CN102769444B - Digital filter group for demodulating multiple paths of asymmetric binary phase shift keying (ABPSK) signals - Google Patents

Abstract

The invention discloses a digital filter group for demodulating a plurality of paths of asymmetric binary phase shift keying (ABPSK) signals and belongs to the field of information modulation and demodulation in digital communication. The digital filter group consists of at least two branch filters, wherein each branch filter is formed by cascaded connection of an impact filter and at least one notching filter; the impact filter consists of a pair of conjugate zero points and at least two pairs of conjugate pole points; the radius of each pole point of the impact filter is determined according to a zero point and pole point placement method; influence of the notching filter on the amplitude-frequency response of the impact filter serves as a cost function; the least square problem of the cost function is converted into the quadratic programming problem by using linear constraint; and parameters of the notching filter are determined. The digital filter group can effectively separate a plurality of paths of ABPSK modulation signals, can transmit a plurality of paths of signals in a narrow band in parallel, and is flexible in use.

Description

For the digital filter bank of demodulation multi-channel A bpsk signal

Technical field

The present invention relates to a kind of numeral for demodulation multi-channel A bpsk signal and impact bank of filters, belong to the modulates information in digital communication technology and demodulation field.

Background technology

Frequency spectrum is non-renewable resource, which carry growing various wireless traffics, is all valuable to countries in the world, has some idea of from the auction valency of the huge frequency Limited Access in Europe.How more efficiently to use limited frequency spectrum resource also most important for the sustainable development of China's modernization construction.

The numeric code rate (taking bps/Hz as dimension) that can transmit in the availability of frequency spectrum available units frequency band of digital communication system is examined, depend primarily on binary data code stream be modulated into send frequency range analog carrier time shared frequency bandwidth.The simplest Ditital modulation method, it is certain parameter utilizing binary message code element " 0 " or " 1 " directly to change (being usually referred to as " skew keying ") sinusoidal carrier, as amplitude, frequency, phase place etc., correspondingly obtain the amplitude shift keying (2-ASK) of binary (binary system), frequency shift keying (2-FSK) and phase shift keying (2-PSK) modulation signal.The antijamming capability of these binary shifted keying modulations is strong, but the availability of frequency spectrum is very low, and wherein the good 2-PSK of combination property also only has 1bps/Hz at most.

The keying period τ of traditional binary phase shift keying (BPSK) modulation system is exactly its code-element period T; this lacks necessary protection interval to tackle multipath channel and intersymbol interference; still expanded to the situation of 0< τ <T; thus obtain unified asymmetric binary phase shift keying (ABPSK:Asymmetric Binary Phase Shift Keying) modulation (see patent of invention " unified orthogonal binary shifted key modulation and demodulation method ", the patent No.: ZL200710025203.6).The availability of frequency spectrum can be improved by the number of constellation points (such as from 2-PSK and BPSK → 4-PSK and QPSK → 8-PSK →...) increasing modulation space, but transmitting power required under equal receptivity also wants corresponding increase, particularly for severe short wave channel, more the digital modulation mode effect of high-order is unsatisfactory.

Summary of the invention

The present invention is directed to the deficiency that prior art exists, and propose a kind of numeral impact bank of filters that effectively can be separated multi-channel A BPSK modulation signal, to improve transmission code rate and the availability of frequency spectrum.

This digital filter bank is made up of at least two branch filters, each branch filter is all formed by shock filter and at least one notch filter cascade, the mixed signal being input as multi-channel A BPSK modulation of this bank of filters, exports the separation signal into each branch road.

Described shock filter is by forming at a pair conjugation zero point and at least two pairs of conjugate poles, all pole frequencies are all higher than zero frequency, and signal carrier frequency is between zero frequency and all pole frequencies, the close degree of zero frequency and pole frequency is at least 10 of signal carrier frequency ^-3magnitude.

The trap frequency limit phase angle of described notch filter is the pole radius of the shock filter according to place branch road, utilizes linear restriction to convert the least square problem of cost function to quadratic programming problem and obtains.

Technique effect:

The present invention can effectively be separated ABPSK modulation signal, and the impact demodulation of each road signal can be realized when effectively suppressing the interference of other branch road carrier frequency, realize the multiple signals parallel transmission in arrowband, further increase transmission code rate and the availability of frequency spectrum, and there is wider code check accommodation, use flexibly.

Accompanying drawing explanation

Fig. 1 is the transmission system block diagram of multi-channel A BPSK modulation signal.

Fig. 2 is the concrete enforcement block diagram of multi-channel A BPSK modulation signal each branch receivers in 400MHz frequency range.

Fig. 3 is the oscillogram of anti-phase modulation signal impact filtering response, and in this figure, sample rate is 10 times of signal frequency.

Fig. 4 is the zero pole point relative position schematic diagram of a pair conjugated zero limit shock filter.

Fig. 5 is the zero pole point vector geometrical relationship figure of a pair conjugated zero limit shock filter of partial enlargement.

The amplitude-frequency response figure of the shock filter of Fig. 6 Wei Dai tri-road trap.

Fig. 7 is that the 1/2CP-EBPSK modulation signal of two-way mixing is through bank of filters Hou mono-road of the present invention output time-domain oscillogram.

Fig. 8 is 1/2CP-EBPSK modulation signal another road output time-domain oscillogram after bank of filters of the present invention of two-way mixing.

Fig. 9 is the demodulation performance curve chart of 1/2CP-EBPSK modulation signal after bank of filters of the present invention of two-way mixing.

Embodiment

At the asymmetric binary phase shift keying of ABPSK() modulation in, the waveform g that code element " 0 " and " 1 " are modulated ₀(t) and g ₁t the uniform expression of () is:

g ₀(t)=Asin(2πf _ct),0≤t≤T

$g_1\left(t\right)=\left\{\begin{array}{cc}B\sin (2\mathrm{\&pi;}{f}_{c}t\&PlusMinus;\mathrm{\&sigma;}),& 0\&le;t<\mathrm{\&tau;}\\ A\sin \left(2\mathrm{\&pi;}{f}_{c}t\right),& \mathrm{\&tau;}\&le;t<T\end{array}\right.---\left(1\right)$

In formula: A and B is signal amplitude, f _cfor carrier frequency, T is code-element period, and τ is the keying period, and t is time variable; When modulation waveform is hard saltus step, σ ∈ [0, π]; When modulation waveform consecutive hours, σ=± ξ △ sin (η * 2 π f _ct), 0≤△≤1,0≤η≤1, and ξ ∈ { value of-1,1} and the polarity of phase-modulation can control by a pseudo random sequence.

The modulation system of each branch road in multi-channel A bpsk signal can be identical with signal type, also can be different, only need select different modulation parameters according to formula (1), sample rate also can be different, therefore can adapt to different channels and realize cost, key is then the design of receiving terminal bank of filters.

Digital filter bank of the present invention is made up of at least two branch filters, each branch filter is all formed by shock filter and at least one notch filter cascade, the mixed signal being input as multi-channel A BPSK modulation of this bank of filters, exports the separation signal into each branch road.

Described shock filter is by forming at a pair conjugation zero point and at least two pairs of conjugate poles, all pole frequencies are all higher than zero frequency, and signal carrier frequency is between zero frequency and all pole frequencies, and the close degree of zero frequency and pole frequency at least will reach 10 of signal carrier frequency ^-3magnitude, thus in being modulated by ABPSK, the small different wave shape of " 0 ", " 1 " symbol signal gives prominence to the obvious amplitude impact into " 1 " code element information modulation place produces.

The trap frequency limit phase angle of the notch filter of described cascade requires former shock filter impact minimum, its optimal design is the pole radius of the shock filter according to this branch road, utilizes linear restriction that the least square problem of cost function is changed into quadratic programming problem and obtains.

Different from the design of conventional multicarrier ripple transmission system; the each branch road intercarrier of multi-channel A BPSK modulation signal is without the need to protecting interval or orthogonality condition; each branch road arranges the digital shock filter (namely above-mentioned branch filter) of different band traps; because the centre frequency of shock filter is different, thus utilize its extremely narrow service area can carry out the separation of each tributary signal.In order to eliminate monkey chatter, trap frequency is set to the carrier frequency of all the other each tributary signals except this branch road, thus realizes the impact demodulation of this tributary signal while suppressing the interference of bypass carrier frequency.

The asymmetric modulating characteristic of ABPSK modulation signal makes the demodulation performance of shock filter closely related with sampling multiple, the change that filter coefficient could give prominence to signal is rationally set, for this reason, the coefficient of shock filter group selects the sampling multiple one_to_one corresponding with each branch road carrier wave.The carrier wave f of each branch road _ci, sample frequency f _siand symbol width N _ibetween meet following relation:

F _si× N _i/ f _ci=f _sj× N _j/ f _cj, in formula: subscript i, j represent different branch numbers.

The digital shock filter of described band trap i.e. single channel ABPSK digital demodulator as shown in Figure 2, by each branch road, the corresponding corresponding ABPSK modulation signal of different parameters is set, ABPSK digital demodulator group is sent into after mixing, respective frequencies signal is separated by the filter matched from mixed signal, and be converted to the similar amplitude-modulated signal having obvious amplitude scintillation corresponding to code element " 1 " shown in Fig. 3, each branch road detects (can get amplitude judgement simply) respective demodulated output signal, the conventional treatment such as bit synchronization, thus realize separation and the demodulation of multi-channel A BPSK modulation signal very simply.

For realizing the present invention better, again part implementation detail is described further below.

I, according to the pole radius of the shock filter of this branch road of bandwidth calculation of each branch road shock filter.

For simplicity, with a pair conjugated zero limit shock filter for analytic target.Its transfer function is:

$H\left(z\right)=K\frac{(1-r_z{e}^{j{\mathrm{\&omega;}}_c}{z}^{-1})(1-r_z{e}^{-j{\mathrm{\&omega;}}_c}{z}^{-1})}{(1-r_p{e}^{j{\mathrm{\&omega;}}_c}{z}^{-1})(1-r_p{e}^{j{\mathrm{\&omega;}}_c}{z}^{-1})}---\left(2\right)$

For shock filter, be positioned at zero point on unit circle, therefore datum radius r _z=1, DC current gain K generally gets 1.If the given centre frequency of filter, so the response of filter just only with pole radius r _prelevant.Z-plane marks the zeros and poles that number punch hits filter, and zero pole point vector is at unit circle e ^{j ω}upper movement.Identify zero pole point in order to easy analysis and signal know in the diagram distant, in fact zeros and poles is at a distance of extremely closely (being at least 10 of this branch road carrier frequency ^-3magnitude), and limit is near unit circle.Z in the diagram ₁, z ₂for zero point, be positioned on unit circle; p ₁, p ₂for limit, very near unit circle, its vector is at unit circle e ^{j ω}upper movement; A ₁, ψ ₁for z at zero point ₁corresponding mould and phase angle; A ₂, ψ ₂for z at zero point ₂corresponding mould and phase angle; B ₁, θ ₁for limit p ₁corresponding mould and phase angle; B ₂, θ ₂for limit p ₂corresponding mould and phase angle; ω ₁and ω ₂be respectively zero frequency and the pole frequency of shock filter.The frequency characteristic of digital filter has periodically, cycle ω _s=2 π, therefore only need study 0< ω < ω _s/ 2 one sections, i.e. 0 ~ π.

$\left|H\left(e^{\mathrm{j\&omega;}}\right)\right|=K\frac{A_1\&CenterDot;A_2}{B_1\&CenterDot;B_2}---\left(3\right)$

Due to zero pole point near and close to unit circle, so zero pole point vector is at 0< ω < ω ₁and ω ₂< ω < ω _swhen/2 intervals are mobile, the modulus value approximately equal of zero point and limit, namely | H (e ^{j ω}) |=K, again because limit is near unit circle and near zero point, so can think and work as ω ₁< ω < ω ₂time, with A ₁, B ₁compare, complex conjugate zero pole point is to unit circle e ^{j ω}distance approximately equal, i.e. A ₂≈ B ₂, then:

$\left|H\left(e^{\mathrm{j\&omega;}}\right)\right|=K\frac{A_1}{B_1}---\left(4\right)$

Figure 5 shows that and amplify ω ₁< ω < ω ₂zero pole point behind interval and e ^{j ω}vector geometrical relationship.Here have ignored the impact of complex conjugate zero pole point on frequency response.By the definition of 3dB filter bandwidht, have:

$\left|H\left(e^{j({\mathrm{\&omega;}}_c-B_w/2)}\right)\right|=\frac{1}{\sqrt{2}}\&CenterDot;\left|H\left(e^{j{\mathrm{\&omega;}}_c}\right)\right|---\left(5\right)$

Obtain:

$\frac{\sin [({\mathrm{\&omega;}}_2-{\mathrm{\&omega;}}_1)/2]}{\sin [({\mathrm{\&omega;}}_2-B_w/2-{\mathrm{\&omega;}}_1)/2]}\&CenterDot;\frac{\sqrt{{r_p}^2-2r_p\cos (B_w/2)+1}}{1-r_p}=\sqrt{2}---\left(6\right)$

In formula: r _pfor pole radius; B _wfor the bandwidth of shock filter.

For the shock filter determining zero pole point phase angle, ω ₂-ω ₁=φ is constant.So meeting bandwidth B _wwhen, Ke Yiji also be a constant, then formula (6) can arrange and obtain:

$r_p=\frac{M-\cos (B_w/2)\&PlusMinus;\sqrt{{\cos }^2(B_w/2)-2M\cos (B_w/2)+2M-1}}{M-1}---\left(7\right)$

Because φ and B _wvalue very little, in order to avoid there is r _pthe situation of >1, cast out the situation of addition, obtain:

$r_p=\frac{M-\cos (B_w/2)-\sqrt{{\cos }^2(B_w/2)-2M\cos (B_w/2)+2M-1}}{M-1}---\left(8\right)$

The present invention is the design based on a pair conjugated zero limit shock filter, ensure that amplitude-frequency and the phase-frequency response curve shape of branch road shock filter.As well known to those skilled in the art, if zero pole point leaves j ω axle far (namely their real part is much larger than imaginary part), so these zeros and poles are very little for the shape impact of amplitude-frequency response and phase-frequency response curve, and their effect just makes the relative size of total amplitude and phase place increase and decrease to some extent.Based on this, the basis that above-mentioned pole radius designs is added multipair limit to strengthen amplitude-frequency and phase-frequency response, tighten bandwidth further and obtain higher saltus step wave forms impact amplitude.

II, the optimum choice of trap frequency limit phase angle.

Usual design notch filter is at wanted blanketing frequency ω _nkcorresponding unit circle places zero point, limit is placed in footpath, pole at zero point, the asymmetric of the uneven of filter freguency response and gain can be caused like this, multistage trap is set simultaneously and then easily causes system unstable.Provide the Principles and measurements rationally placing trap frequency place limit in the present invention below.

The general expression with the notch filter transfer function of l trap frequency is:

$H_1\left(z\right)=\frac{B\left(z\right)}{A\left(z\right)}=\frac{\underset{k=1}{\overset{l}{\mathrm{\&Pi;}}}(1-2\cos \left({\mathrm{\&omega;}}_{\mathrm{Nk}}\right)z^{-1}+z^{-2})}{\underset{i=1}{\overset{l}{\mathrm{\&Pi;}}}(1-2r_i\cos \left({\mathrm{\&omega;}}_{\mathrm{pi}}\right)z^{-1}+{{r_i}^{2}z}^{-2})}---\left(9\right)$

In formula: r _ifor trap frequency place pole radius, namely limit is

In specific design, in order to ensure the stability of filter, be placed on zero point on unit circle, zero point, phase angle was trap frequency ω _nk, and provide r in advance _ivalue (0≤r _i<1), the determination of so corresponding pole location is only relevant with limit phase angle.Make notch filter coefficient a _i=2cos (ω _pi), then the limit phase angle ω that trap frequency place is corresponding _pi=arccos (a _i/ 2) ,-2≤a _i≤ 2, ω _nk-ε≤ω _pi≤ ω _nk+ ε, transfer function is deformed into:

$H_1\left(z\right)=\frac{\underset{k=1}{\overset{l}{\mathrm{\&Pi;}}}(1-b_k{z}^{-1}+z^{-2})}{\underset{i=1}{\overset{l}{\mathrm{\&Pi;}}}(1-r_i{a}_i{z}^{-1}+{r_i}^2{z}^{-2})}---\left(10\right)$

In formula: b _k=2cos (ω _nk), k=1 ... l, when trap frequency is determined, b _kfor definite value.

For simplicity, discuss for single notch filter here.Fixed trap zero frequency is ω _n1, pole radius is r ₁, then formula (10) is deformed into:

$H_1\left(z\right)=\frac{B\left(z\right)}{A\left(z\right)}=\frac{1-b_1\&CenterDot;z^{-1}+z^{-2}}{1-2r_1\cos \left({\mathrm{\&omega;}}_{p1}\right)z^{-1}+{r_1}^2{z}^{-2}}---\left(11\right)$

Make notch filter resonance frequency be greater than shock filter centre frequency, add in order to what ensure notch filter the amplitude-frequency response not affecting shock filter, therefore cost function is:

C(a)=∫ _RW(ω)|K-H ₁(e ^jω)| ²dω （12）

In formula: W (ω) is weighting function; K is the DC current gain of shock filter; H ₁(e ^{j ω}) be the transfer function of notch filter; Integrating range R=[ω ₂, ω _n1-ε] U [ω _n1+ ε, π], ω ₂for the pole frequency of shock filter, ε is trap zeros frequencies omega _n1an epsilon neighborhood, appoint and get minimum arithmetic number, and ω _n1>=ω ₂+ B _w/ 2.For the trap zeros frequencies omega determined _n1with corresponding pole radius r ₁, the design of notch filter is reduced to the limit phase angle ω that searching makes cost function C (a) value minimum _p1, formula (11) is substituted into (12), obtains:

$C\left(a_k\right)={\&Integral;}_R\frac{W\left(\mathrm{\&omega;}\right)}{{\left|A_t\left(e^{\mathrm{j\&omega;}}\right)\right|}^2}{\left|\right[(K{r_1}^2-1)e^{-2\mathrm{j\&omega;}}+2\cos \left({\mathrm{\&omega;}}_{N1}\right)e^{-\mathrm{j\&omega;}}]-{\mathrm{Kr}}_1{a}_{1t}{e}^{-\mathrm{j\&omega;}}+K-1|}^2\mathrm{d\&omega;}---\left(13\right)$

In formula: W (ω)/| A _t(e ^{j ω}) | ²overall as new weighting function, t is iterations here.

Make p (ω)=(Kr ₁ ²-1) e ^{-2j ω}+ b ₁e ^{-j ω}, q (ω)=-Kr ₁e ^{-j ω}, K-1=c, m=c ²+ 2cp (ω), then formula (13) is deformed into:

$C\left(a_{1t}\right)={\&Integral;}_R\frac{W\left(\mathrm{\&omega;}\right)}{{\left|A_t\left(e^{\mathrm{j\&omega;}}\right)\right|}^2}[{a_{1t}}^2{\left|q\left(\mathrm{\&omega;}\right)\right|}^2+2a_{1t}(\mathrm{Re}\left(p\left(\mathrm{\&omega;}\right)q^{*}\left(\mathrm{\&omega;}\right)\right)+\mathrm{cq}\left(\mathrm{\&omega;}\right))+{\left|p\left(\mathrm{\&omega;}\right)\right|}^2+m]\mathrm{d\&omega;}---\left(14\right)$

In order to ensure the stability of filter, A _t(e ^{j ω}) zero point all must be positioned at unit circle, therefore A _t(e ^{j ω}) parameter be subject to a series of linear restriction.| A _t(e ^{j ω}) | value can obtain according to the frequency computation part in iterative process, according to iteration situation upgrade weighting function W (ω)/| A _t(e ^{j ω}) | value.

Order:

${\mathrm{\&alpha;}}_t={\&Integral;}_R\frac{W\left(\mathrm{\&omega;}\right)}{{\left|A_t\left(e^{\mathrm{j\&omega;}}\right)\right|}^2}{\left|q\left(\mathrm{\&omega;}\right)\right|}^2\mathrm{d\&omega;}$

${\mathrm{\&beta;}}_t={\&Integral;}_R\frac{W\left(\mathrm{\&omega;}\right)}{{\left|A_t\left(e^{\mathrm{j\&omega;}}\right)\right|}^2}\mathrm{Re}(p\left(\mathrm{\&omega;}\right)q^{*}\left(\mathrm{\&omega;}\right)+\mathrm{cq}\left(\mathrm{\&omega;}\right))\mathrm{d\&omega;}$

${\mathrm{\&chi;}}_t={\&Integral;}_R\frac{W\left(\mathrm{\&omega;}\right)}{{\left|A_t\left(e^{\mathrm{j\&omega;}}\right)\right|}^2}({\left|p\left(\mathrm{\&omega;}\right)\right|}^2+m)\mathrm{d\&omega;}$

The problems referred to above become the least square problem of linear constraint, i.e. parameter a _1tquadratic programming problem.

min α _ta _1t ²+2β _ta _1t+χ _t

0≤r ₁<1

（15）

s.t. -2≤a _1t≤2

ω _N1-ε≤ω _p1≤ω _N1+ε

Can find out, target function is the parabola of opening upwards, there is closed optimal solution.Based on above analysis, obtain notch filter coefficient a ₁=2cos (ω _p1) Novel Algorithm as follows:

1, pole radius r is provided ₁, trap zeros frequencies omega _n1, shock filter gain K, cost function integral domain parameter ε and weighting function W (ω);

2, a is provided _1tinitial value, general a ₁₁=2cos (ω _n1), t=1;

3, the value of each coefficient of calculation cost function, i.e. α _t, β _t, χ _t;

4, according to formula (15), Novel Algorithm is adopted to obtain new a _1t;

5, as | a _{1 (t+1)}-a _1t| finishing iteration (design accuracy requires ξ >0, and a desirable minimum arithmetic number, as 0.0001) during≤ξ, otherwise t=t+1, return the 3rd step.

In sum, the invention provides a kind of design of filter for demodulation ABPSK modulation signal.Analyze the amplitude-frequency response of a pair conjugated zero limit shock filter by zero pole point placement methods intuitively, obtain the computing formula of shock filter pole radius; Using cascade notch filter on the impact of shock filter amplitude-frequency response as cost function, introduce linear restriction the least square problem of cost function is changed into quadratic programming problem, finally obtained the best value of trap frequency limit phase angle.

Below for the multiplexing of the MCP-EBPSK modulation signal of M=1/2, the invention will be further described by reference to the accompanying drawings:

Shock filter according to method for designing design of the present invention band trap as shown in Figure 6:

1, by the optimum configurations of 1/2CP-EBPSK modulation signal be: f _c1=10MHz, f _c2=10.04MHz, f _s1=160MHz, f _s2=100.4MHz, A=1; B=1; △=0.1; η=0.5; K=2; N ₁=100; N ₂=160;

2, according to the multi-channel A BPSK modulation signal transmission system block diagram shown in Fig. 1, its receiver mainly comprises the shock filter group of analog to digital converter (ADC), band multichannel trap, and the envelope detector of each branch road and integration decision device:

1) ADC gives the shock filter group of band multichannel trap after the multi-channel A BPSK modulation signal received is converted to digital signal;

2) gone out the impact filtering signal of each branch road by the shock filter group selection of band multichannel trap, and parallel output gives respective branch road envelope detector respectively;

3) envelope detector low-pass filtering again after the branch road impact filtering signal that bank of filters exports is taken absolute value;

4) threshold judgement again after integration decision device Ze Duizhe road envelope detection output signal sample integration (adding up) of each branch road, thus realize demodulation;

5) utilize parallel-serial conversion to be merged by multichannel court verdict to export, namely obtain final information sequence demodulation result.

3, get 3,000,000 code elements to test.Be respectively two-way time domain waveform and the error rate of system performance of demodulation output shown in Fig. 7,8,9, can find out that designed bank of filters can realize detection and the demodulation of two-way 1/2CP-EBPSK modulation signal.

Claims (3)

1. the digital filter bank for demodulation multi-channel A bpsk signal, it is characterized in that: this bank of filters is made up of at least two branch filters, each branch filter is all formed by shock filter and at least one notch filter cascade, the mixed signal being input as multi-channel A BPSK modulation of this bank of filters, exports the separation signal into each branch road;

The trap frequency limit phase angle of described notch filter is the pole radius of the shock filter according to place branch road, utilizes linear restriction to convert the least square problem of cost function to quadratic programming problem and obtains;

Described cost function uses following formula to determine:

C(a)＝∫ _RW(ω)|K-H ₁(e ^jω)| ²dω

In formula: W (ω) is weighting function; K is the DC current gain of shock filter; H ₁(e ^{j ω}) be the transfer function of notch filter; Integrating range R=[ω ₂, ω _n1-ε] ∪ [ω _n1+ ε, π], ω ₂for the pole frequency of shock filter, ω _n1for trap zeros frequency, ε is ω _n1an epsilon neighborhood.

2. the digital filter bank for demodulation multi-channel A bpsk signal according to claim 1, it is characterized in that: described shock filter is by forming at a pair conjugation zero point and at least two pairs of conjugate poles, all pole frequencies are all higher than zero frequency, and signal carrier frequency is between zero frequency and all pole frequencies, the close degree of zero frequency and pole frequency is at least 10 of signal carrier frequency ^-3magnitude.

3. the digital filter bank for demodulation multi-channel A bpsk signal according to claim 1, is characterized in that: described pole radius uses following formula to determine:

$r_p=\frac{M-\cos (B_w/2)-\sqrt{{\cos }^2(B_w/2)-2M\cos (B_w/2)+2M-1}}{M-1}$

In formula: ω ₁for the zero frequency of shock filter, ω ₂for the pole frequency of shock filter; r _pfor pole radius; B _wfor the bandwidth of shock filter.