CN103177161A - Design method of switched current wavelet filter - Google Patents
Design method of switched current wavelet filter Download PDFInfo
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Abstract
The invention discloses a design method of a switched current wavelet filter. The design method comprises following steps of (1) adopting a time domain approximation method to obtain a time domain approximating function of a wavelet filter; (2) sampling to obtain a time domain approximation sequence, and conducting standard z conversion to obtain a z domain transfer function of the wavelet filter; and (3) adopting IIR digital filter technology and switched current circuit comprehensive wavelet filter z domain transfer function. With the method, laplace transformation does not need conducting, design steps are beneficial to simplifying, pre-warping compensation dealing does not need conducting, and the standard z conversion is adopted to replace bilinearity z conversion so as to be beneficial to avoiding a frequency warping effect; and the IIR digital filter technology is adopted to design a switched current first-section circuit and a switched current second-section circuit so as to be beneficial to reducing and improving circuit parameters, the circuit parameters are small and excellent, and most parameters are decreased in an index law mode along with decreasing of a sampling period T.
Description
Technical field
The invention belongs to the Electronics and Information Engineering field, relate to a kind of switching current method for designing wavelet filter.
Background technology
Wavelet transformation is with its good time-frequency local characteristics, is widely used in non-stationary and transient signal and processes, one of the most effective mathematical tool that has become now that each engineering field signal processes.Wavelet transformation can be realized also can realizing with hardware with software.Realize wavelet transformation with hardware, particularly realize with mimic channel that low in energy consumption owing to having, fireballing advantage is subject to more and more the attention.Mimic channel realizes that wavelet transformation can regard the linear combination of the yardstick wavelet filter different with displacement as, so the design of wavelet filter is the basis of realizing wavelet transformation.Switching current is a kind of novel analog current data sampling technology, and is compatible with Standard Digital CMOS, and having overcome switched capacitor technique needs the linear restriction that float electric capacity, has advantages 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.The switching current wavelet filter bank has the step of two keys, and the one, the approaching of wavelet filter, the 2nd, the circuit design of wavelet filter.Wavelet filter approaches and seeks in fact a shock response and wavelet function to be approached similar wave filter as much as possible.The wavelet filter approach method of having reported can be divided into time domain and approach with frequency domain and approach two classes.Typical frequency domain approximatioss has Pad é method and Maclaurin series approximatioss.Adopt Pad é method and Maclaurin series approximatioss to ask for the frequency domain transfer function approximation accuracy of wavelet filter not high, and can not guarantee that the frequency domain transfer function of the wavelet filter that obtains is stable.In addition, because the part small echo does not have clear and definite expression formula at frequency domain, so the frequency domain approach method is restricted.And that time domain approximate method has effect is directly perceived, and can guarantee the advantage that wavelet filter is stable, so time domain approximate method is the method that generally adopts.
At present, no matter be that time domain is approached or frequency domain approaches, be all finally in order to obtain a wavelet filter frequency domain transfer function H (s).If frequency domain approaches, can directly obtain frequency domain transfer function H (s), if time domain is approached, need time domain approximating function h (t) is obtained frequency domain transfer function H (s) by Laplace transform.Obtain frequency domain transfer function H (s) and adopt afterwards Switched-Current Circuit design wavelet filter, existing method for designing generally adopts traditional switching current single order joint and two second order economize on electricitys road.Be that 2011102989344 patent of invention " a kind of method for designing wavelet filter " adopts Maclaurin series that the wavelet frequency domain function is approached as the patent No., then adopt the biquadratic joint based on the switching current differentiator to design the wavelet filter of cascaded structure for elementary cell; The patent No. is that 2011100545508 patent of invention " switching current self-adaptation chaos differential evolution method for designing wavelet filter " adopts self-adaptation chaos differential evolution optimization algorithm to carry out the wavelet filter time domain to approach, then adopt Laplace transform to obtain the 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. is that 2010102503863 patent of invention " a kind of simulation continuous wavelet transform circuit based on switched current technique " adopts to save based on the single order joint of switched-current integrator and biquadratic and carries out filter synthesis.
There are several point defects in above-mentioned method for designing.1, design procedure is comparatively loaded down with trivial details.Take time domain approximate method as example, need through time domain approach, Laplace transform obtains frequency domain transfer function, bilinearity z conversion obtains z territory transport function, the comprehensive wavelet filter of switching current single order joint and biquadratic economize on electricity road.2, bilinearity z conversion causes frequency warpage effect.Existing switching current single order joint and the biquadratic road of economizing on electricity is for comprehensive frequency domain transfer function, derives out according to switched-capacitor circuit, wherein is implied with bilinearity z shift step, therefore easily bring frequency warpage effect, usually need to carry out pre-warp compensation.3, circuit parameter is undesirable.Traditional switching current single order saves and biquadratic is economized on electricity, and the road parameter is more, and most parameters dwindled and forms square-law and descend along with the sampling period of bilinearity z conversion, can cause circuit parameter very little, make troubles for 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 defects that existing method for designing exists, and a kind of switching current method for designing wavelet filter based on the iir digital filter technology is provided.The design procedure that the method can effectively be simplified the 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 the time domain approach method to obtain the time domain approximating function of wavelet filter; (2) sampling obtains the time domain Approximate Sequence, then carries out standard z conversion and obtain wavelet filter z territory transport function; (3) adopt iir digital filter technology and the comprehensive wavelet filter z of Switched-Current Circuit territory transport function.
In described step (1), when described employing time domain approach method obtains the time domain approximating function of wavelet filter, need at first wavelet function to be overturn and the time shift processing.It is the purpose that reaches wavelet transformation when making signal by wavelet filter that upset is processed.Described wavelet function is carried out the necessity that time shift processes is non-causal because of common wavelet function, can not directly realize by hardware circuit, makes wavelet function have causality so need be processed by time shift.The shock response expression formula h (r, t) of definition wavelet filter is
（1），
In formula, i and j represent subscript;
Expression single order joint time-domain expression,
Expression second order joint time-domain expression; M represents single order joint sum, and N represents second order joint sum, and M and N are determined by wavelet filter exponent number n, satisfy M+2N=n;
,
Be parameter to be asked, r=[
] be parameter vector to be asked; In order to guarantee the stability of wavelet filter, parameter here
With
Should be strictly greater than zero; T represents the time, and for satisfying the causality of wavelet filter, t should be greater than 0.
The shock response expression formula h (r, t) of wavelet filter and small echo to be approached
Error sum of squares be
In formula,
The expression norm square; R=[
] be parameter vector to be asked; T represents the time; The shock response expression formula of h (r, t) expression wavelet filter;
Represent wavelet function to be approached, by wavelet function
Pass through upset and time shift and obtain, in formula
t 0Expression time shift amount.
Formula (2) illustrates parameter
rChoose the approximation accuracy that has determined wavelet filter, parameter is chosen and properly can greatly be improved approximation accuracy.The small echo optimization model of determining according to wavelet filter shock response expression formula and the square error of wavelet function to be approached is
In formula, i and j represent subscript; Min represents to get the minimum value of e (r); S.t. represent that constraint condition meets;
The expression upper limit of integral is determined by the time domain width of small echo to be approached; Constraint condition:
Formula (3) is a typical nonlinear optimal problem, can adopt optimized algorithm to find the solution.
Pass through Optimal Parameters
rThe shock response waveform that makes wavelet filter is very approaching with the waveform of wavelet function to be approached, and this process is referred to as the time domain of wavelet filter and approaches, 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 the time domain Approximate Sequence, and the concrete steps that the column criterion of going forward side by side z conversion obtains wavelet filter z territory transport function are:
1, each ingredient in formula (1) (being single order joint and second order joint time-domain expression) is sampled, sampling should be carried out in accordance with sampling thheorem.By sampling operation, the time domain approximating function is become the time domain Approximate Sequence by discretize, therefore comprise three kinds of sequences after formula (1) sampling
,
With
(in formula,
The parameter that expression is tried to achieve by step (1), n represents the sampled point numbering, T represents the sampling period).Above-mentioned three kinds of sequences are carried out standard z conversion
In formula,
The parameter that expression is tried to achieve by step (1), n represents the sampled point numbering, T represents the sampling period.
2, then obtain wavelet filter z territory transport function
In formula, M represents single order joint sum, and N represents second order joint sum; I and j represent subscript;
,
The parameter that expression is tried to achieve by step (1); T represents the sampling period;
Expression single order joint z territory expression formula,
Expression second order joint z territory expression formula.
In described step (3), the concrete grammar of described employing iir digital filter technology and the comprehensive wavelet filter z of Switched-Current Circuit territory transport function is:
1, adopt iir digital filter technical design switching current single order joint and second order economize on electricity road.
First the joint of the single order in formula (7) is abbreviated as
（8），
In formula,
,
Be the parameter of single order joint z territory expression formula, the single order joint z territory expression formula in contrast (8) formula and (7) formula can be tried to achieve
,
:
In formula,
aWith
bParameter in the wavelet filter time domain approximating function that represents to try to achieve by step (1), T represents the sampling period.
Correspondingly, the joint of the second order in formula (7) is abbreviated as
In formula,
,
,
,
The parameter of second order joint z territory expression formula, the second order joint z territory expression formula in contrast (10) formula and (7) can be tried to achieve
,
,
,
:
,
,
,
（11），
In formula,
Parameter in the wavelet filter time domain approximating function that represents to try to achieve by step (1), T represents the sampling period.
When the switching current second order of employing iir digital filter technical design economizes on electricity the road, 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 the iir digital filter technology, design switching current single order joint and the second order road of economizing on electricity., the switch in circuit is by the two-phase non-overlapping clock
f1 He
f2 control, and high level switch is closed, and low level 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: the one, circuit parameter is few.Single order provided by the invention economize on electricity road only has 2 parameters, and second order economize on electricity road only has four parameters, and existing single order joint and the biquadratic road of economizing on electricity has respectively 3 and 6.The 2nd, circuit parameter is more excellent.Single order provided by the invention economize on electricity road and second order economize on electricity road, most parameters is along with the sampling period
TThe index law that is reduced to descend, and existing single order joint and the biquadratic road of economizing on electricity, most parameters is along with the sampling period
TThe square law that is reduced to descend.So the present invention can (namely reduce the sampling period by improving sample frequency
T) improve the resolution of the shock response of wavelet filter, and can not cause circuit parameter to become very little and make troubles to circuit layout design.The 3rd, do not use bilinearity z conversion, avoided frequency warpage effect.
2, according to above-mentioned switching current single order joint and second order economize on electricity road design wavelet filter.
Based on above-mentioned switching current single order joint and the second order road of economizing on electricity, take the parallel-connection structure of iir digital filter as prototype, the circuit structure of the wavelet filter of design.
The present invention than the beneficial effect that prior art exists is: use the present invention, do not need to carry out Laplace transform, be conducive to the simplified design step, only take that the territory is approached, sampling and standard z conversion, three steps of design wavelet filter circuit, do not need to carry out pre-warp compensation and process; Employing standard z conversion replaces bilinearity z conversion, is conducive to and avoids frequency warpage 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 reduce and improve circuit parameter, circuit parameter is few and excellent, and most parameters is along with the sampling period
TThe index law that is reduced to descend, and existing single order joint and the biquadratic road of economizing on electricity, most parameters is along with the sampling period
TThe square law that is reduced to descend.So the present invention can (namely reduce the sampling period by improving sample frequency
T) improve the resolution of wavelet filter shock response, and can not cause circuit parameter to become very little and bring difficulty to circuit layout design.
Description of drawings
Fig. 1 is switching current method for designing wavelet filter process flow diagram of the present invention;
Fig. 2 is switching current single order joint circuit diagram provided by the invention;
Fig. 3 is switching current second order joint circuit diagram provided by the invention;
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;
Fig. 7 (a) is the shock response ideal waveform of the single order joint of five rank Gauss wavelet wave filters of acquisition;
Fig. 7 (b) is the shock response ideal waveform of first second order joint of five rank Gauss wavelet wave filters of acquisition;
Fig. 7 (c) is the shock response ideal waveform of second second order joint of five rank Gauss wavelet wave filters of acquisition;
Fig. 7 (d) is the shock response ideal waveform of five rank Gauss wavelet overall filter;
Fig. 8 (a) is the shock response simulation waveform on the single order economize on electricity road of switching current five rank Gauss wavelet wave filters;
Fig. 8 (b) is the shock response simulation waveform on first second order economize on electricity road of switching current five rank Gauss wavelet wave filters;
Fig. 8 (c) is the shock response simulation waveform on second second order economize on electricity road of switching current five rank Gauss wavelet wave filters;
Fig. 8 (d) is the shock response simulation waveform of switching current five rank Gauss wavelet filter circuit integral body;
Fig. 9 is the switching current five rank Gauss wavelet filter circuit pole-zero plots that the present invention obtains.
Embodiment
The invention will be further described below in conjunction with accompanying drawing and example.
With reference to Fig. 1, a kind of switching current method for designing wavelet filter comprises the following steps: (1) adopts the time domain approach method to obtain the time domain approximating function of wavelet filter; (2) sampling obtains the time domain Approximate Sequence, then carries out standard z conversion and obtain wavelet filter z territory transport function; (3) adopt iir digital filter technology and the comprehensive wavelet filter z of Switched-Current Circuit territory transport function.
In described step (1), when described employing time domain approach method obtains the time domain approximating function of wavelet filter, need at first wavelet function to be overturn and the time shift processing.It is the purpose that reaches wavelet transformation when making signal by wavelet filter that upset is processed.Described wavelet function is carried out the necessity that time shift processes is non-causal because of common wavelet function, can not directly realize by hardware circuit, makes wavelet function have causality so need be processed by time shift.The shock response expression formula h (r, t) of definition wavelet filter is
（1），
In formula, i and j represent subscript;
Expression single order joint time-domain expression,
Expression second order joint time-domain expression; M represents single order joint sum, and N represents second order joint sum, and M and N are determined by wavelet filter exponent number n, satisfy M+2N=n;
,
Be parameter to be asked, r=[
] be parameter vector to be asked; In order to guarantee the stability of wavelet filter, parameter here
With
Should be strictly greater than zero; T represents the time, and for satisfying the causality of wavelet filter, t should be greater than 0.
The shock response expression formula h (r, t) of wavelet filter and small echo to be approached
Error sum of squares be
，
t>0 （2），
In formula,
The expression 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
Pass through upset and time shift and obtain, in formula
t 0Expression time shift amount.
Formula (2) illustrates parameter
rChoose the approximation accuracy that has determined wavelet filter, parameter is chosen and properly can greatly be improved approximation accuracy.The small echo optimization model of determining according to wavelet filter shock response expression formula and the square error of wavelet function to be approached is
In formula, i and j represent subscript; Min represents to get the minimum value of e (r); S.t. represent that constraint condition meets;
The expression upper limit of integral is determined by the time domain width of small echo to be approached; Constraint condition:
Pass through Optimal Parameters
rThe shock response waveform that makes wavelet filter is very approaching with the waveform of wavelet function to be approached, and this process is referred to as the time domain of wavelet filter and approaches, 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 the time domain Approximate Sequence, and the concrete steps that the column criterion of going forward side by side z conversion obtains wavelet filter z territory transport function are:
1, each ingredient in formula (1) (being single order joint and second order joint time-domain expression) is sampled, sampling should be carried out in accordance with sampling thheorem.By sampling operation, the time domain approximating function is become the time domain Approximate Sequence by discretize, therefore comprise three kinds of sequences after formula (1) sampling
,
With
(in formula,
The parameter that expression is tried to achieve by step (1), n represents the sampled point numbering, T represents the sampling period).Above-mentioned three kinds of sequences are carried out standard z conversion
（5） ，
In formula,
The parameter that expression is tried to achieve by step (1), n represents the sampled point numbering, T represents the sampling period.
2, then obtain wavelet filter z territory transport function
（7），
In formula, M represents single order joint sum, and N represents second order joint sum; I and j represent subscript;
,
The parameter that expression is tried to achieve by step (1); T represents the sampling period;
Expression single order joint z territory expression formula,
Expression second order joint z territory expression formula.
The concrete grammar of described employing iir digital filter technology and the comprehensive wavelet filter z of Switched-Current Circuit territory transport function is:
1, adopt iir digital filter technical design switching current single order joint and second order economize on electricity road.
First the joint of the single order in formula (7) is abbreviated as
In formula,
,
The parameter of single order joint z territory expression formula, the single order joint z territory expression formula in contrast (8) formula and (7) can be tried to achieve
,
:
In formula,
aWith
bThe parameter that expression is tried to achieve by step (1), T represents the sampling period.
Correspondingly, the joint of the second order in formula (7) is abbreviated as
In formula,
,
,
,
The parameter of second order joint z territory expression formula, the second order joint z territory expression formula in contrast (10) formula and (7) can be tried to achieve
,
,
,
:
In formula,
The parameter that expression is tried to achieve by step (1), T represents the sampling period.
Adopt the switching current second order economize on electricity road of iir digital filter technical design 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 the iir digital filter technology, design switching current single order joint and the second order road of economizing on electricity.The switching current single order of design economizes on electricity the road as shown in Figure 2.In Fig. 2, VDD represents power supply; J、
With
Represent respectively size be 1,
With
Current source;
The expression input current signal;
The expression 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
fThe 2nd, two-phase non-overlapping clock, switching current second order economize on electricity the 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;
The expression input current signal;
The expression 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
fThe 2nd, the two-phase non-overlapping clock, the switch in circuit is by the two-phase non-overlapping clock
f1 He
f2 control, and high level switch is closed, and low level switch disconnects.Fig. 4 (a) and 4 (b) are respectively the contracted notations on switching current single order economize on electricity road and second order economize on electricity road.In Fig. 4 (a) and 4 (b), 1st z-Sect represents that switching current single order economize on electricity road, 2nd z-Sect represent switching current second order economize on electricity road;
The expression input current signal;
The expression output current signal;
f1 He
fThe 2nd, the two-phase non-overlapping 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: the one, circuit parameter is few.Single order provided by the invention economize on electricity road only has 2 parameters, and second order economize on electricity road only has four parameters, and existing single order joint and the biquadratic road of economizing on electricity has respectively 3 and 6.The 2nd, circuit parameter is more excellent.Single order provided by the invention economize on electricity road and second order economize on electricity road, most parameters is along with the sampling period
TThe index law that is reduced to descend, and existing single order joint and the biquadratic road of economizing on electricity, most parameters is along with the sampling period
TThe square law that is reduced to descend.So the present invention can (namely reduce the sampling period by improving sample frequency
T) improve the resolution of the shock response of wavelet filter, and can not cause circuit parameter to become very little and make troubles to circuit layout design.The 3rd, do not use bilinearity z conversion, avoided frequency warpage effect.
2, based on above-mentioned switching current single order joint and second order economize on electricity road design wavelet filter.
Based on above-mentioned switching current single order joint and the second order road of economizing on electricity, take the parallel-connection structure of iir digital filter as prototype, the circuit structure of the wavelet filter of design as shown in Figure 5.In Fig. 5, Current copier represents the input current copy cell; 1st z-Sect represents that switching current single order economize on electricity road, 2nd z-Sect represent switching current second order economize on electricity road;
The expression input current signal;
The expression output current signal;
f1 He
fThe 2nd, the two-phase non-overlapping clock;
,
,
With
Be circuit parameter, determine according to formula (9) and formula (11) respectively.
The inventive method is fit to the Switched-Current Circuit design of arbitrary continuation wavelet filter.For the convenience that illustrates, the below describes as an example of the Gauss wavelet design of filter example.Concrete implementation step as shown in Figure 1.
1, the time domain of Gauss wavelet is approached.
Yardstick is that 1 Guass wavelet function time-domain expression is
In formula,
Be wavelet function,
tBe time variable.In order to make signal reach the purpose of wavelet transformation by wavelet filter, formula (12) is carried out turning operation, obtain
Wave filter is causal system, and formula (13) is non-causal, in order to obtain causal system, need 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 the time shift amount
t 0=2, obtain overturning and time shift Guass wavelet function afterwards
Here approaching as the example explanation take five rank Gauss wavelet wave filters.According to formula (1), determine that the time domain approximating function formula of five rank Gauss wavelet wave filters is
In formula,
Be parameter to be asked; T represents the time, and for satisfying the causality of wavelet filter, t should be greater than 0; In addition, in formula, r represents parameter vector, namely
r = [
] （16），
Because the length of Gauss wavelet non-zero waveform on time shaft is about 4, choose upper limit of integral here
=8, can determine following five rank Gauss wavelet filter approximating Optimized models according to formula (3)
In formula, min represents to get the minimum value of e (r); S.t. represent that constraint condition meets; 8 expression 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 improved Hybrid Particle Swarm to ask the optimum solution of formula (17), obtain one group of optimization solution, see Table 1.
Table 1: the parameter of five rank Gauss wavelet wave 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 |
Found optimized parameter, namely the time domain time domain approximating function of five rank Gauss wavelet wave filters is
In formula (18), t is time variable.
2, carry out standard z conversion and obtain wavelet filter z territory transport function.
Because the frequency band range of Gauss wavelet is 0 to arrive
Between rad, according to sampling thheorem, the sampling period
TShould less than 0.5s, select here
T=0.05s samples to formula (18) and obtains the time domain Approximate Sequence.Then time domain Approximate Sequence operative norm z conversion is obtained the z territory transport function of following five rank Gauss wavelet wave filters
The z territory transport function of above-mentioned five rank Gauss wavelet wave filters is comprised of a single order joint and two second orders joints, and the shock response ideal waveform of each joint and integral body as shown in Figure 7.Fig. 7 (a) is the shock response ideal waveform of single order joint, 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.Very near the waveform of Gauss wavelet, square error (MSE) has reached 2.75 * 10 by the shock response waveform of the visible five rank Gauss wavelet wave filters that obtain of Fig. 7 (d)
-4, illustrate that Approximation effect is splendid.
3, comprehensive wavelet filter z territory transport function.
Based on switching current single order provided by the invention economize on electricity road and second order economize on electricity road, adopts wavelet filter circuit structure shown in Figure 5, to the z territory transport function of five rank Gauss wavelet wave filters of acquisition
H(
z) carry out circuit synthesis, obtain switching current five rank Gauss wavelet filter circuits as shown in Figure 6, comprising three building blocks, i.e. 1 single order economize on electricity road and 2 second orders economize on electricity roads.Parameter in circuit is calculated acquisition according to formula (9) and formula (11), and parameter value sees Table 2.Circuit has 10 parameters, and the breadth length ratio (W/L) by these 10 metal-oxide-semiconductors of the M0 to M9 in circuit realizes respectively.10 circuit parameters that obtain are more even, do not have very little parameter to occur, are beneficial to the layout design of circuit.
In order to verify the performance of designed wavelet filter circuit, adopt ASIZ switching current simulation software to carry out emulation here.Emulation arranges: the input stimulus electric current of circuit is 1mA, and output resistance is 1 Ω, and the switch clock frequency is 1.First respectively each joint in circuit is carried out emulation, then integrated circuit is carried out emulation.The shock response simulation waveform of each joint of the switching current five rank Gauss wavelet filter circuits that obtain and integral body 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 integral body.Contrast ideal waveform (as shown in Figure 7), each building block of designed switching current five rank Gauss wavelet filter circuits is working properly as can be known, and overall performance is outstanding.
The pole-zero plot of the switching current five rank Gauss wavelet filter circuits of design as shown in Figure 9, visible all limits are positioned at unit circle, therefore, designed switching current Gauss wavelet filter circuit is stable.
Comprehensive above-mentioned simulation result and the analysis showed that adopts the present invention to design the switching current wavelet filter and has advantages of following several respects.1, simplified design procedure.Only take that the territory is approached, sampling and standard z conversion, three steps of design wavelet filter circuit.2, not needing to carry out pre-warp compensation processes.Because the present invention adopts standard z conversion, there is no frequency warpage effect, need not to carry out pre-warp compensation and process.3, improved circuit parameter.Single order provided by the invention economize on electricity road and biquadratic economize on electricity road have advantages of that parameter is few, and most parameters is along with the sampling period
TThe index law that is reduced to descend, and existing single order joint and the biquadratic road of economizing on electricity, most parameters is along with the sampling period
TThe square law that is reduced to descend.So the present invention can (reduce the sampling period by improving sample frequency
T) measure improve the resolution of wavelet filter shock response, and can not cause circuit parameter to become very little and design makes troubles to circuit layout.
Claims (4)
1. a switching current method for designing wavelet filter, is characterized in that, comprises the following steps: (1) adopts the time domain approach method to obtain the time domain approximating function of wavelet filter; (2) sampling obtains the time domain Approximate Sequence, then carries out standard z conversion and obtain wavelet filter z territory transport function; (3) adopt iir digital filter technology and the comprehensive wavelet filter z of Switched-Current Circuit territory transport function.
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 the comprehensive wavelet filter z of Switched-Current Circuit 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 economize on electricity road design wavelet filter.
3. switching current method for designing wavelet filter according to claim 2, is characterized in that, in described step (3), when the switching current single order of employing iir digital filter technical design economizes on electricity the road, relates generally to two parameters, is respectively:
,
, wherein
aWith
bThe parameter in wavelet filter time domain approximating function,
b0,
TIt is the sampling period.
4. switching current method for designing wavelet filter according to claim 2, is characterized in that, when the switching current second order of employing iir digital filter technical design economizes on electricity the road, 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.
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Non-Patent Citations (2)
| Title |
|---|
| YAONAN TONG,ET AL.: "Analog Implementation of Wavelet Transform in Switched-Current Circuits with High Approximation Precision and Minimum Circuits Coefficients", 《CIRCUITS SYST SIGNAL PROCESS》 * |
| 赵文山等: "一种改进的开关电流滤波器实现小波变换的方法", 《物理学报》 * |
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