CN103177161B - A kind of switching current method for designing wavelet filter - Google Patents
A kind of switching current method for designing wavelet filter Download PDFInfo
- Publication number
- CN103177161B CN103177161B CN201310111167.0A CN201310111167A CN103177161B CN 103177161 B CN103177161 B CN 103177161B CN 201310111167 A CN201310111167 A CN 201310111167A CN 103177161 B CN103177161 B CN 103177161B
- Authority
- CN
- China
- Prior art keywords
- wavelet filter
- wavelet
- switching current
- filter
- electricity road
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Abstract
A kind of switching current method for designing wavelet filter, comprises the following steps: (1) adopts time domain approach method to obtain the time domain approximating function of wavelet filter; (2) sampling obtains time domain Approximate Sequence, then carries out standard z conversion acquisition wavelet filter z territory transport function; (3) iir digital filter technology and Switched-Current Circuit comprehensive wavelet filter z territory transport function is adopted.Use the present invention, do not need to carry out Laplace transform, be conducive to simplified design step, do not need to carry out pre-warping compensation deals; Employing standard z converts and replaces bilinear z-transform, is conducive to and avoids fre-quency warpping effect; Adopt iir digital filter technical design switching current single order economize on electricity road and second order economize on electricity road, be conducive to reducing and improving circuit parameter, circuit parameter is few and excellent, and most parameters declines along with the exponential law that is reduced to of sampling period T.
Description
Technical field
The invention belongs to Electronics and Information Engineering field, relate to a kind of switching current method for designing wavelet filter.
Background technology
Wavelet transformation, with its good time-frequency local characteristics, is widely used in non-stationary and transient signal process, has now become one of the most effective mathematical tool of each engineering field signal transacting.Wavelet transformation also can use hardware implementing with software simulating.Use hardware implementing wavelet transformation, particularly realize with mimic channel, owing to having low in energy consumption, fireballing advantage, be subject to more and more attention.Mimic channel realizes the linear combination that wavelet transformation can regard the yardstick wavelet filter different with displacement as, so the design of wavelet filter is the basis realizing wavelet transformation.Switching current is a kind of novel analog current data sampling techniques, compatible with Standard Digital CMOS, overcomes the restriction that switched capacitor technique needs linear floating capacity, has the advantage of high speed, low-voltage, low-power consumption.Therefore, be of great immediate significance and using value based on switched current technique design wavelet filter.Switching current wavelet filter bank has two crucial steps, and one is approaching of wavelet filter, and two is circuit design of wavelet filter.Wavelet filter approaches finds in fact the shock response wave filter similar as much as possible to wavelet function to be approached.The wavelet filter approach method reported, can be divided into time domain to approach and approach two classes with frequency domain.Typical frequency domain approximatioss has Pad é method and Maclaurin series approximatioss.The frequency domain transfer function approximation accuracy that employing Pad é method and Maclaurin series approximatioss ask for wavelet filter is not high, and the frequency domain transfer function that can not ensure the wavelet filter obtained is stable.In addition, because part small echo does not have clear and definite expression formula at frequency domain, so frequency domain approach method is restricted.And time domain approximate method has effect intuitively, and can ensure the advantage that wavelet filter is stable, therefore time domain approximate method is the method generally adopted.
At present, no matter be that time domain is approached or frequency domain approaches, be all finally to obtain wavelet filter frequency domain transfer function H (s).If frequency domain approaches, directly frequency domain transfer function H (s) can be obtained, if time domain is approached, time domain approximating function h (t) frequency domain transfer function H (s) need be obtained by Laplace transform.Adopt Switched-Current Circuit design wavelet filter after obtaining frequency domain transfer function H (s), existing method for designing generally adopts traditional switching current single order joint and two second order economize on electricity road.The patent of invention " a kind of method for designing wavelet filter " being 2011102989344 as the patent No. adopts Maclaurin series to approach wavelet frequency domain function, then adopts the biquadratic joint based on switching current differentiator to design the wavelet filter of cascaded structure for elementary cell; The patent No. be 2011100545508 patent of invention " switching current self-adaptation chaos differential evolution method for designing wavelet filter " adopt self-adaptation chaos differential evolution optimization algorithm to carry out wavelet filter time domain to approach, then adopt Laplace transform to obtain frequency domain transfer function H (s) of wavelet filter, then adopt the biquadratic joint based on switched-current integrator to carry out filter synthesis; The patent No. be 2010102503863 patent of invention " a kind of simulation continuous wavelet transform circuit based on switched current technique " adopt based on switched-current integrator single order joint and biquadratic save carry out filter synthesis.
There is a few point defect in above-mentioned method for designing.1, design procedure is comparatively loaded down with trivial details.For time domain approximate method, need to approach through time domain, Laplace transform obtains frequency domain transfer function, bilinear z-transform obtains z territory transport function, switching current single order joint and biquadratic joint circuit synthesis wavelet filter.2, bilinear z-transform causes fre-quency warpping effect.Existing switching current single order joint and biquadratic economize on electricity road are in order to comprehensive frequency domain transfer function, derive, are wherein implied with bilinear z-transform step, therefore easily bring fre-quency warpping effect, usually need to carry out pre-warping compensation according to switched-capacitor circuit.3, circuit parameter is undesirable.It is more that traditional switching current single order joint and biquadratic save circuit parameter, and most parameters forms square-law decline along with sampling period of bilinear z-transform reduces, circuit parameter can be caused very little, make troubles to the layout design of circuit, also can increase chip area and power consumption simultaneously.
Summary of the invention
The technical problem to be solved in the present invention is, overcomes the above-mentioned defect that existing method for designing exists, provides a kind of switching current method for designing wavelet filter based on iir digital filter technology.The method effectively can simplify the design procedure of switching current wavelet filter, improves circuit parameter.
The technical solution adopted for the present invention to solve the technical problems is:
A kind of switching current method for designing wavelet filter, comprises the following steps: (1) adopts time domain approach method to obtain the time domain approximating function of wavelet filter; (2) sampling obtains time domain Approximate Sequence, then carries out standard z conversion acquisition wavelet filter z territory transport function; (3) iir digital filter technology and Switched-Current Circuit comprehensive wavelet filter z territory transport function is adopted.
In described step (1), when described employing time domain approach method obtains the time domain approximating function of wavelet filter, need first overturn wavelet function and time shift process.Upset process is to make signal by reaching the object of wavelet transformation during wavelet filter.Described necessity of wavelet function being carried out to time shift process is non-causal because of common wavelet function, can not directly be realized by hardware circuit, so wavelet function need be made to have causality by time shift process.The shock response expression formula h (r, t) of definition wavelet filter is
（1），
In formula, i and j represents subscript;
represent single order joint time-domain expression,
represent second order joint time-domain expression; M represents single order joint sum, and N represents second order joint sum, M and N is determined by wavelet filter exponent number n, meets M+2N=n;
,
;
for parameter to be asked, r=[
] be parameter vector to be asked; In order to ensure the stability of wavelet filter, parameter here
with
strictly should be greater than zero; T represents the time, and for meeting the causality of wavelet filter, t should be greater than 0.
Shock response expression formula h (r, t) and the small echo to be approached of wavelet filter
error sum of squares be
，
t>0 （2），
In formula,
represent norm square; R=[
] be parameter vector to be asked; T represents the time; H (r, t) represents the shock response expression formula of wavelet filter;
represent wavelet function to be approached, by wavelet function
obtain, in formula through upset and time shift
t 0represent time shift amount.
Formula (2) illustrates parameter
rchoose the approximation accuracy determining wavelet filter, parameter choose is proper can improve approximation accuracy greatly.According to the wavelets approximation Optimized model that wavelet filter shock response expression formula and the square error of wavelet function to be approached are determined be
（3），
In formula, i and j represents subscript; Min represents the minimum value of getting e (r); S.t. represent that constraint condition meets;
represent upper limit of integral, determined by the time domain width of small echo to be approached; Constraint condition:
.Formula (3) is a typical nonlinear optimal problem, and optimized algorithm can be adopted to solve.
Pass through Optimal Parameters
rmake the waveform of the shock response waveform of wavelet filter and wavelet function to be approached closely, the time domain that this process is referred to as wavelet filter is approached, and the shock response expression formula of the wavelet filter of acquisition is referred to as the time domain approximating function of wavelet filter.
In described step (2), described sampling obtains time domain Approximate Sequence, and the column criterion z that goes forward side by side converts the concrete steps obtaining wavelet filter z territory transport function and is:
1, sample to each ingredient in formula (1) (i.e. single order joint and second order joint time-domain expression), sampling should be carried out in accordance with sampling thheorem.By sampling operation, time domain approximating function, by discretize, becomes time domain Approximate Sequence, therefore comprises three kinds of sequences after formula (1) sampling
,
with
(in formula,
represent the parameter of being tried to achieve by step (1), n represents that sampled point is numbered, and T represents the sampling period).Standard z conversion is carried out to above-mentioned three kinds of sequences
（4），
（5），
（6），
In formula,
represent the parameter of being tried to achieve by step (1), n represents that sampled point is numbered, and T represents the sampling period.
2, then wavelet filter z territory transport function is obtained
（7），
In formula, M represents single order joint sum, and N represents second order joint sum; I and j represents subscript;
,
;
represent the parameter of being tried to achieve by step (1); T represents the sampling period;
represent single order joint z territory expression formula,
represent second order joint z territory expression formula.
In described step (3), the concrete grammar of described employing iir digital filter technology and Switched-Current Circuit comprehensive wavelet filter z territory transport function is:
1, iir digital filter technical design switching current single order joint and second order economize on electricity road is adopted.
First the single order joint in formula (7) is abbreviated as
（8），
In formula,
,
for the parameter of single order joint z territory expression formula, contrast (8) formula and the single order joint z territory expression formula in (7) formula, can try to achieve
,
:
,
（9），
In formula,
awith
brepresent the parameter in the wavelet filter time domain approximating function of being tried to achieve by step (1), T represents the sampling period.
Correspondingly, the second order joint in formula (7) is abbreviated as
（10），
In formula,
,
,
,
the parameter of second order joint z territory expression formula, contrast (10) formula and the second order joint z territory expression formula in (7), can try to achieve
,
,
,
:
,
,
,
（11），
In formula,
represent the parameter in the wavelet filter time domain approximating function of being tried to achieve by step (1), T represents the sampling period.
When adopting the switching current second order economize on electricity road of iir digital filter technical design, relate generally to four parameters, be respectively:
,
,
,
, wherein
c,
d, σ and
wthe parameter in wavelet filter time domain approximating function, σ >0,
tit is the sampling period.
Adopt iir digital filter technology, design switching current single order joint and second order economize on electricity road., the switch in circuit is by two-phase non-overlapp-ing clock
f1 He
f2 control, and high level then switch closes, and low level then switch disconnects.Circuit parameter is determined according to formula (9) and formula (11) respectively.Contrast existing single order economize on electricity road and biquadratic economize on electricity road and can find out that single order provided by the invention economize on electricity road and second order economize on electricity road have the following advantages: one is that circuit parameter is few.Single order economize on electricity road provided by the invention only has 2 parameters, and second order economize on electricity road only has four parameters, and existing single order joint and biquadratic economize on electricity road have 3 and 6 respectively.Two is that circuit parameter is more excellent.Single order economize on electricity road provided by the invention and second order economize on electricity road, most parameters is along with the sampling period
tbe reduced to exponential law decline, and existing single order joint and biquadratic economize on electricity road, most parameters is along with the sampling period
tbe reduced to square law decline.So the present invention (namely reduces the sampling period by improving sample frequency
t) improve the resolution of the shock response of wavelet filter, and circuit parameter can not be caused to become very little and make troubles to circuit layout design.Three is do not use bilinear z-transform, avoids fre-quency warpping effect.
2, according to above-mentioned switching current single order joint and second order joint circuit design wavelet filter.
Based on above-mentioned switching current single order joint and second order economize on electricity road, with the parallel-connection structure of iir digital filter for prototype, the circuit structure of the wavelet filter of design.
The beneficial effect that the present invention exists compared to prior art is: use the present invention, do not need to carry out Laplace transform, be conducive to simplified design step, only take territory approach, sample and standard z conversion, design wavelet filter circuit three steps, do not need to carry out pre-warping compensation deals; Employing standard z converts and replaces bilinear z-transform, is conducive to and avoids fre-quency warpping effect; Adopt iir digital filter technical design switching current single order economize on electricity road and second order economize on electricity road, be conducive to reducing and improving circuit parameter, circuit parameter is few and excellent, and most parameters is along with the sampling period
tbe reduced to exponential law decline, and existing single order joint and biquadratic economize on electricity road, most parameters is along with the sampling period
tbe reduced to square law decline.So the present invention (namely reduces the sampling period by improving sample frequency
t) improve the resolution of wavelet filter shock response, and circuit parameter can not be caused to become very little and bring difficulty to circuit layout design.
Accompanying drawing explanation
Fig. 1 is switching current method for designing wavelet filter process flow diagram of the present invention;
Fig. 2 is switching current single order provided by the invention joint circuit diagram;
Fig. 3 is switching current second order provided by the invention joint circuit diagram;
Fig. 4 (a) is the contracted notation figure on switching current single order economize on electricity road;
Fig. 4 (b) is the contracted notation figure on switching current second order economize on electricity road;
Fig. 5 is wavelet filter circuit structure diagram provided by the invention;
Fig. 6 is switching current five rank Gauss wavelet filter circuit figure;
The shock response ideal waveform that the single order that Fig. 7 (a) is the five rank Gauss wavelet wave filters obtained saves;
The shock response ideal waveform that first second order that Fig. 7 (b) is the five rank Gauss wavelet wave filters obtained saves;
The shock response ideal waveform that second second order that Fig. 7 (c) is the five rank Gauss wavelet wave filters obtained saves;
Fig. 7 (d) is the shock response ideal waveform of five rank Gauss wavelet overall filter;
The shock response simulation waveform on the single order economize on electricity road that Fig. 8 (a) is switching current five rank Gauss wavelet wave filter;
The shock response simulation waveform on first second order economize on electricity road that Fig. 8 (b) is switching current five rank Gauss wavelet wave filter;
The shock response simulation waveform on second second order economize on electricity road that Fig. 8 (c) is switching current five rank Gauss wavelet wave filter;
Fig. 8 (d) is the shock response simulation waveform of switching current five rank Gauss wavelet filter circuit entirety;
Fig. 9 is the switching current five rank Gauss wavelet filter circuit pole-zero plot that the present invention obtains.
Embodiment
Below in conjunction with accompanying drawing and example, the invention will be further described.
With reference to Fig. 1, a kind of switching current method for designing wavelet filter, comprises the following steps: (1) adopts time domain approach method to obtain the time domain approximating function of wavelet filter; (2) sampling obtains time domain Approximate Sequence, then carries out standard z conversion acquisition wavelet filter z territory transport function; (3) iir digital filter technology and Switched-Current Circuit comprehensive wavelet filter z territory transport function is adopted.
In described step (1), when described employing time domain approach method obtains the time domain approximating function of wavelet filter, need first overturn wavelet function and time shift process.Upset process is to make signal by reaching the object of wavelet transformation during wavelet filter.Described necessity of wavelet function being carried out to time shift process is non-causal because of common wavelet function, can not directly be realized by hardware circuit, so wavelet function need be made to have causality by time shift process.The shock response expression formula h (r, t) of definition wavelet filter is
（1），
In formula, i and j represents subscript;
represent single order joint time-domain expression,
represent second order joint time-domain expression; M represents single order joint sum, and N represents second order joint sum, M and N is determined by wavelet filter exponent number n, meets M+2N=n;
,
;
for parameter to be asked, r=[
] be parameter vector to be asked; In order to ensure the stability of wavelet filter, parameter here
with
strictly should be greater than zero; T represents the time, and for meeting the causality of wavelet filter, t should be greater than 0.
Shock response expression formula h (r, t) and the small echo to be approached of wavelet filter
error sum of squares be
，
t>0 （2），
In formula,
represent norm square; R=[
] be parameter vector to be asked; T represents the time; The shock response expression formula h (r, t) of wavelet filter;
represent wavelet function to be approached, by wavelet function
obtain, in formula through upset and time shift
t 0represent time shift amount.
Formula (2) illustrates parameter
rchoose the approximation accuracy determining wavelet filter, parameter choose is proper can improve approximation accuracy greatly.According to the wavelets approximation Optimized model that wavelet filter shock response expression formula and the square error of wavelet function to be approached are determined be
（3），
In formula, i and j represents subscript; Min represents the minimum value of getting e (r); S.t. represent that constraint condition meets;
represent upper limit of integral, determined by the time domain width of small echo to be approached; Constraint condition:
.
Pass through Optimal Parameters
rmake the waveform of the shock response waveform of wavelet filter and wavelet function to be approached closely, the time domain that this process is referred to as wavelet filter is approached, and the shock response expression formula of the wavelet filter of acquisition is referred to as the time domain approximating function of wavelet filter.
In described step (2), described sampling obtains time domain Approximate Sequence, and the column criterion z that goes forward side by side converts the concrete steps obtaining wavelet filter z territory transport function and is:
1, sample to each ingredient in formula (1) (i.e. single order joint and second order joint time-domain expression), sampling should be carried out in accordance with sampling thheorem.By sampling operation, time domain approximating function, by discretize, becomes time domain Approximate Sequence, therefore comprises three kinds of sequences after formula (1) sampling
,
with
(in formula,
represent the parameter of being tried to achieve by step (1), n represents that sampled point is numbered, and T represents the sampling period).Standard z conversion is carried out to above-mentioned three kinds of sequences
（4），
（5） ，
（6），
In formula,
represent the parameter of being tried to achieve by step (1), n represents that sampled point is numbered, and T represents the sampling period.
2, then wavelet filter z territory transport function is obtained
（7），
In formula, M represents single order joint sum, and N represents second order joint sum; I and j represents subscript;
,
;
represent the parameter of being tried to achieve by step (1); T represents the sampling period;
represent single order joint z territory expression formula,
represent second order joint z territory expression formula.
The concrete grammar of described employing iir digital filter technology and Switched-Current Circuit comprehensive wavelet filter z territory transport function is:
1, iir digital filter technical design switching current single order joint and second order economize on electricity road is adopted.
First the single order joint in formula (7) is abbreviated as
（8），
In formula,
,
the parameter of single order joint z territory expression formula, contrast (8) formula and the single order joint z territory expression formula in (7), can try to achieve
,
:
,
（9），
In formula,
awith
brepresent the parameter of being tried to achieve by step (1), T represents the sampling period.
Correspondingly, the second order joint in formula (7) is abbreviated as
（10），
In formula,
,
,
,
the parameter of second order joint z territory expression formula, contrast (10) formula and the second order joint z territory expression formula in (7), can try to achieve
,
,
,
:
,
,
,
（11），
In formula,
represent the parameter of being tried to achieve by step (1), T represents the sampling period.
Adopt the switching current second order of iir digital filter technical design economize on electricity road to comprise four parameters, be respectively:
,
,
,
, wherein
c,
d, σ and
wthe parameter in wavelet filter time domain approximating function, σ >0,
tit is the sampling period.
Adopt iir digital filter technology, design switching current single order joint and second order economize on electricity road.The switching current single order economize on electricity road of design as shown in Figure 2.In Fig. 2, VDD represents power supply; J,
with
represent respectively size be 1,
with
current source;
represent input current signal;
represent output current signal; M1-M4 represents four N-type MOS transistor, and wherein the breadth length ratio of M1 and M2 is that the breadth length ratio of 1, M3 and M4 is respectively
with
,
with
it is the parameter of single order joint z territory expression formula; S1-S4 represents four switches;
f1 He
f2 is two-phase non-overlapp-ing clock, and switching current second order economize on electricity road as shown in Figure 3.In Fig. 3, VDD represents power supply; J, 2J,
,
,
with
represent respectively size be 1,2,
,
,
with
current source;
represent input current signal;
represent output current signal; M1-M13 represents 13 N-type MOS transistor, and wherein the breadth length ratio of M4, M8, M9 and M13 is respectively
,
,
with
(
,
,
with
the parameter of second order joint z territory expression formula), the breadth length ratio of all the other 8 MOS transistor is all 1; S1-S8 represents eight switches;
f1 He
f2 is two-phase non-overlapp-ing clock, and the switch in circuit is by two-phase non-overlapp-ing clock
f1 He
f2 control, and high level then switch closes, and low level then switch disconnects.Fig. 4 (a) and 4 (b) are the contracted notation on switching current single order economize on electricity road and second order economize on electricity road respectively.Fig. 4 (a) is with in 4 (b), and 1st z-Sect represents switching current single order economize on electricity road, and 2nd z-Sect represents switching current second order economize on electricity road;
represent input current signal;
represent output current signal;
f1 He
f2 is two-phase non-overlapp-ing clock; In Fig. 4 (a)
with
the parameter of single order joint z territory expression formula, in Fig. 4 (b)
,
,
with
it is the parameter of second order joint z territory expression formula.Circuit parameter is determined according to formula (9) and formula (11) respectively.Contrast existing single order economize on electricity road and biquadratic economize on electricity road and can find out that single order provided by the invention economize on electricity road and second order economize on electricity road have the following advantages: one is that circuit parameter is few.Single order economize on electricity road provided by the invention only has 2 parameters, and second order economize on electricity road only has four parameters, and existing single order joint and biquadratic economize on electricity road have 3 and 6 respectively.Two is that circuit parameter is more excellent.Single order economize on electricity road provided by the invention and second order economize on electricity road, most parameters is along with the sampling period
tbe reduced to exponential law decline, and existing single order joint and biquadratic economize on electricity road, most parameters is along with the sampling period
tbe reduced to square law decline.So the present invention (namely reduces the sampling period by improving sample frequency
t) improve the resolution of the shock response of wavelet filter, and circuit parameter can not be caused to become very little and make troubles to circuit layout design.Three is do not use bilinear z-transform, avoids fre-quency warpping effect.
2, based on above-mentioned switching current single order joint and second order joint circuit design wavelet filter.
Based on above-mentioned switching current single order joint and second order economize on electricity road, with the parallel-connection structure of iir digital filter for prototype, the circuit structure of the wavelet filter of design as shown in Figure 5.In Fig. 5, Current copier represents input current copy cell; 1st z-Sect represents switching current single order economize on electricity road, and 2nd z-Sect represents switching current second order economize on electricity road;
represent input current signal;
represent output current signal;
f1 He
f2 is two-phase non-overlapp-ing clock;
,
,
with
be circuit parameter, determine according to formula (9) and formula (11) respectively.
The inventive method is applicable to the Switched-Current Circuit design of arbitrary continuation wavelet filter.In order to the convenience illustrated, be described for Gauss wavelet design of filter below.Concrete implementation step as shown in Figure 1.
1, the time domain of Gauss wavelet is approached.
Yardstick be 1 Guass wavelet function time-domain expression be
（12），
In formula,
for wavelet function,
tfor time variable.In order to make signal reach the object of wavelet transformation by wavelet filter, turning operation being carried out to formula (12), obtains
（13）
Wave filter is causal system, and formula (13) is non-causal, in order to obtain causal system, needs to carry out time shift operation to formula (13).Consider Gauss wavelet the non-zero waveform major part of time domain drop on time shaft-2 to 2 between, so determine time shift amount
t 0=2, obtain the Guass wavelet function after upset and time shift
（14），
Here illustrate for five approaching of rank Gauss wavelet wave filter.According to formula (1), determine that the time domain approximating function formula of five rank Gauss wavelet wave filters is
（15），
In formula,
for parameter to be asked; T represents the time, and for meeting the causality of wavelet filter, t should be greater than 0; In addition, in formula, r represents parameter vector, namely
r = [
] （16），
Because Gauss wavelet non-zero waveform length is on a timeline about 4, choose upper limit of integral here
=8, following five rank Gauss wavelet filter approximating Optimized models can be determined according to formula (3)
（17），
In formula, min represents the minimum value of getting e (r); S.t. represent that constraint condition meets; 8 represent upper limit of integral;
constraint condition, for guaranteeing the stability of wavelet filter.
Formula (17) is the optimization problem of one 10 dimension.Adopt a kind of Hybrid Particle Swarm of improvement to ask the optimum solution of formula (17), obtain one group of optimization solution, in table 1.
Table 1: the parameter of five rank Gauss wavelet filter time domain approximating functions
| Parameter name | Numerical value | Parameter name | Numerical value |
| a 1 | 1.63392 | b 1 | 0.77196 |
| c 1 | 1.53867 | c 2 | -4.21959 |
| d 1 | -0.48089 | d 2 | -1.13874 |
| s 1 | 0.75654 | s 2 | 0.84798 |
| ω 1 | 2.81685 | ω 2 | 1.41441 |
Have found optimized parameter, namely the time domain time domain approximating function of five rank Gauss wavelet wave filters is
（18），
In formula (18), t is time variable.
2, carry out standard z conversion and obtain wavelet filter z territory transport function.
Frequency band range due to Gauss wavelet is 0 to arrive
between rad, according to sampling thheorem, the sampling period
tshould 0.5s be less than, select here
t=0.05s carries out sampling to formula (18) and obtains time domain Approximate Sequence.Then time domain Approximate Sequence operative norm z is converted to the z territory transport function obtaining following five rank Gauss wavelet wave filters
（19），
The z territory transport function of above-mentioned five rank Gauss wavelet wave filters is saved by a single order and two second orders joints form, and each joint and overall shock response ideal waveform are as shown in Figure 7.The shock response ideal waveform that Fig. 7 (a) saves for single order, Fig. 7 (b) is the shock response ideal waveform of first second order joint, Fig. 7 (c) is the shock response ideal waveform of second second order joint, and Fig. 7 (d) is the shock response ideal waveform of above-mentioned five rank Gauss wavelet overall filter.The waveform of the shock response waveform of the five rank Gauss wavelet wave filters obtained as seen by Fig. 7 (d) closely Gauss wavelet, square error (MSE) reaches 2.75 × 10
-4, illustrate that Approximation effect is splendid.
3, comprehensive wavelet filter z territory transport function.
Based on switching current single order economize on electricity road provided by the invention and second order economize on electricity road, adopt the wavelet filter circuit structure shown in Fig. 5, to the z territory transport function of the five rank Gauss wavelet wave filters obtained
h(
z) carry out circuit synthesis, obtain switching current five rank Gauss wavelet filter circuit as shown in Figure 6, comprising three building blocks, i.e. 1 single order economize on electricity road and 2 second order economize on electricity roads.Parameter in circuit calculates according to formula (9) and formula (11) and obtains, and parameter value is in table 2.Circuit has 10 parameters, is realized respectively by the breadth length ratio (W/L) of these 10 metal-oxide-semiconductors of the M0 to M9 in circuit.10 circuit parameters obtained are relatively more even, do not have to occur very little parameter, are beneficial to the layout design of circuit.
In order to verify the performance of designed wavelet filter circuit, ASIZ switching current simulation software is adopted to emulate here.Emulation is arranged: the input stimulus electric current of circuit is 1mA, and output resistance is 1 Ω, and switch clock frequency is 1.First respectively joint each in circuit is emulated, then integrated circuit is emulated.The switching current five rank Gauss wavelet filter circuit obtained respectively save and overall shock response simulation waveform as shown in Figure 8.Fig. 8 (a) is the shock response simulation waveform on single order economize on electricity road, Fig. 8 (b) is the shock response simulation waveform on first second order economize on electricity road, Fig. 8 (c) is the shock response simulation waveform on second second order economize on electricity road, and Fig. 8 (d) is the shock response simulation waveform of switching current five rank Gauss wavelet filter circuit entirety.Contrast ideal waveform (as shown in Figure 7), each building block of known designed switching current five rank Gauss wavelet filter circuit is working properly, and overall performance is outstanding.
As shown in Figure 9, visible all limits are positioned at unit circle to the pole-zero plot of the switching current five rank Gauss wavelet filter circuit of design, and therefore, designed switching current Gauss wavelet filter circuit is stable.
Comprehensive above-mentioned simulation result and analysis show, adopt the present invention to design the advantage that switching current wavelet filter has following several respects.1, design procedure is simplified.Only take territory approach, sample and standard z conversion, design wavelet filter circuit three steps.2, do not need to carry out pre-warping compensation deals.Because the present invention adopts standard z to convert, there is no fre-quency warpping effect, without the need to carrying out pre-warping compensation deals.3, circuit parameter is improved.Single order economize on electricity road provided by the invention and biquadratic economize on electricity road have the few advantage of parameter, and most parameters is along with the sampling period
tbe reduced to exponential law decline, and existing single order joint and biquadratic economize on electricity road, most parameters is along with the sampling period
tbe reduced to square law decline.So the present invention (reduces the sampling period by improving sample frequency
t) measure improve the resolution of wavelet filter shock response, and circuit parameter can not be caused to become very little and make troubles to circuit layout design.
Claims (4)
1. a switching current method for designing wavelet filter, is characterized in that, comprises the following steps: (1) adopts time domain approach method to obtain the time domain approximating function of wavelet filter; (2) sampling obtains time domain Approximate Sequence, then carries out standard z conversion acquisition wavelet filter z territory transport function; (3) iir digital filter technology and Switched-Current Circuit comprehensive wavelet filter z territory transport function is adopted.
2. switching current method for designing wavelet filter according to claim 1, it is characterized in that, in described step (3), the concrete grammar of described employing iir digital filter technology and Switched-Current Circuit comprehensive wavelet filter z territory transport function is: (1) adopts iir digital filter technical design switching current single order economize on electricity road and second order economize on electricity road; (2) according to described switching current single order economize on electricity road and second order joint circuit design wavelet filter.
3. switching current method for designing wavelet filter according to claim 2, is characterized in that, in described step (3), when adopting the switching current single order economize on electricity road of iir digital filter technical design, relates generally to two parameters, respectively:
,
, wherein
awith
bthe parameter in wavelet filter time domain approximating function,
b>0,
tit is the sampling period.
4. switching current method for designing wavelet filter according to claim 2, is characterized in that, when adopting the switching current second order economize on electricity road of iir digital filter technical design, relates generally to four parameters, is respectively:
,
,
,
, wherein
c,
d, σ and
wthe parameter in wavelet filter time domain approximating function, σ >0,
tit is the sampling period.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201310111167.0A CN103177161B (en) | 2013-04-02 | 2013-04-02 | A kind of switching current method for designing wavelet filter |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201310111167.0A CN103177161B (en) | 2013-04-02 | 2013-04-02 | A kind of switching current method for designing wavelet filter |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN103177161A CN103177161A (en) | 2013-06-26 |
| CN103177161B true CN103177161B (en) | 2015-09-16 |
Family
ID=48637017
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201310111167.0A Active CN103177161B (en) | 2013-04-02 | 2013-04-02 | A kind of switching current method for designing wavelet filter |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN103177161B (en) |
-
2013
- 2013-04-02 CN CN201310111167.0A patent/CN103177161B/en active Active
Non-Patent Citations (2)
| Title |
|---|
| Analog Implementation of Wavelet Transform in Switched-Current Circuits with High Approximation Precision and Minimum Circuits Coefficients;Yaonan Tong,et al.;《Circuits Syst Signal Process》;20140831;第33卷(第8期);2333-2361 * |
| 一种改进的开关电流滤波器实现小波变换的方法;赵文山等;《物理学报》;20090228;第58卷(第2期);843-851 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN103177161A (en) | 2013-06-26 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN105099200B (en) | The double active bridge DC converter exchange phasor analysis of phase shifting control and modeling method | |
| CN103257271A (en) | Device and method for detecting micro grid harmonic wave and inter-harmonics based on STM32F107VCT6 | |
| CN108229021B (en) | Blocking modeling method of modular multilevel converter based on real-time digital simulator | |
| CN107168100A (en) | A kind of modularization multi-level converter real-time simulation modeling method based on field programmable gate array | |
| CN107241107A (en) | A kind of digital channelizing wave filter group implementation method | |
| CN103296885B (en) | Pulse width modulation (PWM) power converter analog simulation circuit and simulation method | |
| CN105515430A (en) | Control method of three-phase grid-connected inverter | |
| CN110518801A (en) | A kind of lower pair of active full-bridge converter Approach for Modeling of Small-Signal of dual phase shift modulation | |
| CN110635471A (en) | Transformer area power grid theoretical line loss calculation method based on simultaneous section power and electric quantity | |
| CN105631105A (en) | Cable equivalent circuit modeling method containing applied field coupling | |
| CN106886617A (en) | A kind of multi tate electro-magnetic transient subnetting method containing many VSC | |
| CN110532587A (en) | A kind of lower pair of active full-bridge converter large signal modeling method of dual phase shift modulation | |
| CN207882790U (en) | A kind of short circuit current MPPT maximum power point tracking circuit | |
| CN102419785A (en) | Method for designing wavelet filter | |
| CN103177161B (en) | A kind of switching current method for designing wavelet filter | |
| CN102176214B (en) | Method for designing wavelet filter by means of switching current and adaptive chaotic differential evolution | |
| CN101944891B (en) | Switching current technology-based analog continuous wavelet transform circuit | |
| CN110365314A (en) | The design method of separable Two dimensional FIR Filter with sparse coefficient | |
| CN105608256A (en) | Parallel computing network division method capable of absorbing interface delays of different step lengths | |
| CN109033560A (en) | A kind of emulation mode of power electronic circuit | |
| CN203151447U (en) | Current mode five step Marr wavelet filter circuit | |
| CN101267208B (en) | A simulation low-pass filter | |
| CN102946239B (en) | Design method of multi-ring feedback wavelet filter for switching current-fused negative phase differentiator | |
| CN110378020B (en) | Multi-frequency-band dynamic phasor electromagnetic transient simulation method and system for power grid commutation converter | |
| CN103902769A (en) | Model order reduction method of asymptotic waveform estimation algorithm |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| C14 | Grant of patent or utility model | ||
| GR01 | Patent grant |