative communications deception model on the fractional Fourier transform domain, experimentize then and provide experimental data.

1. the carrier wave voice manipulative communications deception model on the fractional Fourier transform domain

For the purpose of the simple analysis, make N=2, λ _i=λ ₀Be constant, make formula (14) at u _cPoint reaches maximum, can make that its exponential term is 0, then has:

f ₂＝2u _cseca-f ₁ (16)

By formula (8) (16) as can be known, if f ₁Determine, then f ₂, τ ₁, τ ₂, all can determine.f ₁Can control by one group of frequency hopping code sequence:

f ₁＝k(n)Δf (17)

In the following formula, Δ f is a frequency interval, and k (n) is the frequency hop sequences on GF (p) territory.Then formula (11) can be:

In chaos sign indicating number sequence, the Chebyshev chaos sequence is better than modified model Logistic chaos sequence in performance aspect correlation properties, distance of swimming characteristic, the balance quality.This paper adopts the Chebyshev chaos sequence to control k (n).

Exponent number is that the Chebyshev chaotic maps of w is as follows:

x _n+1＝cos(warccosx _n) (19)

To x _nCarry out the m bit quantization, then have:

k(n)＝[2 ^mx _n] (20)

[y] is bracket function in the following formula, is expressed as the maximum integer less than y.The k (n) that obtains according to formula (20) is GF (p=2 ^m) frequency hop sequences on the territory.

In order to check the secret information synchronization scenario, introduce following carrier wave voice manipulative communications deception system.In carrier wave voice manipulative communications deception system, the voice messaging bit rate is 64kbit/s, adopts the 2FSK mode to modulate and non-coherent demodulation.The secret information embedded mode adopts low bit mode, and the secret information transmission rate is 32bit/s.

Among Fig. 1, voice signal adopts the 8kHz sampling, 8bit quantizes, per 256 is 1 frame, and the interframe zero lap carries out secret information LSB to speech frame and embeds, be that per 1 frame embeds 1 bit, at speech frame, embedded mode can embed by full frame together, and also can adopt length is whether the binary system random sequence of N=256 is controlled and embedded at current point.The binary system random sequence can be by sample back and carry out normalized and obtain of noise to external world.

When agwn (n)=1, the voice sample point is carried out LSB embed.

If f _C0, f _C1Be the carrier frequency of 2FSK modulating system, then formula (15) the formula centre frequency that provides waveform must fall within the receiver pass-band scope, does not consider the base band speech bandwidth, can make for the purpose of the simple analysis:

f _c0＜f _i+u _ccsca＜f _c1 (22)

In the following formula, f _i(i=1,2) are provided respectively by formula (16) (17).Formula (16) (17) substitution formula (22) can be got:

f _c0cosa＜u _c＜f _c1cosa (23)

Corresponding receiving element as shown in Figure 3.

Carrier wave voice manipulative communications deception system adopts incoherent reception, comes gating two-way band stop filter by output symbol after the 2FSK demodulation as command character among Fig. 3, its objective is the f that removes in the received signal _C0, f _C1Composition makes it include the secret information synchronized component.Make its concentration of energy in u by fractional fourier transform ₀Point is to adjudicate.If u ₀Point value then carries out secret information and receives greater than decision threshold.

2. experiment and analysis

In all experiments of the present invention, the signal of voice signal in the laboratory, recording, sample frequency is 8KHz, sampling resolution 8bit.At stack white Gaussian noise and nonstationary noise (noise source is provided by the Dutch RSRE research center under the Britain TNO perception association) on the clean speech signal.

(a) Chebyshev mapping curve among Fig. 4; (b) Chebyshev mapping time-frequency characteristic; (c) the multi-system Chebyshev sequence after 8bit quantizes; (d) Chebyshev sequence dependent features has provided time domain specification, spectral characteristic and the correlation properties of Chebyshev sequence, and as can be seen from Figure, the Chebyshev sequence is evenly distributed on time-frequency domain, has good correlation properties.

Fig. 5, (a) information sequence among Fig. 6; (b) information sequence after the demodulation; (c) modulation waveform; (d) demodulator input waveform; (e) modulated signal frequency spectrum; (f) demodulator input signal spectrum, the waveform that (a) formula (13) provides among Fig. 7; (b) signal spectrum that provides of formula (13); (c) concealed synchronizing signal; (d) concealed synchronizing signal frequency spectrum; (e) modulated signal frequency spectrum; (f) modulated signal frequency spectrum, (a) demodulator input signal among Fig. 8; (b) demodulator input signal spectrum; (c) by the output signal behind two band resistance devices; (d), provided the 2FSK system modulation demodulation simulation waveform of the employing secret information synchronization scenario under systemview, f by the output signal spectrum behind two band resistance devices _C0=1000Hz, f _C1=2000Hz.Concealed synchronizing signal frequency spectrum is between 1000～2000Hz.Can find out that from Fig. 7,8 under noise circumstance, concealed synchronizing signal is neither on time domain and the frequency domain to be found easily.Concealed synchronizing signal is 1: 1 with the ratio of noise level among Fig. 7,8.

Fig. 9,10,11,12 have provided concealed synchronizing signal amplitude spectrum change curve on fractional Fourier transform domain under stationary noise white Gaussian noise, nonstationary noise pink noise, volvo automobile noise, factory workshop noise circumstance, concealed synchronizing signal is-10dB a=1.082 with the ratio of noise power.Therefrom can find out concealed synchronizing signal u ₀=1400 places have sharp-pointed peak value.White noise distributes more even on score field, and pink noise, workshop noise, volvo automobile noise energy mainly concentrate on low-frequency range, more ironically, the volvo automobile noise also is the concentration of energy characteristic on score field, but mainly concentrates on low-frequency range.

Claims (1)

1. secret signal synchronized method based on fractional Fourier transform domain is characterized in that may further comprise the steps:

(1) fractional Fourier transform domain

The a rank fractional fourier transform algorithm of input voice sequence s (t) is as follows:

S _a(u)＝F ^a(s(t))

$=\left\{\begin{array}{cc}\sqrt{\frac{1-j\cot a}{2\mathrm{\π}}}\underset{-\∞}{\overset{+\∞}{\∫}}\exp (j\frac{u^2+t^2}{2}\cot a-\frac{\mathrm{jut}}{\sin a})s\left(t\right)\mathrm{dt}& a\≠\mathrm{n\π}\\ s\left(t\right)& a=2\mathrm{n\π}\\ s(-t)& a=(2n\±1)\mathrm{\π}\end{array}\right.---\left(1\right)$

In the formula, 0＜| p|＜2, n is an integer, j is an imaginary unit;

(2) based on the overlapping formula of the spectrum on the fractional fourier transform

$X\left(u\right)=\mathrm{\λ}\left(u_c\right)\mathrm{\δ}(u-u_c)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\λ}}_i\exp \left[\mathrm{j\π}(2f_i{u}_c\sec a-f_i^2\tan a)\right]\mathrm{\δ}(u-u_c)---\left(2\right)$

$x\left(t\right)=\frac{\exp (-j\frac{1}{2}a)}{\sqrt{-j\sin a}}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\λ}}_i\exp \left[\mathrm{j\π}(2(f_i+u_c\csc a)t-t^2\mathrm{ctga}-u_c^2\mathrm{ctga})\right]---\left(3\right)$

The centre frequency of each waveform is u in the formula _cCsca+f _i, u _c, λ _i, f _i, (i=1 .. N) are constant, and X (u) and x (t) are respectively the frequency domain and the time domain form of output signal;

(3) secret signal of the hiding system of voice messaging is analyzed synchronously

When sending carrier signal, send one group and be lower than channel noise level, satisfy formula f _iSina+ τ _iCosa=u ₀Condition, amplitude are subjected to the signal of pseudo noise code control, and receiving terminal is u on fractional Fourier transform domain _cThe place is judged.

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