CN102082559B - Method for realizing linear phase IIR (infinite impulse response) filter - Google Patents
Method for realizing linear phase IIR (infinite impulse response) filter Download PDFInfo
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Abstract
The invention discloses a method for realizing a linear phase IIR (infinite impulse response) filter, and the method comprises the following steps: dividing isometric segments and performing time reversal; inversely filtering after prolonging zero input; and performing time reversal again and carrying out forward filtering and the like. By utilizing the method, an infinite continuous signal application in a real-time occasion can be met, the linear phase is realized while the calculation quantity is greatly reduced, the waveform distortion error is reduced, and a good amplitude-frequency characteristic is ensured.
Description
Technical field
The invention belongs to a kind of implementation method of signal process field, particularly Linear phase IIR Digital Filters.
Background technology
Exert an influence for fear of the acquisition and recording process of various interference to signal, filter generally need be set filtering is carried out in these interference.In actual filtering process, often wish not change waveform or reduce wave distortion, if thereby the filter of design linear phase response is arranged, then this can be their very Ideal Characteristics, can make wave distortion seldom.Design process at trapper also is like this.Usually the FIR filter is easy to satisfy linear phase characteristic, but suitable big of its amount of calculation; Arrowband power frequency notch filter with the design of simple integral coefficient method also can finely satisfy linear phase characteristic, but it has bigger time-delay, and can to require sample rate be the integral multiple of trap point, and this design to the different frequency bands trapper also is a restriction; And the IIR trapper of conventional method design can not have more accurate linear phase characteristic, because its zero point and limit can the mirror image symmetries, if require limit about mirror image symmetry at zero point, then limit can cause the filter instability in the outside of unit circle.
Improvement on the method was arranged afterwards, such as, realize the phase place equalization of IIR filtering by all-pass filter, but its amount of calculation increases to some extent also than traditional F IR filter sometimes; By ripple such as grade and maximally-flat group delay method design iir filter, but it does not have desirable amplitude-frequency characteristic; Report more traditional zero phase iir filter in addition, be to be combined by sequential counter-rotating and multichannel filtering, pass through recursive calculation, amplitude-frequency characteristic and linear phase have been kept, but it mainly is to reverse at finite length sequence, and oppositely IIR filtering can not real-time implementation, has limited the application of its occasion of having relatively high expectations in real-times such as continuous signals.
Summary of the invention
For addressing the above problem, the invention provides a kind of implementation method of Linear phase IIR Digital Filters, this method can satisfy the unlimited continuous signal of real-time occasion to be used, and reduces amount of calculation greatly when realizing linear phase, reduce the wave distortion error, guarantee good amplitude-frequency characteristic.
The technical scheme that the present invention adopts for its problem of solution is:
A kind of implementation method of Linear phase IIR Digital Filters may further comprise the steps:
(1) to obtaining x (n)={ x (0), x (1), x (2) after the sampling of endless continuous signal,, be divided into the isoplith that length is L according to sequential, isoplith is carried out the sequential counter-rotating successively, obtain after the counter-rotating a (n)=x (L-1) ..., x (0), x (2L-1) ..., x (L), x (3L-1) ..., x (2L), x (4L-1) ...;
(2) prolongation of L zero input is carried out in the fragment back that obtains after counter-rotating, the reverse iir filter of new segment utilization of the 2L length of gained carries out inverse filtering to prolonging afterwards, output fragment result adds back L filtering output response, i.e. y of a back fragment after the inverse filtering for preceding L filtering output response of current fragment
k=x
k L+ x
K+1 T, y wherein
kBe k the fragment of exporting after the inverse filtering, x
k LBe preceding L filtering output response of k fragment, x
K+1 TBe back L filtering output response of a fragment after k the fragment, the fragment output sequence of inverse filtering is f (n)={ y
0, y
1, y
2...;
(3) the resulting fragment output sequence of step (2) carries out the sequential counter-rotating according to the method for step (1) again;
(4) utilize the forward direction iir filter to carry out forward direction filtering the resulting fragment sequence of step (3), obtain exporting the result.
Wherein, described reverse iir filter is identical with the transfer function of forward direction iir filter.Further preferably, described reverse iir filter adopts 2 identical rank IIR Butterworth filters with the forward direction iir filter.
The method of sequential counter-rotating may further comprise the steps in the step (1):
A. a default length is the register of L, and the two ends of register are respectively first input/output terminal and second input/output terminal;
B. L the signal x (0) of first fragment of x (n) ..., x (L-1) deposits register in successively from first input/output terminal;
C. the L of first a fragment signal takes out successively from first input/output terminal and obtains x (L-1) ..., x (0), the L of second fragment signal x (L) ..., x (2L-1) deposits register in successively from second input/output terminal;
D. the L of second a fragment signal takes out successively from second input/output terminal and obtains x (2L-1) ..., x (L), L the signal x (2L) of the 3rd fragment ..., x (3L-1) deposits register in successively from first input/output terminal;
E. continue circulation according to above-mentioned steps.
The present invention is to carry out the sequential counter-rotating behind the isoplith again with division of signal, and the method for this counter-rotating can satisfy the application of wireless signal occasion, guarantees the real-time requirement; Handle the truncated error that the back causes at burst, the prolongation of zero input is carried out in the fragment back that the present invention obtains after counter-rotating, make the stack of the output after the adjacent segment inverse filtering as the inverse filtering output of current fragment, realize the compensation correction of fragment filtering truncated error, thereby reduce the wave distortion error; In addition, by transfer function is analyzed as can be known, the filter of making based on method of the present invention has good amplitude-frequency characteristic and linear phase characteristic, the implementation method of method of the present invention and FIR filter and realize that by all-pass filter the method for the phase place equalization of IIR filtering compares computation amount.
Description of drawings
The invention will be further described below in conjunction with drawings and Examples:
Fig. 1 is the system block diagram based on linear iir filter of the present invention;
Fig. 2 is for dividing the schematic diagram that isoplith carries out a kind of embodiment of sequential counter-rotating;
Fig. 3 is the schematic diagram of a kind of embodiment of inverse filtering output response;
Fig. 4 is the comparison diagram of a kind of conventional IIR trapper and linear iir filter amplitude-frequency characteristic of the present invention;
Fig. 5 is the phase characteristic figure of linear iir filter of the present invention;
Fig. 6 is that conventional IIR trapper and linear iir filter of the present invention are respectively to the characteristics of signals comparison diagram after the 50Hz signal filtering;
Fig. 7 carries out the effect of trap to the electrocardiosignal that has power frequency to disturb for linear iir filter of the present invention.
Embodiment
The implementation method of Linear phase IIR Digital Filters of the present invention comprises that dividing isoplith carries out carrying out steps such as inverse filtering, sequential counter-rotating again, forward direction filtering after sequential counter-rotating, the zero input prolongation.Describe in detail respectively below.
Step (1): divide isoplith and carry out the sequential counter-rotating.To obtain after the endless continuous signal sampling x (n)=x (0), x (1), x (2) ..., be divided into the isoplith that length is L according to sequential, isoplith is carried out the sequential counter-rotating successively.The method of this sequential counter-rotating generally adopts following steps:
A. a default length is the register of L, and the two ends of register are respectively first input/output terminal and second input/output terminal; B. L the signal x (0) of first fragment of x (n) ..., x (L-1) deposits register in successively from first input/output terminal; C. the L of first a fragment signal takes out successively from first input/output terminal and obtains x (L-1) ..., x (0), the L of second fragment signal x (L) ..., x (2L-1) deposits register in successively from second input/output terminal; D. the L of second a fragment signal takes out successively from second input/output terminal and obtains x (2L-1) ..., x (L), L the signal x (2L) of the 3rd fragment ..., x (3L-1) deposits register in successively from first input/output terminal; E. continue circulation according to above-mentioned steps.Obtain after the counter-rotating a (n)=x (L-1) ..., x (0), x (2L-1) ..., x (L), x (3L-1) ..., x (2L), x (4L-1) ....Utilize specific embodiment that above-mentioned inverting method carries out sequential counter-rotating with reference to Fig. 2, in this embodiment, the length L of register=5, the sequence that obtains after counter-rotating is a (n)={ x (4), x (3), x (2), x (1), x (0), x (9), x (8), x (7), x (6), x (5), x (14) ....As can be seen from the above, what sequential inverting method of the present invention can be unlimited continuously carries out the sequential counter-rotating to signal segment, can satisfy the unlimited continuous signal of real-time occasion and use.
Step (2): carry out inverse filtering after zero input prolongs.The prolongation of L zero input is carried out in the fragment back that obtains after counter-rotating, and the reverse iir filter of new segment utilization of the 2L length of gained carries out inverse filtering to prolonging afterwards.The transfer function of supposing reverse iir filter is H (z), the output y after the inverse filtering
k(n)=h (following formula carries out following formal argument for n) * x (n), the L-1 of kL≤n≤(k+1) wherein:
y
k(n)
=h(-n)*x(n)
=∑n+L?m=nx(m)h(n-m)
=∑(k+1)L-1?m=nx(m)h(n-m)+∑n+L?m=(k+1)Lx(m)h(n-m)
=h(-n)*x
k(n)+h(-n)*x
k+1(n)
Output fragment result exports back L filtering output response, the i.e. y that response adds a back fragment for preceding L filtering of current fragment after the inverse filtering as can be seen from the above equation
k=x
k L+ x
K+1 T, y wherein
kBe k the fragment of exporting after the inverse filtering, x
k LBe preceding L filtering output response of k fragment, x
K+1 TBe back L filtering output response of a fragment after k the fragment.The method of the output of the current fragment of effect as a result of this employing adjacent segment filtering output stack can be regarded as the compensation of error correction that produces in the step (1) signal subsection being blocked, and can reduce and eliminate circular error well.Fragment output sequence after zero input prolongation of process step (2) and inverse filtering are handled is f (n)={ y
0, y
1, y
2....Fig. 3 is the schematic diagram of a kind of embodiment of inverse filtering output response, the length L of each fragment in the present embodiment=5, and as can be seen from the figure, each fragment of inverse filtering output is obtained by two parts addition.
Step (3): the resulting fragment output sequence of step (2) is carried out the sequential counter-rotating according to the method for step (1) again.Fragment output sequence f (n)={ y
0, y
1, y
2..., be divided into the isoplith that length is L according to sequential, isoplith is carried out the sequential counter-rotating successively, obtain b (n)={ y after the counter-rotating
4, y
3, y
2, y
1, y
0, y
9, y
8, y
7, y
6, y
5, y
14....
Step (4): utilize the forward direction iir filter to carry out forward direction filtering the resulting fragment sequence of step (3), obtain exporting the result.As preferred embodiment, this forward direction iir filter is identical with the transfer function of reverse iir filter, and in general trapper system, this forward direction iir filter preferably adopts 2 identical rank IIR Butterworth filters with reverse iir filter.
With reference to Fig. 1, be the system block diagram based on linear iir filter of the present invention.The signal list entries is x (n), and output sequence is y (n), and the A of step of the present invention (1) in figure partly carries out, and the B of step (2) in figure partly carries out, and the C of step (3) in figure partly carries out, and the D of step (4) in figure partly carries out.The transfer function of supposing the reverse iir filter in the B part is H
a(z), the transfer function of the forward direction iir filter in the D part is H
b(z), the ssystem transfer function H of whole filter so
Eq(z)=H
b(z) H
a(z
-1) e
-jw (L-1)/2, the amplitude of system transter | H
Eq(z) |=| H
b(z) | * | H
a(z
-1) |, when the transfer function of reverse iir filter and forward direction iir filter is identical H (z), ssystem transfer function H
Eq(z)=H (z) H (z
-1) e
-jw (L-1)/2, amplitude | H
Eq(z) |=| H (z) |
2, namely the fading depth of system filter device is 2 times of filters H (z) fading depth.
With system's trapper example of removing the interference of 50Hz power frequency effect of the present invention is described below.The forward direction iir filter of wherein using and reverse iir filter all are 2 rank IIR Butterworth filters, and this filter adopts conventional IIR The design of notch method design, and cut-off frequency is respectively 48Hz and 52Hz.With reference to Fig. 4-Fig. 6, wherein Fig. 4 is the comparison diagram of conventional IIR trapper and system's amplitude-frequency characteristic, line 10 is the amplitude-versus-frequency curve of conventional IIR trapper H (z), line 20 is the amplitude-versus-frequency curve of system, as can be seen from the figure, system is better than conventional IIR trapper to the attenuating of 50Hz power frequency.Fig. 5 is the phase characteristic figure of system, and as can be seen from the figure, the phase characteristic of system is linear.Fig. 6 is that conventional IIR trapper and system filter device are respectively to the characteristics of signals comparison diagram after the 50Hz signal filtering, amplitude is carried out filtered signal near 0.02 part for utilizing conventional IIR trapper among the figure, amplitude is significantly smaller than 0.005 and carries out filtered signal near the part at zero point for utilizing native system, as can be seen from the figure, native system is far superior to conventional IIR trapper to the filtration result of 50Hz power frequency interference signals.In addition, experiment shows that further native system is compared with conventional IIR trapper, and square wave overshoot concussion and wave distortion error that it causes when square wave is carried out filtering can be littler.
The present invention can be applied to the processing aspect to electrocardiosignal.Utilizing filter of the present invention that the electrocardiosignal that has power frequency to disturb is carried out the effect of trap can be with reference to Fig. 7, wherein the grey lines M among the figure is original output signal, black line N is the filtered signal of process, as we know from the figure, power frequency ripple through signal original after the filtering is eliminated substantially, and the electrocardiosignal of exporting is cleaner more directly perceived.
Claims (3)
1. a kind of implementation method of Linear phase IIR Digital Filters is characterized in that may further comprise the steps:
(1) to obtaining x (n)={ x (0), x (1), x (2) after the sampling of endless continuous signal,, be divided into the isoplith that length is L according to sequential, isoplith is carried out the sequential counter-rotating successively, obtain after the counter-rotating a (n)=x (L-1) ..., x (0), x (2L-1) ..., x (L), x (3L-1) ..., x (2L), x (4L-1) ..., the method for sequential counter-rotating may further comprise the steps:
A. a default length is the register of L, and the two ends of register are respectively first input/output terminal and second input/output terminal;
B. L the signal x (0) of first fragment of x (n) ..., x (L-1) deposits register in successively from first input/output terminal;
C. the L of first a fragment signal takes out successively from first input/output terminal and obtains x (L-1) ..., x (0), the L of second fragment signal x (L) ..., x (2L-1) deposits register in successively from second input/output terminal;
D. the L of second a fragment signal takes out successively from second input/output terminal and obtains x (2L-1) ..., x (L), L the signal x (2L) of the 3rd fragment ..., x (3L-1) deposits register in successively from first input/output terminal;
E. continue circulation according to above-mentioned steps;
(2) prolongation of L zero input is carried out in the fragment back that obtains after counter-rotating, the reverse iir filter of new segment utilization of the 2L length of gained carries out inverse filtering to prolonging afterwards, output fragment result adds back L filtering output response, i.e. y of a back fragment after the inverse filtering for preceding L filtering output response of current fragment
k=x
k L+ x
K+1 T, y wherein
kBe k the fragment of exporting after the inverse filtering, x
k LBe preceding L filtering output response of k fragment, x
K+1 TBe back L filtering output response of a fragment after k the fragment, the fragment output sequence of inverse filtering is f (n)={ y
0, y
1, y
2...;
(3) the resulting fragment output sequence of step (2) carries out the sequential counter-rotating according to the method for step (1) again;
(4) utilize the forward direction iir filter to carry out forward direction filtering the resulting fragment sequence of step (3), obtain exporting the result.
2. a kind of implementation method of Linear phase IIR Digital Filters according to claim 1 is characterized in that described reverse iir filter is identical with the transfer function of forward direction iir filter.
3. a kind of implementation method of Linear phase IIR Digital Filters according to claim 2 is characterized in that described reverse iir filter adopts 2 identical rank IIR Butterworth filters with the forward direction iir filter.
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|---|---|---|---|---|
| CN1408143A (en) * | 1999-10-04 | 2003-04-02 | 艾利森公司 | Simplified digital FIR filter for direct sequence spread spectrum communication system |
| CN1511374A (en) * | 2001-03-30 | 2004-07-07 | ض� | Two-dimensional pyramid filter architecture |
| CN101741350A (en) * | 2009-12-09 | 2010-06-16 | 北京天碁科技有限公司 | Method and device for compensating Infinite Impulse Response (IIR) filter in non-linear manner |
| CN101807902A (en) * | 2010-03-11 | 2010-08-18 | 复旦大学 | Complex coefficient linear-phase infinite impulse response digital filter |
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Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1408143A (en) * | 1999-10-04 | 2003-04-02 | 艾利森公司 | Simplified digital FIR filter for direct sequence spread spectrum communication system |
| CN1511374A (en) * | 2001-03-30 | 2004-07-07 | ض� | Two-dimensional pyramid filter architecture |
| CN101741350A (en) * | 2009-12-09 | 2010-06-16 | 北京天碁科技有限公司 | Method and device for compensating Infinite Impulse Response (IIR) filter in non-linear manner |
| CN101807902A (en) * | 2010-03-11 | 2010-08-18 | 复旦大学 | Complex coefficient linear-phase infinite impulse response digital filter |
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