CN102419785A - Method for designing wavelet filter - Google Patents
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- CN102419785A CN102419785A CN2011102989344A CN201110298934A CN102419785A CN 102419785 A CN102419785 A CN 102419785A CN 2011102989344 A CN2011102989344 A CN 2011102989344A CN 201110298934 A CN201110298934 A CN 201110298934A CN 102419785 A CN102419785 A CN 102419785A
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Abstract
The invention discloses a method for designing a wavelet filter. The method comprises the following steps of: (1) performing Fourier transformation on a time domain basic wavelet function to acquire a frequency domain wavelet function; (2) approximating a frequency domain transmission function by adopting a Maclaurin series; (3) calculating a frequency domain approximated transmission function of the wavelet filter; and (4) designing the wavelet filter with a series structure by taking a switching current differentiator as a basic unit. In the method, the frequency domain transmission function is approximated by adopting the Maclaurin series; a proper number of items of the Maclaurin series can be selected according to a requirement for the design precision of the filter, so the simple transmission function is acquired; therefore, the circuit structure and the design process of the filter can be simplified. Besides, a summation gain amplifier is not needed, so the circuit structure is simple; the noise suppression characteristic and the stability of a high-pass or band-pass filter designed by adopting the switching current differentiator are higher than those of a switching current integrator; and the designed wavelet filter can be widely applied to low voltage/low power consumption and high frequency/high speed real-time signal processing equipment.
Description
Technical field
The present invention relates to a kind of wavelet filter method for designing, especially relate to a kind of wavelet filter method for designing based on Maclaurin series and switching current differentiator.
Background technology
Wavelet transformation is with its good time-frequency local characteristics, is widely used in non-stationary and transient signal and handles, and become one of efficient mathematical instrument of each engineering field signal Processing at present.Wavelet transformation can be regarded the linear combination of yardstick and displacement different wavelet wave filter as, and therefore, the design of research wavelet filter has most important theories meaning and engineering actual value.
In the wavelet filter method for designing of at present having reported; Mainly comprise two kinds of methods: a kind of is to prove that at first being studied function is wavelet function; Adopting the Design of Filter technical design to go out impulse response then is the wave filter that is studied function, and this kind method for designing has characteristics such as design accuracy height, design process be fairly simple, but major defect is can only be to specific its wave filter of wavelet function design; Because be not all to be studied function all be wavelet function, and this kind method versatility is relatively poor; Another kind method is time domain or the frequency domain approximate model that makes up wavelet function earlier, the employing approximate algorithm (for example: Pad é method,
L 2Norm method and optimized Algorithm etc.) try to achieve the parameter of approximate model, obtain filter transfer function, design corresponding wave filter at last; The highly versatile of this method be fit to various wavelet filter designs, but the quality of performance of filter receives the influence of approximation accuracy; The process that obtains filter transfer function is loaded down with trivial details; Corresponding filter construction is more complicated also, and the approximate algorithm that adopts usually has deficiency separately, for example: adopt Pad é method to ask in the frequency domain transfer function process of wave filter; The optimum number of times of the molecule of transport function and denominator polynomial expression is difficult to confirm, and can not guarantees that the system of approaching that obtains is stable;
L 2When the norm method is approached the time domain wavelet function,, promptly be absorbed in local optimum, and selection of initial value is difficult to confirm because this algorithm is a Local Optimization Algorithm; When utilizing optimized Algorithm to ask approximating function, iterations is more, and each parameter is provided with the comparison difficulty in the algorithm, and operation time is long.Design of Filter circuit commonly used also has two kinds: a kind of is continuous time filter; Like OTA-C wave filter, Log-Domain Filters etc.; The OTA-C filter time constant is decided by the absolute value of component parameter, makes the precision and the stable needs that are difficult to satisfy system of its frequency characteristic of filter; The time constant of log-domain integrator and thermal voltage
V TTo be directly proportional, to be prone to cause that frequency characteristic of filter is unstable, in addition, transistorized in order obtaining
I-
VIndicial response requires transistor to be operated in sub-threshold region, and the bias current of causes system can not be too big, so the bandwidth of operation of wave filter is restricted.Another kind is a discrete time filter, and like switching capacity and Switched-Current Filter etc., because the type filter time constant is by clock frequency or capacity ratio, the decision of transistor breadth length ratio, so filter accuracies is high, and available clock carries out tuning.But switched-capacitor circuit is the voltage-mode circuit, and along with supply voltage reduces, the circuit dynamic range descends, and making and digital CMOS process are incompatible.Switched-Current Circuit belongs to the current-mode circuit, has that high frequency characteristics is good, dynamic range is big, with characteristics such as the complete compatibility of digital CMOS process, is the particularly direction of System on Chip/SoC (Soc) development of DA combination circuit.
Summary of the invention
In order to overcome the above-mentioned defective that prior art exists, the present invention provides a kind of highly versatile, is applicable to the wavelet filter method for designing based on Maclaurin series and switching current differentiator of low pressure, low-power consumption and high frequency, signal Processing practical applications at a high speed.
Technical scheme of the present invention is: it may further comprise the steps: Fourier transform is carried out to the basic wavelet function of time domain in (1), obtains the frequency-domain small wave function; (2) adopt Maclaurin series that frequency domain transfer function is approached; The frequency domain of (3) trying to achieve wavelet filter approaches transport function; (4) be elementary cell with the switching current differentiator, the wavelet filter of design cascaded structure.
Said frequency domain transfer function approximation theory is meant that common wavelet function is a non-causal, can not directly comprehensively realize through hardware circuit, for design can reality the wavelet filter circuit, at first utilize Fourier transform to ask for the time domain wavelet function
ψ(
t) frequency-domain expression
H(
J ω), order then
S=j ωWith time delay do
T, obtain frequency domain and approach transport function
H(
s).
Said Maclaurin series is approached the exponential function that is meant in the frequency domain transfer function of wavelet filter
e x Approach, promptly
, wherein
xBe function variable.
The universal expression formula that the frequency domain of said wavelet filter approaches transport function does
, wherein,
,
Be respectively the coefficient of molecule and denominator,
nBe filter order.
Said switching current is meant the analog sample data-signal treatment technology based on current-mode, and it adopts the discrete time sampled data system to handle simulating signal continuous time.
Said switching current differentiator is an elementary cell; The wavelet filter of design cascaded structure; Being meant that the wavelet filter frequency domain transfer function is resolved into second order cuts apart form, is basic module with the biquadratic joint based on the switching current differentiator, and wave filter tandem compounds at different levels are constituted wavelet filter.
Principle of the present invention is: at first, the time domain wavelet function is carried out Fourier transform, obtain the frequency-domain small wave function; Then; Utilize Maclaurin series that frequency domain transfer function is approached, the frequency domain of trying to achieve wavelet filter approaches transport function, and is last; With the switching current differentiator is the basic circuit unit, and design impulse response is the wave filter that approaches wavelet function.
The present invention compared with prior art; Adopt Maclaurin series to approach frequency domain transfer function; Can select the item number of suitable Maclaurin series according to the Design of Filter accuracy requirement, obtain simple transport function, simplify the circuit structure and the design process of wave filter; Compare with the Design of Filter of parallel-connection structure, in the low-frequency range of cascaded structure in low Q (quality factor) circuit good frequency characteristic is arranged, and this structure gain amplifier of need not suing for peace, advantage such as circuit structure is simple relatively; Adopt the high pass of switching current differentiator design or the noise suppression feature and the stability of BPF. to be better than switched-current integrator; The method for designing highly versatile is suitable for various wavelet filter designs; Switched-Current Filter and digital CMOS VLSI technology are compatible fully, are suitable for low pressure, low-power consumption and high frequency, real time signal processing equipment at a high speed.
Description of drawings
Fig. 1 is an embodiment of the invention FB(flow block);
Fig. 2 is the Marr small echo approximating function based on Maclaurin series;
Fig. 3 is a Marr small echo approximating function pole-zero plot (yardstick
a=1);
Fig. 4 is based on the biquadratic of differentiator joint
zThe territory block diagram;
Fig. 5 is the biquadratic economize on electricity road based on the switching current differentiator;
Fig. 6 is a switching current Marr wavelet filter;
Fig. 7 is a switching current Marr wavelet filter impulse response (yardstick
a=1);
Fig. 8 is a switching current Marr wavelet filter pole-zero plot (yardstick
a=1);
Fig. 9 is the Marr wavelet filter impulse response (yardstick when having error
a=1).
Embodiment
Below in conjunction with accompanying drawing and embodiment the present invention is described further.
With reference to Fig. 1, the present invention includes following steps: step 01, the basic wavelet function of time domain is carried out Fourier transform, obtain the frequency-domain small wave function; Step 02 adopts Maclaurin series that frequency domain transfer function is approached; Step 03, the frequency domain of trying to achieve wavelet filter approaches transport function; Step 04 is an elementary cell with the switching current differentiator, the wavelet filter of design cascaded structure.
The inventive method is fit to the Design of Filter of arbitrarily small wave function.For the convenience of explaining, be designed to example with the Marr wavelet filter below and describe.
1, Marr wavelet frequency domain function approaches computing method
Yardstick does
aThe time Marr wavelet function time domain expression formula do
In the formula,
Be wavelet function,
tBe time variable.
Formula (1) is carried out Fourier transform, obtain frequency-domain function and do
(2)
Because the corresponding system of formula (1) is a non-causal, in order to obtain causal system, formula (1) should be carried out time delay, makes do time delay
T,
S=j ω, then formula (2) can be expressed as
Can find out that by formula (2) because denominator is an irrational expression, therefore, this transport function can not be by the directly comprehensive realization of circuit.Utilize Maclaurin series to approach the denominator exponential term, the acquisition frequency domain approaches transport function and does at present
Get
a=1,
T=4, then 6 rank of frequency domain transfer function approach into
In the formula,
sBe complex frequency domain.
Fig. 2 is the Marr small echo approximating function figure based on Maclaurin series.The pole-zero plot that formula (5) median filter frequency domain transfer function is corresponding is as shown in Figure 3, and all limit is positioned at the left half-plane of the imaginary axis, and therefore, this system is stable.Can find out that by formula (6) its corresponding one 6 rank wave filter can be made up of 3 second order filter series connection.The transport function of other yardstick Marr small echo approximating function wave filter can be tried to achieve according to the change of scale character of Laplace transform, behind the acquisition different scale filter transfer function, adopts based on the biquadratic joint of switching current differentiator and realizes corresponding wavelet filter.
2, the general expression formula of switching current biquadratic joint transport function does
In the formula,
Be coefficient,
Be quality factor,
Be pole frequency,
sBe complex frequency.
Bilinear transformation is carried out in (7); I.e.
obtains z territory transport function
and does
In the formula,
,
TBe the clock period,
Be coefficient.Fig. 4 is the biquadratic joint z territory block diagram based on differentiator.Can derive transport function
by Fig. 4 does
(9)
Contrast formula (8) and formula (9) can confirm that the coefficient value
in
is:
;
;
;
;
.The current mirror gain factor in the corresponding Switched-Current Circuit of these coefficients, according to coefficient can confirm respective transistor breadth length ratio (
W/L).Fig. 5 realizes the biquadratic economize on electricity road of Fig. 4 block diagram for adopting second generation switching current differentiator; Wherein
,
are respectively input, output current;
is current source;
,
are two phase non-overlapping clocks, and
is coefficient.
After formula (6) gone normalization, can try to achieve the parameter of switching current biquad filter circuit according to expression formula
.
sThe territory with
zIn the conversion process in territory, owing to exist nonlinear relationship to cause that frequency between the two is unequal between continuous domain and the discrete domain conversion, cause the frequency characteristic of wave filter of conversion gained inequality; Promptly produce frequency warpage effect; Therefore, need carry out preparatory warpage during design and handle, its formula does
, wherein
Expression
zThe territory frequency,
Expression
sThe territory frequency.But frequency of operation selected among the present invention is much smaller than sampling frequency, and this frequency warpage effect is less and can ignore.The parameter of trying to achieve the biquad filter circuit through said method is as shown in table 1.
Table 1 is based on the biquad filter circuit parameter of switching current differentiator
| α i | The 1st joint | The 2nd joint | The |
| α | |||
| 0 | 0 | 1.259763 | 0.630517 |
|
|
0 | 0 | 0 |
| α 2 | -43.794992 | 0.314941 | 0.157630 |
| α 3 | 1.000000 | 1.000000 | 1.000000 |
| α 4 | 9.917661 | 5.628622 | 0.452711 |
| α 5 | 32.095068 | 23.220522 | 10.564628 |
It is the Marr wavelet filter circuit of basic module that Fig. 6 has provided the biquadratic joint of drawing in the ASIZ simulation software with based on the switching current differentiator, and all current sources are owing to software requirement omits among the figure, and grounding switch does not need in the side circuit design yet.With corresponding metal-oxide-semiconductor in the listed parameter setting circuit of table 1
W/LValue, other metal-oxide-semiconductor
W/LAll be set to 1, and order
I s =1A,
r=1 Ω.According to the characteristic of Switched-Current Filter, can obtain the Marr wavelet function of other different scale through the clock frequency of regulating wave filter.Get clock frequency at present and circuit is carried out emulation when being 20MHz, obtain yardstick and do
a=1 Marr filter impulse responses is as shown in Figure 7; Comparison diagram 7 can be found out with the waveform shape among Fig. 2; It is more satisfactory that Marr wavelet filter impulse response that the employing switched current technique is realized and original function approach effect, and the peak value of its impulse response waveform and original function remove the amplitude basically identical after the normalization.Fig. 8 is the pole-zero plot of Marr wavelet filter, and limit " * " all in unit circle, explains that the system that designs is stable among the figure.Improve the design accuracy of Marr wavelet filter if desired, can improve the approximation accuracy of wavelet function through increasing the item number of Maclaurin series.In addition, through revising output transistor (like M among Fig. 6
O6)
W/LCan change the amplitude or the gain of Marr wavelet filter output waveform.
Because there is the imperfection MOS transistor in side circuit in making, and therefore, can produce imperfect output during circuit working, designs the performance of circuit in order to check, and considers transistorized output-input conductance ratio error.Suppose transistorized input conductance (
g m ) with output conductance (be drain conductance
g Ds ) ratio (
g m / g Ds ) be 1000, other parameter is all constant in the circuit, and the impulse response of circuit is as shown in Figure 9, can find out that with Fig. 7 contrast the amplitude of output waveform reduces, but the not variation of the grown form of Marr small echo approximating function explains that circuit receives the type error effect smaller.
Comprehensive above-mentioned simulation result and analysis show that the method for design switching current Marr wavelet filter is feasible.
Claims (3)
1. a wavelet filter method for designing is characterized in that, may further comprise the steps: Fourier transform is carried out to the basic wavelet function of time domain in (1), obtains the frequency-domain small wave function; (2) adopt Maclaurin series that frequency domain transfer function is approached; The frequency domain of (3) trying to achieve wavelet filter approaches transport function; (4) be elementary cell with the switching current differentiator, the wavelet filter of design cascaded structure.
2. wavelet filter method for designing according to claim 1 is characterized in that, said switching current is meant the analog sample data-signal treatment technology based on current-mode, and it adopts the discrete time sampled data system to handle simulating signal continuous time.
3. wavelet filter method for designing according to claim 1 and 2; It is characterized in that; Said switching current differentiator is an elementary cell, and the wavelet filter of design cascaded structure is meant that the wavelet filter frequency domain transfer function is resolved into second order cuts apart form; Biquadratic joint with based on the switching current differentiator is a basic module, and wave filter tandem compounds at different levels are constituted wavelet filter.
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN102946239A (en) * | 2012-11-19 | 2013-02-27 | 合肥工业大学 | Design method of multi-ring feedback wavelet filter for switching current-fused negative phase differentiator |
| CN103226542A (en) * | 2013-05-07 | 2013-07-31 | 合肥工业大学 | Method for simulating wavelet base frequency domain approximation |
| CN103678809A (en) * | 2013-12-16 | 2014-03-26 | 北京经纬恒润科技有限公司 | Designing method of filter model |
| CN103997314A (en) * | 2014-06-05 | 2014-08-20 | 山东大学 | Improved secondary FRM filter designing method |
| CN113139291A (en) * | 2021-04-23 | 2021-07-20 | 广东电网有限责任公司电力科学研究院 | Method and device for obtaining optimal sliding window filtering model of controlled process |
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Cited By (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102946239A (en) * | 2012-11-19 | 2013-02-27 | 合肥工业大学 | Design method of multi-ring feedback wavelet filter for switching current-fused negative phase differentiator |
| CN102946239B (en) * | 2012-11-19 | 2015-02-18 | 合肥工业大学 | Design method of multi-ring feedback wavelet filter for switching current-fused negative phase differentiator |
| CN103226542A (en) * | 2013-05-07 | 2013-07-31 | 合肥工业大学 | Method for simulating wavelet base frequency domain approximation |
| CN103678809A (en) * | 2013-12-16 | 2014-03-26 | 北京经纬恒润科技有限公司 | Designing method of filter model |
| CN103997314A (en) * | 2014-06-05 | 2014-08-20 | 山东大学 | Improved secondary FRM filter designing method |
| CN103997314B (en) * | 2014-06-05 | 2015-02-25 | 山东大学 | Improved secondary FRM filter designing method |
| CN113139291A (en) * | 2021-04-23 | 2021-07-20 | 广东电网有限责任公司电力科学研究院 | Method and device for obtaining optimal sliding window filtering model of controlled process |
| CN113139291B (en) * | 2021-04-23 | 2022-09-16 | 广东电网有限责任公司电力科学研究院 | Method and device for obtaining optimal sliding window filtering model of controlled process |
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Application publication date: 20120418 |