CN107104741A - A kind of index coefficient of low time delay digital filter determines method - Google Patents
A kind of index coefficient of low time delay digital filter determines method Download PDFInfo
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Abstract
Method is determined the present invention relates to a kind of index coefficient of low time delay digital filter, including：Determine matched filter index coefficient desired value；Performance of filter is allocated, performance of filter index is specifically divided into amplitude response requirement, phase response requirement and delay requirement；And ideal filter frequency response function is worth to according to index coefficient target, with its corresponding amplitude response, phase response, group delay response (phase change rate) value, and it is used as the desired value of optimization；The frequency domain response for setting up digital filter distributes objective cost function rationally；According to cost function, by every discretization respectively in cost function, and application genetic algorithm and nonlinear optimization method solve the optimal solution of cost function, and its result is the wave filter of design.
Description
Technical field
The invention belongs to moving communicating field, especially for the wave filter used in private network Mobile communication direct base station it is low when
The index coefficient for prolonging digital filter determines method.
Background technology
With the growing of mobile communication digital technology and popularization, communication network optimization is equipment digitalized, intelligent
Inexorable trend as current network construction with optimization.Digital high-frequency amplification station is used as in current mobile communications network construction and optimization one
The scheme for planting high performance-price ratio increasingly obtains the attention of client, but because digital high-frequency amplification station uses digital filtering technique, introduces time delay
Greatly, the popularization in some regions is constrained.
Contemporary Digital repeater uses digital filtering technique, to ensure with outer resistance index, generally with sacrificial system time delay
To realize.A delay dispersion is introduced into mobile communication GSM standard networks, in mobile communications network the problem of multipath to ask
Topic, the repeater equipment area of coverage with base station information source cell category with sector due to covering, and the intrinsic time delay of its equipment will increase time delay color
Risk is dissipated, time delay is bigger, and its problem will be more prominent.According to GSM specifications, as shown in figure 1, delay inequality t=link L2 time delay (optical fiber
+ space time delay 1)-link L1 time delays≤4TA, i.e. delay inequality requirement≤4TA, 1 TA is 3.7us, i.e., delay inequality requirement≤
14.8us.Due to belonging to, same sector is overlapping to be covered the repeater area of coverage with base station, and its overlapping coverage areas user has both links, all the way
Directly launch time delay L1 from base station, be the chain-circuit time delay L2=optical-fiber time-delay I1+ repeaters sheet after being amplified by repeater all the way
Body time delay I+ area of coverage time delays I2.Required according to GSM delay dispersions, L delay inequalitys≤14.8us, i.e. L2-L1 delay inequalitys≤
14.8us, I1+I+I2-L1 delay inequality≤14.8us.
It will be seen from figure 1 that repeater equipment time delay is bigger, overlapping coverage areas distance is more limited, will be straight if dealing with improperly
Practice midwifery raw delay dispersion, reduce speech quality, increase cutting off rate.
The above shows that repeater equipment time delay does not allow more than 8us, while the requirement of communication repeater station equipment standard is set
Standby to have higher Out-of-band rejection ability, it was found from the realization of wave filter, the two requirements are mutually restricted, and degree of suppression is well then
Time delay is big, and the small delay for being then used to calculate of time delay is just small, and the time that wave filter is used to calculate is just short, suppresses nature just poor.
Conventional FIR filter design is Strict linear phase by filter configuration, that is, sets H (ejω)=FT [h (n)] is
The Frequency Response function of FIR filter.H(ejω) be represented by
H(ejω)=Hg(ω)ejθ(ω)
Hg(ω) is referred to as amplitude function, the real function for being ω.It should be noted that Hg(ω) and amplitude versus frequency characte function | H (ejω) | area
Not, | H (ejω) | it is ω positive real function, and Hg(ω) can use negative value.
θ (ω) is referred to as phase characteristic function, as θ (ω)=- ω τ, referred to as the first kind (A classes) linear phase characteristic；Work as θ
(ω)=θ0During-ω τ, referred to as Equations of The Second Kind (B classes) linear phase characteristic.
A classes：
B classes：
According to above feature, FIR filter design method is broadly divided into：
(1) window function metht
(2) Frequency Sampling Method
(3) Chebyshev approximation
I, the design procedure of window function metht and main points
If Hd(ejω)=FT [hd(n)] to wish the Frequency Response function that approaches, Hd(ejω)=FT [h (n)] is to use window letter
The frequency response function of the practical filter of number method design.Generally take H (ejω) corresponding preferable Frequency Response is used as Hd(ejω).Because
Finite Impulse Response filter typically requires to be designed to linear phase characteristic, so Hd(ejω) it must is fulfilled for above-mentioned linear phase FIR filter
The frequency domain feature of device.
Table 1
| Window function | Side lobe peak amplitude/dB | Transition band width | Minimum attenuation in stop band/dB |
| Rectangular window | -13 | 4π/N | -21 |
| Triangular window | -25 | 8π/N | -25 |
| Hanning window | -31 | 8π/N | -44 |
| Hamming code window | -41 | 8π/N | -53 |
| Blackman window | -57 | 12π/N | -74 |
| Kaiser window (α=7.865) | -57 | 10π/N | -80 |
Window function type is selected according to minimum attenuation in stop band in design process, window letter is selected further according to intermediate zone width index
Number length N values.
II, design procedure and main points with Frequency Sampling Method design Finite Impulse Response filter
1) concept and theoretical foundation of frequency sampling design method
It is exactly to seek a kind of wave filter unit impulse response h (n) for meeting design requirement or be to design Finite Impulse Response filter
Unite function H (z).
It is theoretical according to frequency sampling, if h (n) length is M, H (z)=ZT [h (n)], at equal intervals to H on unit circle
(z) sampling N points are obtained
As long as N >=M, then have
H (n)=IDFT [H (k)], n=0,1 ..., N-1
As can be seen here, only it is to be understood that N point equal interval sampling H (k) of the Finite Impulse Response filter frequency response function on [0,2 π],
Just can determine that the unit impulse response h (n) or system function H (z) of wave filter, here it is frequency sampling design method it is theoretical according to
According to.
Frequency Sampling Method is exactly theoretical according to above frequency domain sample, and the wave filter for wishing to approach is constructed by filtering characteristic index
Frequency response function Hd(ejω), it is obtained in [0,2 π] up-sampling
Then, unit impulse response h (n) is tried to achieve, or tries to achieve system function H (z).So, h (n) or H (z) are exactly FIR numbers
The design result of word wave filter.
III, the equiripple approximation design method of FIR filter
Equiripple approximation design method is theoretical using Chebyshev's best uniformity approximation, can design practical filter frequency response H
(ejω) and desired frequency response Hd(ejω) between worst error minimize best fit wave filter.The filter of this method design
The ripple Frequency Responses such as ripple device presentation, so referred to as equiripple approximation design method.Because error homogeneus distribution is in whole frequency band,
To fixed exponent number N, most excellent filtering characteristic can be obtained；Passband is most flat, and minimum attenuation in stop band reaches maximum.Therefore,
Equiripple approximation method is used widely in FIR filter design, particularly there is ready-made design program, so that design letter
It is single easy.So, on the basis of above-mentioned concept is set up, design program is correctly called, it is to obtain to set suitable parameter
Ripple approaches FIR filter coefficient h (n).
Conventional filter design method is due to being set as Strict linear phase, and wave filter is corresponding on Central Symmetry, because
This have impact on the configuration flexibility of wave filter, virtually add design complexities, passband fluctuation, transition band width, stopband attenuation,
The performances such as group delay are difficult to optimize simultaneously.Need to make improvements and perfect.
The content of the invention
The invention solves the problems that current technology problem, overcome deficiency of the prior art, the present invention using genetic algorithm and
Nonlinear Convex Programming theory is optimized to wave filter, reduces Time Delay of Systems.
A kind of index coefficient of low time delay digital filter determines method, it is characterised in that：Methods described includes following step
Suddenly：
Step 1：Determine matched filter index coefficient desired value；
Step 2：Performance of filter is allocated, performance of filter index is specifically divided into amplitude response requirement, phase
Position response is required and delay requirement；And ideal filter frequency response function is worth to according to the index coefficient target in step 1, with it
Corresponding amplitude response, phase response, group delay response (phase change rate) value, and it is used as the desired value of optimization；
Step 3：The frequency domain response for setting up digital filter distributes objective cost function rationally；
Step 4：According to the cost function of step 3, by every discretization, and apply genetic algorithm respectively in cost function
The optimal solution of cost function is solved with nonlinear optimization method, its result is the wave filter of design.
In the step 1, sample rate 3.84MHz, design wave filter meets for 45 ranks：120K passband passband fluctuation 0.1dB,
400KHz stopbands suppress to be more than or equal to 65dB, and group delay is less than or equal to 3us.
In the step 2, digital band [0,2 π) in quantified, obtain ideal filter frequency response function Hd(ejω),
With its corresponding amplitude response | Hd(ejω) |, phase response arg (Hd(ejω)), group delay response (phase change rate) τ (ejω)
Value, and it is used as the desired value of optimization.
In the step 3, the step includes 3.1) setting vector variable h=[h (0), h (1) ... h (N-1)]TRepresent real
Border can obtain the parameter of wave filter, and N represents the exponent number of target filter, and T represents vectorial transposition；Then the frequency domain response of wave filter is represented
For following formula：
Its corresponding amplitude response is | H (ejω) |,
Phase response is arg (H (ejω)),
Group delay response is
Step 3.2) ideal low-pass filter passband is set as [0, ω 1], stopband is [ω 2, π], sets cost function
Δ 0, Δ 1 and Δ 2 are scale factor, for adjusting passband, stopband and the degree of optimization of group delay；When finding h,
Make above-mentioned cost function minimum, so that the frequency domain response of design wave filter and the frequency domain response of ideal filter farthest connect
Closely；.
In step 4, the items in cost function discrete are respectively turned to：
In step 4, using genetic algorithm and combination Nonlinear Convex Programming theoretical optimization method solution cost function
Compared with prior art, the beneficial effects of the present invention are：
Under identical working environment, have that group delay is smaller relative to prior art, suppression performance is more preferable outside cake resistancet
Effect.The reason is that existing conventional art uses all kinds of design methods in background introduction, have to the filter parameter of design
Parameter is symmetrical, and the requirement of Strict linear phase, these requirements limit the optimality of parameter designing, have impact on passband fluctuation, resistance
Band is suppressed, intermediate zone width, the index such as flora of filters time delay, while design result is difficult the characteristic with minimum phase.Relatively
In the conventional method present invention not to parameters symmetry, linear phase characteristic is strict with, but with a series of cost functions
Compromised, relax limited degree during parameter optimization, while introducing the genetic algorithm for solving Non-Linear Programming, enter one
Step improves the effect of optimization, therefore is significantly better than in design result prior art design result.
Brief description of the drawings
Fig. 1 is that delay dispersion influence requires schematic diagram.
The system amplitude response of Fig. 2 FDAtool designs.
The group delay response of Fig. 3 FDAtool designs.
The filter amplitudes response that Fig. 4 present invention is designed.
The group delay response that Fig. 5 present invention is designed.
Fig. 6 applicating examples numerical portion is connected.
Fig. 7 applicating example system block diagrams.
Embodiment
Firstly the need of explanation, the present invention relates to computer technology moving communicating field application.The present invention's
In implementation process, the application of multiple software function modules can be related to.It is applicant's understanding that such as reading over application documents, standard
Really after the realization principle and goal of the invention of the understanding present invention, in the case where combining existing known technology, people in the art
Member can realize the present invention with the software programming technical ability of its grasp completely.Category this model that all the present patent application files are referred to
Farmland, applicant will not enumerate.
A kind of applicating example of the present invention is described in detail below in conjunction with accompanying drawing：
To solve its technical problem, the present invention is achieved through the following technical solutions its purpose：
(1) based on simulating superhet mixing structure, the docking collection of letters number carries out an analog down, obtains analog intermediate frequency letter
Number；It is f by sample frequencysamThe analog-digital converter (ADC) of clock control processing is digitized to analog if signal, obtain
To digital medium-frequency signal；Then Digital Down Convert and the down-sampled processing of numeral are carried out by digital DDC, obtains digital baseband GSM biographies
Defeated signal；
(2) digital baseband GSM transmission signals are delivered into Digital GSM wave filter, frequency-selective filtering processing is carried out, after output filtering
GSM baseband signals；
(3) GSM baseband signals after filtering are delivered into digital DUC and carries out up-conversion, through digital-to-analogue conversion, simulation up-conversion, put
Greatly to radio frequency, transmitting antenna is transported to；
The step (2) is theoretical excellent to the progress of GSM filter parameters by using genetic algorithm and Nonlinear Convex Programming
Change what design was achieved, specifically include following steps：
(G) using the wave filter obtained by step (F), the digital baseband GSM transmission signals of output in step (1) are filtered
Ripple processing, digital baseband GSM transmission signal after output filtering.
It is that the digital baseband GSM exported with digital DUC to the step (G) transmits signal in step (3) of the present invention
Carry out rising sampling and frequency up-conversion operation, export digital medium-frequency signal；Then using a sample frequency as fsamClock control digital-to-analogue
The digital medium-frequency signal is carried out simulated processing by converter (DAC), exports analog if signal；It is mixed again with simulating superhet
Based on structure, the analog if signal that digital analog converter is exported carries out simulated frequency conversion and is amplified to radio frequency, is transported to transmitting day
Line.
According to GSM indexs, GSM digital high-frequency amplification stations are designed.
Working frequency range：
■ is descending：934MHz~954MHz；
■ is up：889MHz~909MHz；
System connection block diagram is as shown in Figure 7.System is by coupling GSM signals, by analog frequency mixing, ADC, digital processing,
DAC, analog frequency mixing step completes to handle the frequency-selective filtering of GSM signals, signal delivers to transmitting antenna after processing, completes signal
Relay flow.
Numerical portion connection is as shown in Figure 6.System connects, up-downgoing data flow one consistent with the description of specification part
Cause, be：AD, DDC, digital filter, DUC, DA.
A kind of index coefficient of low time delay digital filter determines method, the described method comprises the following steps：
Step 1：Determine matched filter index coefficient desired value；
Step 2：Performance of filter is allocated, performance of filter index is specifically divided into amplitude response requirement, phase
Position response is required and delay requirement；And ideal filter frequency response function is worth to according to the index coefficient target in step 1, with it
Corresponding amplitude response, phase response, group delay response (phase change rate) value, and it is used as the desired value of optimization；
Step 3：The frequency domain response for setting up digital filter distributes objective cost function rationally；
Step 4：According to the cost function of step 3, by every discretization, and apply genetic algorithm respectively in cost function
The optimal solution of cost function is solved with nonlinear optimization method, its result is the wave filter of design.
In the step 2, digital band [0,2 π) in quantified, obtain ideal filter frequency response function Hd(ejω),
With its corresponding amplitude response | Hd(ejω) |, phase response arg (Hd(ejω)), group delay response (phase change rate) τ (ejω)
Value, and it is used as the desired value of optimization.
In the step 3, the step includes 3.1) setting vector variable h=[h (0), h (1) ... h (N-1)]TRepresent real
Border can obtain the parameter of wave filter, and N represents the exponent number of target filter, and T represents vectorial transposition；Then the frequency domain response of wave filter is represented
For following formula：
Its corresponding amplitude response is | H (ejω) |,
Phase response is arg (H (ejω)),
Group delay response is
Step 3.2) ideal low-pass filter passband is set as [0, ω 1], stopband is [ω 2, π], sets cost function
Δ 0, Δ 1 and Δ 2 are scale factor, for adjusting passband, stopband and the degree of optimization of group delay；When finding h,
Make above-mentioned cost function minimum, so that the frequency domain response of design wave filter and the frequency domain response of ideal filter farthest connect
Closely；.
In step 4, the items in cost function discrete are respectively turned to：
In step 4, using genetic algorithm and combination Nonlinear Convex Programming theoretical optimization method solution cost function
Using the above method, digital filter section is specific as follows：
(A) matched filter index is：Sample rate 3.84MHz, passband 120KHz, stopband 400KHz.Passband passband fluctuation
0.1db, stopband suppresses to be more than or equal to 65db, group delay 3us, and design wave filter is 45 ranks.
(B) in step (A) each require digital band [0,2 π) in quantified, specially：Passband [0,12]
π/384, stopbandIdeal filter frequency response function Hd(ejω), it is divided into its corresponding amplitude responsePhase response
Group delay response (phase change rate) τ (ejω)=
3*3.84w ∈ [0,12] π/384 are used as the target optimized；
(C) vector variable h=[h (0), h (1) ... h (N-1)] is setTExpression can actually obtain the parameter of wave filter, N=
45, T represent vectorial transposition；Then the frequency domain response of wave filter is expressed as following formula：
Its corresponding amplitude response is | H (ejω) |,
Phase response is arg (H (ejω)),
Group delay response is
(D) cost function is set
Δ 0=1, Δ 1=1 and Δ 2=5；
(E) according to the calculation features of digital computer, discretization is carried out to above-mentioned continuous cost function, is specially by frequency band
[0,2 π) uniform quantization is 2048 sample points；2048 be engineering experience parameter, is adjusted and obtained by simulation result, if amount
Change sample value and obtain few, then optimize that the program overall calculation machine speed of service is fast, but the description of frequency band details, which is portrayed, will also subtract
Weak, if quantifying sample value obtains many, the description to frequency band details is portrayed by force, and performance parameters are more preferable, but computer is run
Speed will be significantly increased, and 2048 be the value of a compromise, according to parameter above, and once about 6 are run on I5 computers
Hour or so.
Then the items in step (D) in cost function discrete are respectively turned to：
(F) according to the form of discretization in step (E), cost letter is solved using genetic algorithm and Nonlinear Convex Programming theory
(optimal solution refers to optimize the cost wave function described in project D several optimal solutions, it is therefore an objective to try to achieve optimal h, i.e.,
Wave filter is responded), its result is the wave filter of design.
As a comparison, software kit FDAtool design result is carried using existing Universal Designing Software Matlab V2009
It is compared.Comparative result is as shown in Figures 2 to 5：
The outer 400KHz of FDAtool design result band is compressed to 65db, and group delay is 5.3us.The method of the present invention is set
The outer 400KHz of meter result band is compressed to 70db, and group delay is 3us.Under conditions of stopband suppression is better than FDAtool design results,
The inventive method is better than FDAtool design result 2.3us in group delay index, improves systematic function.
Claims (7)
1. a kind of index coefficient of low time delay digital filter determines method, it is characterised in that：It the described method comprises the following steps：
Step 1：Determine matched filter index coefficient desired value；
Step 2：Performance of filter is allocated, performance of filter index is specifically divided into amplitude response requirement, phase rings
It should require and delay requirement；And ideal filter frequency response function is worth to according to the index coefficient target in step 1, with its correspondence
Amplitude response, phase response, group delay response (phase change rate) value, and be used as optimization desired value；
Step 3：The frequency domain response for setting up digital filter distributes objective cost function rationally；
Step 4：According to the cost function of step 3, the items in cost function are distinguished into discretization, and apply genetic algorithm and non-
Linear optimization method solves the optimal solution of cost function, and its result is the wave filter of design.
2. coefficient according to claim 1 determines method, it is characterised in that in the step 1, sample rate 3.84MHz, if
Wave filter is counted to meet for 45 ranks：120K passband passband fluctuation 0.1dB, 400KHz stopband suppress to be more than or equal to 65dB, and group delay is small
In equal to 3us.
3. coefficient according to claim 1 determines method, it is characterised in that in the step 2, digital band [0,2 π)
It is interior to be quantified, obtain ideal filter frequency response function Hd(ejω), with its corresponding amplitude response | Hd(ejω) |, phase response
arg(Hd(ejω)), group delay response (phase change rate) τ (ejω) value, and it is used as the desired value of optimization.
4. coefficient according to claim 1 determines method, it is characterised in that in the step 3, the step includes 3.1) setting
Put vector variable h=[h (0), h (1) ... h (N-1)]TExpression can actually obtain the parameter of wave filter, and N represents target filter
Exponent number, T represents vectorial transposition；Then the frequency domain response of wave filter is expressed as following formula：
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Its corresponding amplitude response is | H (ejω) |,
Phase response is arg (H (ejω)),
Group delay response is
Step 3.2) ideal low-pass filter passband is set as [0, ω 1], stopband is [ω 2, π], sets cost function
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Δ 0, Δ 1 and Δ 2 are scale factor, for adjusting passband, stopband and the degree of optimization of group delay；When finding h, make
Cost function minimum is stated, so that the frequency domain response of design wave filter and the frequency domain response of ideal filter are farthest approached；.
5. coefficient according to claim 1 determines method, it is characterised in that in step 4, by the items in cost function
It is discrete respectively to turn to：
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<mo>)</mo>
</mrow>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
<mi>d</mi>
<mi>&omega;</mi>
<mo>&RightArrow;</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mrow>
<mi>k</mi>
<mn>1</mn>
</mrow>
</munderover>
<mo>|</mo>
<mi>F</mi>
<mrow>
<mo>(</mo>
<mi>h</mi>
<mo>,</mo>
<mi>i</mi>
<mo>/</mo>
<mi>K</mi>
<mo>&times;</mo>
<mn>2</mn>
<mi>&pi;</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>H</mi>
<mi>d</mi>
</msub>
<mrow>
<mo>(</mo>
<msup>
<mi>e</mi>
<mrow>
<mi>j</mi>
<mo>&times;</mo>
<mi>i</mi>
<mo>/</mo>
<mi>K</mi>
<mo>&times;</mo>
<mn>2</mn>
<mi>&pi;</mi>
</mrow>
</msup>
<mo>)</mo>
</mrow>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<msubsup>
<mo>&Integral;</mo>
<mrow>
<mi>&omega;</mi>
<mn>2</mn>
</mrow>
<mi>&pi;</mi>
</msubsup>
<mo>|</mo>
<mi>F</mi>
<mrow>
<mo>(</mo>
<mi>h</mi>
<mo>,</mo>
<mi>&omega;</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>H</mi>
<mi>d</mi>
</msub>
<mrow>
<mo>(</mo>
<msup>
<mi>e</mi>
<mrow>
<mi>j</mi>
<mi>&omega;</mi>
</mrow>
</msup>
<mo>)</mo>
</mrow>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
<mi>d</mi>
<mi>&omega;</mi>
<mo>&RightArrow;</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mi>k</mi>
<mn>2</mn>
</mrow>
<mrow>
<mi>K</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
</munderover>
<mo>|</mo>
<mi>F</mi>
<mrow>
<mo>(</mo>
<mi>h</mi>
<mo>,</mo>
<mi>i</mi>
<mo>/</mo>
<mi>K</mi>
<mo>&times;</mo>
<mn>2</mn>
<mi>&pi;</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>H</mi>
<mi>d</mi>
</msub>
<mrow>
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<mrow>
<mi>j</mi>
<mo>&times;</mo>
<mi>i</mi>
<mo>/</mo>
<mi>K</mi>
<mo>&times;</mo>
<mn>2</mn>
<mi>&pi;</mi>
</mrow>
</msup>
<mo>)</mo>
</mrow>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<msubsup>
<mo>&Integral;</mo>
<mn>0</mn>
<mrow>
<mi>&omega;</mi>
<mn>1</mn>
</mrow>
</msubsup>
<mo>|</mo>
<mfrac>
<mrow>
<mi>d</mi>
<mi> </mi>
<mi>arg</mi>
<mrow>
<mo>(</mo>
<mi>F</mi>
<mo>(</mo>
<mrow>
<mi>h</mi>
<mo>,</mo>
<mi>&omega;</mi>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mi>d</mi>
<mi>&omega;</mi>
</mrow>
</mfrac>
<mo>-</mo>
<mi>&tau;</mi>
<mrow>
<mo>(</mo>
<msup>
<mi>e</mi>
<mrow>
<mi>j</mi>
<mi>&omega;</mi>
</mrow>
</msup>
<mo>)</mo>
</mrow>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
<mi>d</mi>
<mi>&omega;</mi>
<mo>&RightArrow;</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mi>k</mi>
<mn>1</mn>
</mrow>
</munderover>
<mo>|</mo>
<mi>arg</mi>
<mrow>
<mo>(</mo>
<mi>F</mi>
<mo>(</mo>
<mrow>
<mi>h</mi>
<mo>,</mo>
<mrow>
<mo>(</mo>
<mrow>
<mi>i</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>/</mo>
<mi>K</mi>
<mo>&times;</mo>
<mn>2</mn>
<mi>&pi;</mi>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>arg</mi>
<mrow>
<mo>(</mo>
<mi>F</mi>
<mo>(</mo>
<mrow>
<mi>h</mi>
<mo>,</mo>
<mi>i</mi>
<mo>/</mo>
<mi>K</mi>
<mo>&times;</mo>
<mn>2</mn>
<mi>&pi;</mi>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>&tau;</mi>
<mrow>
<mo>(</mo>
<msup>
<mi>e</mi>
<mrow>
<mi>j</mi>
<mo>&times;</mo>
<mi>i</mi>
<mo>/</mo>
<mi>K</mi>
<mo>&times;</mo>
<mn>2</mn>
<mi>&pi;</mi>
</mrow>
</msup>
<mo>)</mo>
</mrow>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mi>k</mi>
<mn>1</mn>
<mo>=</mo>
<mfrac>
<mrow>
<mi>&omega;</mi>
<mn>1</mn>
</mrow>
<mrow>
<mn>2</mn>
<mi>&pi;</mi>
</mrow>
</mfrac>
<mo>&times;</mo>
<mi>K</mi>
<mo>,</mo>
<mi>k</mi>
<mn>2</mn>
<mo>=</mo>
<mfrac>
<mrow>
<mi>&omega;</mi>
<mn>2</mn>
</mrow>
<mrow>
<mn>2</mn>
<mi>&pi;</mi>
</mrow>
</mfrac>
<mo>&times;</mo>
<mi>K</mi>
<mo>.</mo>
</mrow>
1
6. coefficient according to claim 1 determines method, it is characterised in that in step 4, using genetic algorithm and combine
Nonlinear Convex Programming theoretical optimization method solves cost function
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<mi>&phi;</mi>
<mrow>
<mo>(</mo>
<mi>h</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>&Delta;</mi>
<mn>0</mn>
<mo>&times;</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mrow>
<mi>k</mi>
<mn>1</mn>
</mrow>
</munderover>
<mo>|</mo>
<mi>F</mi>
<mrow>
<mo>(</mo>
<mi>h</mi>
<mo>,</mo>
<mi>i</mi>
<mo>/</mo>
<mi>K</mi>
<mo>&times;</mo>
<mn>2</mn>
<mi>&pi;</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>H</mi>
<mi>d</mi>
</msub>
<mrow>
<mo>(</mo>
<msup>
<mi>e</mi>
<mrow>
<mi>j</mi>
<mo>&times;</mo>
<mi>i</mi>
<mo>/</mo>
<mi>K</mi>
<mo>&times;</mo>
<mn>2</mn>
<mi>&pi;</mi>
</mrow>
</msup>
<mo>)</mo>
</mrow>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
<mo>+</mo>
<mi>&Delta;</mi>
<mn>1</mn>
<mo>&times;</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mi>k</mi>
<mn>2</mn>
</mrow>
<mrow>
<mi>K</mi>
<mo>/</mo>
<mn>2</mn>
</mrow>
</munderover>
<mo>|</mo>
<mi>F</mi>
<mrow>
<mo>(</mo>
<mi>h</mi>
<mo>,</mo>
<mi>i</mi>
<mo>/</mo>
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<mo>&times;</mo>
<mn>2</mn>
<mi>&pi;</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msub>
<mi>H</mi>
<mi>d</mi>
</msub>
<mrow>
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<mi>e</mi>
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<mo>&times;</mo>
<mi>i</mi>
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<mo>&times;</mo>
<mn>2</mn>
<mi>&pi;</mi>
</mrow>
</msup>
<mo>)</mo>
</mrow>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
<mo>+</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>&Delta;</mi>
<mn>2</mn>
<mo>&times;</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mrow>
<mi>k</mi>
<mn>1</mn>
</mrow>
</munderover>
<mo>|</mo>
<mi>arg</mi>
<mrow>
<mo>(</mo>
<mi>F</mi>
<mo>(</mo>
<mrow>
<mi>h</mi>
<mo>,</mo>
<mrow>
<mo>(</mo>
<mrow>
<mi>i</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>/</mo>
<mi>K</mi>
<mo>&times;</mo>
<mn>2</mn>
<mi>&pi;</mi>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>arg</mi>
<mrow>
<mo>(</mo>
<mi>F</mi>
<mo>(</mo>
<mrow>
<mi>h</mi>
<mo>,</mo>
<mi>i</mi>
<mo>/</mo>
<mi>K</mi>
<mo>&times;</mo>
<mn>2</mn>
<mi>&pi;</mi>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>&tau;</mi>
<mrow>
<mo>(</mo>
<msup>
<mi>e</mi>
<mrow>
<mi>j</mi>
<mo>&times;</mo>
<mi>i</mi>
<mo>/</mo>
<mi>K</mi>
<mo>&times;</mo>
<mn>2</mn>
<mi>&pi;</mi>
</mrow>
</msup>
<mo>)</mo>
</mrow>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>.</mo>
</mrow>
7. the coefficient according to claim 1 to 6 any one determines method, it is characterised in that (A) matched filter index
For：Sample rate 3.84MHz, design wave filter meets for 45 ranks：120K passband passband fluctuation 0.1dB, 400KHz stopband suppress big
In equal to 65dB, group delay is less than or equal to 3us.
(B) in step (A) each require digital band [0,2 π) in quantified, specially：Passband [0,12] π/
384, stopband [40,19 π 2)/.Ideal filter frequency response function Hd(ejω), it is divided into its corresponding amplitude responsePhase response
Group delay response (phase change rate) τ (ejω)=3*
3.84w ∈ [0,12] π/384 are used as the target optimized；
(C) vector variable h=[h (0), h (1) ... h (N-1)] is setTExpression can actually obtain the parameter of wave filter, N=45, T tables
Show vectorial transposition；Then the frequency domain response of wave filter is expressed as following formula：
<mrow>
<mi>H</mi>
<mrow>
<mo>(</mo>
<msup>
<mi>e</mi>
<mrow>
<mi>j</mi>
<mi>&omega;</mi>
</mrow>
</msup>
<mo>)</mo>
</mrow>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>n</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mrow>
<mi>n</mi>
<mo>=</mo>
<mn>44</mn>
</mrow>
</munderover>
<mi>h</mi>
<mrow>
<mo>(</mo>
<mi>n</mi>
<mo>)</mo>
</mrow>
<mo>&times;</mo>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<mi>j</mi>
<mi>&omega;</mi>
<mi>n</mi>
</mrow>
</msup>
<mo>=</mo>
<mi>F</mi>
<mrow>
<mo>(</mo>
<mi>h</mi>
<mo>,</mo>
<mi>&omega;</mi>
<mo>)</mo>
</mrow>
</mrow>
Its corresponding amplitude response is | H (ejω) |,
Phase response is arg (H (ejω)),
Group delay response is
(D) cost function is set
<mrow>
<mi>&phi;</mi>
<mrow>
<mo>(</mo>
<mi>h</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>&Delta;</mi>
<mn>0</mn>
<mo>&times;</mo>
<msubsup>
<mo>&Integral;</mo>
<mn>0</mn>
<mrow>
<mfrac>
<mn>12</mn>
<mn>384</mn>
</mfrac>
<mi>&pi;</mi>
</mrow>
</msubsup>
<mo>|</mo>
<mi>F</mi>
<mrow>
<mo>(</mo>
<mi>h</mi>
<mo>,</mo>
<mi>&omega;</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mn>1</mn>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
<mi>d</mi>
<mi>&omega;</mi>
<mo>+</mo>
<mi>&Delta;</mi>
<mn>1</mn>
<mo>&times;</mo>
<msubsup>
<mo>&Integral;</mo>
<mrow>
<mfrac>
<mn>40</mn>
<mn>384</mn>
</mfrac>
<mi>&pi;</mi>
</mrow>
<mrow>
<mfrac>
<mn>192</mn>
<mn>384</mn>
</mfrac>
<mi>&pi;</mi>
</mrow>
</msubsup>
<mo>|</mo>
<mi>F</mi>
<mrow>
<mo>(</mo>
<mi>h</mi>
<mo>,</mo>
<mi>&omega;</mi>
<mo>)</mo>
</mrow>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
<mi>d</mi>
<mi>&omega;</mi>
<mo>+</mo>
<mi>&Delta;</mi>
<mn>2</mn>
<mo>&times;</mo>
<msubsup>
<mo>&Integral;</mo>
<mn>0</mn>
<mrow>
<mfrac>
<mn>12</mn>
<mn>384</mn>
</mfrac>
<mi>&pi;</mi>
</mrow>
</msubsup>
<mo>|</mo>
<mfrac>
<mrow>
<mi>d</mi>
<mi> </mi>
<mi>arg</mi>
<mrow>
<mo>(</mo>
<mi>F</mi>
<mo>(</mo>
<mrow>
<mi>h</mi>
<mo>,</mo>
<mi>&omega;</mi>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mi>d</mi>
<mi>&omega;</mi>
</mrow>
</mfrac>
<mo>-</mo>
<mn>11.52</mn>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
<mi>d</mi>
<mi>&omega;</mi>
</mrow>
Δ 0=1, Δ 1=1 and Δ 2=5；
(E) according to the calculation features of digital computer, discretization is carried out to above-mentioned continuous cost function, is specially by frequency band [0,2
π) uniform quantization is 2048 sample points；
Then the items in step (D) in cost function discrete are respectively turned to：
<mrow>
<msubsup>
<mo>&Integral;</mo>
<mn>0</mn>
<mrow>
<mfrac>
<mn>12</mn>
<mn>384</mn>
</mfrac>
<mi>&pi;</mi>
</mrow>
</msubsup>
<mo>|</mo>
<mi>F</mi>
<mrow>
<mo>(</mo>
<mi>h</mi>
<mo>,</mo>
<mi>&omega;</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mn>1</mn>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
<mi>d</mi>
<mi>&omega;</mi>
<mo>&RightArrow;</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mn>64</mn>
</munderover>
<mo>|</mo>
<mi>F</mi>
<mrow>
<mo>(</mo>
<mi>h</mi>
<mo>,</mo>
<mi>i</mi>
<mo>/</mo>
<mn>2048</mn>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mn>1</mn>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<msubsup>
<mo>&Integral;</mo>
<mrow>
<mfrac>
<mn>40</mn>
<mn>384</mn>
</mfrac>
<mi>&pi;</mi>
</mrow>
<mrow>
<mfrac>
<mn>192</mn>
<mn>384</mn>
</mfrac>
<mi>&pi;</mi>
</mrow>
</msubsup>
<mo>|</mo>
<mi>F</mi>
<mrow>
<mo>(</mo>
<mi>h</mi>
<mo>,</mo>
<mi>&omega;</mi>
<mo>)</mo>
</mrow>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
<mi>d</mi>
<mi>&omega;</mi>
<mo>&RightArrow;</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>213</mn>
</mrow>
<mn>1024</mn>
</munderover>
<mo>|</mo>
<mi>F</mi>
<mrow>
<mo>(</mo>
<mi>h</mi>
<mo>,</mo>
<mi>i</mi>
<mo>/</mo>
<mn>2048</mn>
<mo>)</mo>
</mrow>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<msubsup>
<mo>&Integral;</mo>
<mn>0</mn>
<mrow>
<mfrac>
<mn>12</mn>
<mn>384</mn>
</mfrac>
<mi>&pi;</mi>
</mrow>
</msubsup>
<mo>|</mo>
<mfrac>
<mrow>
<mi>d</mi>
<mi> </mi>
<mi>arg</mi>
<mrow>
<mo>(</mo>
<mi>F</mi>
<mo>(</mo>
<mrow>
<mi>h</mi>
<mo>,</mo>
<mi>&omega;</mi>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mi>d</mi>
<mi>&omega;</mi>
</mrow>
</mfrac>
<mo>-</mo>
<mn>11.52</mn>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
<mi>d</mi>
<mi>&omega;</mi>
<mo>&RightArrow;</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mn>64</mn>
</munderover>
<mo>|</mo>
<mi>arg</mi>
<mrow>
<mo>(</mo>
<mi>F</mi>
<mo>(</mo>
<mrow>
<mi>h</mi>
<mo>,</mo>
<mrow>
<mo>(</mo>
<mrow>
<mi>i</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
<mo>)</mo>
</mrow>
<mo>/</mo>
<mn>2048</mn>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>arg</mi>
<mrow>
<mo>(</mo>
<mi>F</mi>
<mo>(</mo>
<mrow>
<mi>h</mi>
<mo>,</mo>
<mi>i</mi>
<mo>/</mo>
<mn>2048</mn>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mn>11.52</mn>
<msup>
<mo>|</mo>
<mn>2</mn>
</msup>
</mrow>
2
(F) according to the form of discretization in step (E), cost function is solved most using genetic algorithm and nonlinear optimization method
Excellent solution, its result is the wave filter of design.
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Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107592149A (en) * | 2017-09-22 | 2018-01-16 | 北京大学 | A kind of full duplex filtering forward relay structure and its discrete frequency domain response design method |
| CN111181527A (en) * | 2020-01-06 | 2020-05-19 | 北京中科飞鸿科技股份有限公司 | Realization method of FIR filter |
| CN113162044A (en) * | 2021-02-25 | 2021-07-23 | 国网陕西省电力公司经济技术研究院 | Method and device for optimizing FIR filter for realizing frequency measurement by DN-PMU |
| WO2021147628A1 (en) * | 2020-01-20 | 2021-07-29 | 诺思(天津)微系统有限责任公司 | Method for designing low group-delay fluctuation filter |
| CN113919187A (en) * | 2021-12-14 | 2022-01-11 | 成都星联芯通科技有限公司 | Method and device for determining simulation parameters of filter, electronic equipment and storage medium |
| CN115834307A (en) * | 2022-11-23 | 2023-03-21 | 宸芯科技有限公司 | Signal compensation method and device, electronic equipment and storage medium |
Citations (1)
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| CN102664646A (en) * | 2011-05-17 | 2012-09-12 | 杭州畅鼎科技有限公司 | Filtering method for optimizing parameters by adopting genetic algorithm and nonlinear convex programming theory |
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| CN102664646A (en) * | 2011-05-17 | 2012-09-12 | 杭州畅鼎科技有限公司 | Filtering method for optimizing parameters by adopting genetic algorithm and nonlinear convex programming theory |
Cited By (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107592149A (en) * | 2017-09-22 | 2018-01-16 | 北京大学 | A kind of full duplex filtering forward relay structure and its discrete frequency domain response design method |
| CN107592149B (en) * | 2017-09-22 | 2020-02-11 | 北京大学 | Full-duplex filtering forwarding relay structure and discrete frequency domain response design method thereof |
| CN111181527A (en) * | 2020-01-06 | 2020-05-19 | 北京中科飞鸿科技股份有限公司 | Realization method of FIR filter |
| WO2021147628A1 (en) * | 2020-01-20 | 2021-07-29 | 诺思(天津)微系统有限责任公司 | Method for designing low group-delay fluctuation filter |
| CN113162044A (en) * | 2021-02-25 | 2021-07-23 | 国网陕西省电力公司经济技术研究院 | Method and device for optimizing FIR filter for realizing frequency measurement by DN-PMU |
| CN113162044B (en) * | 2021-02-25 | 2023-09-01 | 国网陕西省电力公司经济技术研究院 | Optimization method and device for frequency measurement of frequency-dependent impulse response (FIR) filter by digital subscriber unit (DN-PMU) |
| CN113919187A (en) * | 2021-12-14 | 2022-01-11 | 成都星联芯通科技有限公司 | Method and device for determining simulation parameters of filter, electronic equipment and storage medium |
| CN113919187B (en) * | 2021-12-14 | 2022-03-11 | 成都星联芯通科技有限公司 | Method and device for determining simulation parameters of filter, electronic equipment and storage medium |
| CN115834307A (en) * | 2022-11-23 | 2023-03-21 | 宸芯科技有限公司 | Signal compensation method and device, electronic equipment and storage medium |
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