CN106374878A - Digital notch filter filtering method enabling high-frequency distortion to be reduced - Google Patents

Abstract

The invention discloses a digital notch filter filtering method enabling high-frequency distortion to be reduced. The method comprises the following steps: determining target center frequency of a notch filter; according to the target center frequency of the notch filter, constructing a digital notch filter model; and according to the digital notch filter model, determining a relation between input and output of the notch filter on a missile-borne computer to construct a digital notch filter. The digital notch filter model for convenience of the missile-borne computer is directly generated according to the center frequency of the notch filter, thus preventing amplitude feature distortion caused by a phenomenon that the center frequency of the notch filter approaches calculated frequency of the missile-borne computer and also ensuring that the filter has a certain amplitude attenuation effect within the high frequency band.

Description

A kind of digital wave trap filtering method reducing high frequency distortion

Technical field

The present invention relates to wave trap technical field of filtering is and in particular to a kind of digital wave trap of reduction high frequency distortion is filtered Wave method.

The application of the present invention is that tactical weapon automatic pilot high-frequency noise suppresses, and it is characterized in that avoiding due to trap Filter centre frequency and missile-borne computer resolve frequency close to the amplitude characteristic distortion causing, and improve automatic pilot to high frequency The inhibition of noise.

Background technology

High-frequency noise suppression is an important content of tactical weapon Autopilot Design, can improve system stability, And provide good working environment for the affiliated subsystem of automatic pilot and unit it is ensured that system reliability service.

The source of automatic pilot high-frequency noise is mainly the vibration of aircraft natural resiliency, subsystem and unit own resonance Deng having the features such as amplitude is big, frequency is high.

Notch filter is generally adopted to suppress high-frequency noise in Autopilot Design.Conventional notch filter design stream Journey is to determine notch filter mid frequency according to target frequency, forms analog filter model；Adopt bilinear transformation again Analog filter model is converted to digital filter model, is easy to missile-borne computer and realizes.

The major defect of this method for designing is the process that analog filter model is converted to digital filter model In, because notch filter mid frequency resolves frequency relatively with missile-borne computer, lead to notch filter amplitude characteristic There is distortion in high band, affect filter effect.

Content of the invention

It is an object of the invention to provide a kind of digital wave trap filtering method reducing high frequency distortion, filtered according to trap Ripple device mid frequency directly generates the digital filter model being easy to missile-borne computer realization, it is to avoid due in notch filter Frequency of heart and missile-borne computer resolve frequency close to the amplitude characteristic distortion causing, and ensure that wave filter has one in high band simultaneously Tentering value attenuating.

In order to achieve the above object, the present invention is achieved through the following technical solutions: a kind of reduce high frequency distortion digital Wave trap filtering method, is characterized in, comprises the steps of

Determine the target center frequency of notch filter；

According to the target center frequency of notch filter, set up a digital notch filter model；

In missile-borne computer, according to digital notch filter model, determine the relation of notch filter input and output, Complete the foundation of digital wave trap.

Described digital notch filter model representation is:

$g_2\left(z^{-1}\right)=\frac{y\left(z^{-1}\right)}{u\left(z^{-1}\right)}=\frac{\[1+a_1\·z^{-1}+z^{-2}\]\·(1-\mathrm{\ρ})}{1+(1-\mathrm{\ρ})a_2\·z^{-1}+(1-2\mathrm{\ρ})\·z^{-2}}\×\frac{2+a_2}{2+a_1}$

a₁=-2cos (2 π f₁t)

a₂=-2cos (2 π f₂t)

In formula, y represents that notch filter exports, and u represents that notch filter inputs, and ρ represents notch filter parameter, f₁Table Show notch filter mid frequency, f₂Represent notch filter parameter, t represents system communication cycle, and z domain with the relation of frequency domain is Z=e^jωt, ω is the frequency of input signal, and j is imaginary number, g₂(z^-1) when ω → 0 gain be 1, ω → 2 π f₁Shi Zengyi is 0, ω During → π/t, gain is less than 1.

Described notch filter input and the relation of output are expressed as:

Y (k)=- a₁y(k-1)-a₂y(k-2)+b₀u(k)+b₁u(k-1)+b₂u(k-2)

In formula, y (k) represents the output of kt moment notch filter, and y (k-1) represents the output of (k-1) t notch filter, Y (k-2) represents the output of (k-2) t notch filter, and u (k) represents the input of kt moment notch filter, and u (k-1) represents (k-1) input of t notch filter, u (k-2) represents the input of (k-2) t notch filter, a₁, a₂, b₀, b₁, b₂Table Show notch filter parameter, a₁=(1- ρ) × a₂, a₂=1-2 ρ, a₁=-2cos (2 π f₁T), a₂=-2cos (2 π f₂T), t represents system communication cycle, and ρ represents trap Filter parameter, f₁Represent notch filter mid frequency, f₂Represent notch filter parameter.

A kind of digital wave trap filtering method reducing high frequency distortion of the present invention compared with prior art has following excellent Point: the present invention directly generates digital filter model according to notch filter mid frequency, simplifies according to filter center The analog filter model of Frequency Design, then the design cycle being converted to digital model by analog filter model；This Bright avoid resolving frequency close to the amplitude characteristic distortion causing due to filter centre frequency and missile-borne computer；Solve tradition to fall into Wave filter is in the problem on the weak side of the high band filter effect higher than mid frequency it is ensured that wave filter has a tentering in high band Value attenuating.

Brief description

Fig. 1 is a kind of flow chart of the digital wave trap filtering method reducing high frequency distortion of the present invention；

Before Fig. 2 is the digital notch filter being converted in prior art and conversion using bilinearity changing method Analog notch filter frequency Character Comparison curve；

Fig. 3 is in the embodiment of the present invention, and mid frequency is the digital notch filter frequency characteristic curve of 120hz.

Specific embodiment

Below in conjunction with accompanying drawing, by describing a preferably specific embodiment in detail, the present invention is further elaborated.

As shown in figure 1, a kind of digital wave trap filtering method reducing high frequency distortion, comprise the steps of

S1, determine the target center frequency of notch filter.

The mid frequency of notch filter directly affects the calculating of digital notch filter parameter, according to notch filter In the amplitude attenuation demand of high band, select the parameter of digital notch filter.

S2, the target center frequency according to notch filter, set up a digital notch filter model.

Digital notch filter model representation is:

$g_2\left(z^{-1}\right)=\frac{y\left(z^{-1}\right)}{u\left(z^{-1}\right)}=\frac{\[1+a_1\·z^{-1}+z^{-2}\]\·(1-\mathrm{\ρ})}{1+(1-\mathrm{\ρ})a_2\·z^{-1}+(1-2\mathrm{\ρ})\·z^{-2}}\×\frac{2+a_2}{2+a_1}$

a₁=-2cos (2 π f₁t)

a₂=-2cos (2 π f₂t)

In formula, y represents that notch filter exports, and u represents that notch filter inputs, and ρ represents notch filter parameter, f₁Table Show notch filter mid frequency, f₂Represent notch filter parameter, t represents system communication cycle, and z domain with the relation of frequency domain is Z=e^jωt, ω is the frequency of input signal, and j is imaginary number, g₂(z^-1) when ω → 0 gain be 1, ω → 2 π f₁Shi Zengyi is 0, ω During → π/t, gain is less than 1.

Notch filter is not decayed to low-band signal amplitude, to target frequency signal complete attenuation, high band is believed Number amplitude has certain decay, has preferable frequency characteristic in whole frequency range.

S3, in missile-borne computer, according to digital notch filter model, determine the pass of notch filter input and output System, completes the foundation of digital wave trap.

Notch filter input is expressed as with the relation of output:

Y (k)=- a₁y(k-1)-a₂y(k-2)+b₀u(k)+b₁u(k-1)+b₂u(k-2)

In formula, y (k) represents the output of kt moment notch filter, and y (k-1) represents the defeated of (k-1) t notch filter Go out, y (k-2) represents the output of (k-2) t notch filter, u (k) represents the input of kt moment notch filter, u (k-1) table Show the input of (k-1) t notch filter, u (k-2) represents the input of (k-2) t notch filter, a₁, a₂, b₀, b₁, b₂ Represent notch filter parameter, a₁=(1- ρ) × a₂, a₂=1-2 ρ, a₁=-2cos (2 π f₁T), a₂=-2cos (2 π f₂T), t represents system communication cycle, and ρ represents trap Filter parameter, f₁Represent notch filter mid frequency, f₂Represent notch filter parameter.

Concrete application: as shown in Figures 2 and 3, missile-borne computer resolves frequency and is 400hz, figure it is seen that existing There is the notch filter mid frequency being converted in technology to be changed into 96.2hz, be not inconsistent with target center frequency 120hz, trap is filtered There is distortion in high band in ripple device；From figure 3, it can be seen that the notch filter of the present invention is in the target at frequency of heart 120hz Amplitude attenuation is 140db, and the amplitude attenuation that frequency is more than with 120hz high-frequency signal is not less than 5.56db, illustrates that the present invention is effective Solve the problems, such as notch filter high frequency distortion, ensure that notch filter has certain amplitude attenuation effect in high band simultaneously.

The major parameter of decision notch filter performance is f₁、f₂And ρ.In notch filter design process, basis first Notch filter mid frequency determines f₁, as a example the notch filter as 120hz for the mid frequency shown in Fig. 3, f₁Take 120；f₂ Size determine notch filter in the filter effect of high band, typically take f₂<f₁, f₂Less notch filter is in high band Amplitude attenuation is bigger, Fig. 3 corresponding notch filter f₂Take 100；The size of ρ determines the width of notch filter, the bigger trap of ρ Wave filter is wider, and Fig. 3 corresponding notch filter ρ takes 0.27.

By adjusting f₁, f₂With the size of ρ, can have the digital notch filter model of ideal frequency characteristic, and root Tie up to according to the pass of notch filter input and output and realize on missile-borne computer.

Although present disclosure has been made to be discussed in detail by above preferred embodiment, but it should be appreciated that above-mentioned Description is not considered as limitation of the present invention.After those skilled in the art have read the above, for the present invention's Multiple modifications and substitutions all will be apparent from.Therefore, protection scope of the present invention should be limited to the appended claims.

Claims (3)

1. a kind of digital wave trap filtering method reducing high frequency distortion is it is characterised in that comprise the steps of

Determine the target center frequency of notch filter；

According to the target center frequency of notch filter, set up a digital notch filter model；

In missile-borne computer, according to digital notch filter model, determine notch filter input and the relation of output, complete The foundation of digital wave trap.

2. as claimed in claim 1 digital wave trap filtering method it is characterised in that described digital notch filter Model representation is:

$g_2\left(z^{-1}\right)=\frac{y\left(z^{-1}\right)}{u\left(z^{-1}\right)}=\frac{\&lsqb;1+a_1\&centerdot;z^{-1}+z^{-2}\&rsqb;\&centerdot;(1-\mathrm{\&rho;})}{1+(1-\mathrm{\&rho;})a_2\&centerdot;z^{-1}+(1-2\mathrm{\&rho;})\&centerdot;z^{-2}}\&times;\frac{2+a_2}{2+a_1}$

a₁=-2cos (2 π f₁t)

a₂=-2cos (2 π f₂t)

In formula, y represents that notch filter exports, and u represents that notch filter inputs, and ρ represents notch filter parameter, f₁Represent and fall into Wave filter mid frequency, f₂Represent notch filter parameter, t represents system communication cycle, z domain is z=e with the relation of frequency domain^{j ωt}, ω is the frequency of input signal, and j is imaginary number, g₂(z^-1) when ω → 0 gain be 1, ω → 2 π f₁Shi Zengyi is 0, ω → π/t Shi Zengyi is less than 1.

3. as claimed in claim 2 digital wave trap filtering method it is characterised in that the input of described notch filter with The relation of output is expressed as:

Y (k)=- a₁y(k-1)-a₂y(k-2)+b₀u(k)+b₁u(k-1)+b₂u(k-2)

In formula, y (k) represents the output of kt moment notch filter, and y (k-1) represents the output of (k-1) t notch filter, y (k-2) represent the output of (k-2) t notch filter, u (k) represents the input of kt moment notch filter, and u (k-1) represents (k-1) input of t notch filter, u (k-2) represents the input of (k-2) t notch filter, a₁, a₂, b₀, b₁, b₂Table Show notch filter parameter, a₁=(1- ρ) × a₂, a₂=1-2 ρ, a₁=-2cos (2 π f₁T), a₂=-2cos (2 π f₂T), t represents system communication cycle, and ρ represents trap Filter parameter, f₁Represent notch filter mid frequency, f₂Represent notch filter parameter.