CN110601678A - Method and device for realizing zero phase of IIR filter - Google Patents
Method and device for realizing zero phase of IIR filter Download PDFInfo
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- CN110601678A CN110601678A CN201910819813.6A CN201910819813A CN110601678A CN 110601678 A CN110601678 A CN 110601678A CN 201910819813 A CN201910819813 A CN 201910819813A CN 110601678 A CN110601678 A CN 110601678A
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- 238000000034 method Methods 0.000 title claims abstract description 27
- 238000001914 filtration Methods 0.000 claims abstract description 26
- 238000012546 transfer Methods 0.000 claims description 6
- 230000003321 amplification Effects 0.000 claims description 3
- 238000003199 nucleic acid amplification method Methods 0.000 claims description 3
- 230000010363 phase shift Effects 0.000 abstract description 28
- 238000012545 processing Methods 0.000 abstract description 18
- 230000009286 beneficial effect Effects 0.000 abstract 1
- 230000000694 effects Effects 0.000 description 6
- 238000010586 diagram Methods 0.000 description 4
- 230000018199 S phase Effects 0.000 description 3
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H17/00—Networks using digital techniques
- H03H17/02—Frequency selective networks
- H03H17/0202—Two or more dimensional filters; Filters for complex signals
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H17/00—Networks using digital techniques
- H03H17/02—Frequency selective networks
- H03H17/0283—Filters characterised by the filter structure
- H03H17/0286—Combinations of filter structures
- H03H17/0288—Recursive, non-recursive, ladder, lattice structures
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H17/00—Networks using digital techniques
- H03H2017/0072—Theoretical filter design
- H03H2017/009—Theoretical filter design of IIR filters
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
- Y02E40/40—Arrangements for reducing harmonics
Abstract
The application relates to a method and a device for realizing zero phase of an IIR filter, which are applied to a device provided with a first filter and a second filter, wherein the method comprises the following steps: inputting the continuous signal into the first filter for filtering to generate a first filtered signal; inputting the first filtering signal into the second filter for filtering, and generating and outputting a second filtering signal with a zero phase; wherein the phases of the first and second filters are symmetric up and down along the X-axis. The beneficial effects are that: the problem of phase distortion caused by the nonlinear phase of an IIR filter is solved, the problem of phase distortion of a sound frequency divider is solved, and the problem of phase distortion of audio and video signal processing is solved. The accuracy and the calculation efficiency of the zero phase shift filter are improved, the effective bandwidth of the zero phase shift filter is improved, and zero phase shift exists in the effective bandwidth of signals.
Description
Technical Field
The present application relates to the field of audio/video signal processing technologies, and in particular, to a method and an apparatus for implementing a zero phase in an IIR filter.
Background
At present, all frequency dividers of the sound equipment generate phase shift, so that harmonic waves and fundamental waves of music have different phases, some details of the music can be lost, and the fidelity is influenced. Patent application No. 2007100755694 "zero phase implementation method of IIR filter and zero phase IIR filter apparatus" requires dividing an input signal into N blocks, performing backward filtering, performing phase correction, and then performing forward filtering. Another patent application No. 2013106755763, "digital filtering processing method for an online zero-phase shift IIR digital filter", is similar, and the method is complex, delayed, distorted and limited in precision; is not suitable for real-time processing of audio and video continuous signals.
Disclosure of Invention
In order to solve the above technical problem, the present application provides a method for implementing a zero phase for an IIR filter, which is applied to a device provided with a first filter and a second filter, and includes:
inputting the continuous signal into the first filter for filtering to generate a first filtered signal;
inputting the first filtering signal into the second filter for filtering, and generating and outputting a second filtering signal with a zero phase;
wherein the phases of the first and second filters are symmetric up and down along the X-axis.
Optionally, when the first filter is a low-pass filter, the second filter may be a low-pass filter or an all-pass filter.
Optionally, when the first filter is a high-pass filter, the second filter may be a high-pass filter or an all-pass filter.
Optionally, the first filter and the second filter comprise at least one addition operation, at least one amplification operation, and at least one delay operation.
Optionally, the transfer function of the first filter is:
wherein a1, a2, b0, b1 and b2 are coefficients of the first filter.
Optionally, the transfer function of the second filter is:
wherein c1, c2, d0, d1 and d2 are coefficients of the second filter.
Optionally, the first filter and the second filter are IIR filters.
In addition, the present application also provides an apparatus for implementing a zero phase for an IIR filter, including a first filter and a second filter, the apparatus being configured to: transmitting an input signal into the first filter for filtering to generate a first signal; and transmitting the first signal into the second filter for filtering to generate a second signal.
Optionally, the first filter and the second filter each comprise at least one adder, at least one amplifier, and at least one delay.
The method and the device for realizing the zero phase of the IIR filter have the advantages that: the problem of phase distortion caused by the nonlinear phase of an IIR filter is solved, the problem of phase distortion of a sound frequency divider is solved, and the problem of phase distortion of audio and video signal processing is solved. The accuracy and the calculation efficiency of the zero phase shift filter are improved, the effective bandwidth of the zero phase shift filter is improved, and zero phase shift exists in the effective bandwidth of signals. This application simple structure, it is convenient to implement, the hardware requirement can support direct II type's IIR filter can, low time delay, continuous signal can real-time response, the accurate compensation of phase place, zero phase shift effect ideal. The method and the device have the advantages that the added calculation amount is small, and compared with the existing DSP digital signal frequency divider, the calculation amount of a second-order IIR filter is increased at most, and the calculation amount is extremely low. The method and the device can also be used for audio and video signal processing and other phase-sensitive signal processing.
Drawings
FIG. 1 is a signal flow diagram through a first filter and a second filter according to an embodiment of the present application;
fig. 2 is a schematic structural diagram of a first filter and a second filter according to an embodiment of the present application;
FIG. 3 is a Bode diagram of a first filter as a first order low pass filter according to an embodiment of the present application;
FIG. 4 is a Bode diagram of a second filter as a first order low pass filter according to an embodiment of the present application;
FIG. 5 is a Bode plot of the output signal through the first filter and the second filter according to an embodiment of the present application;
f1-the first filter, and F2 the second filter.
Detailed Description
The following detailed description of the preferred embodiments of the present application, taken in conjunction with the accompanying drawings, will make the advantages and features of the present application more readily appreciated by those skilled in the art, and thus will more clearly define the scope of the invention.
In an embodiment as shown in fig. 1, the present application proposes a method for an IIR filter to implement a zero phase, applied to an apparatus provided with a first filter and a second filter, the method including:
inputting the continuous signal into a first filter for filtering to generate a first filtered signal;
inputting the first filtering signal into a second filter for filtering, and generating and outputting a second filtering signal with a zero phase;
wherein the phases of the first filter and the second filter are vertically symmetric along the X-axis.
In one implementation of this embodiment, the continuous signal that is continuously input is filtered by the first filter and the second filter. The problem of phase distortion caused by the nonlinear phase of an IIR filter is solved, the problem of phase distortion of a sound frequency divider is solved, and the problem of phase distortion of audio and video signal processing is solved. The accuracy and the calculation efficiency of the zero phase shift filter are improved, the effective bandwidth of the zero phase shift filter is improved, and zero phase shift exists in the effective bandwidth of signals. This application simple structure, it is convenient to implement, the hardware requirement can support direct II type's IIR filter can, low time delay, continuous signal can real-time response, the accurate compensation of phase place, zero phase shift effect ideal. The method and the device have the advantages that the added calculation amount is small, and compared with the existing DSP digital signal frequency divider, the calculation amount of a second-order IIR filter is increased at most, and the calculation amount is extremely low. The method and the device can also be used for audio and video signal processing and other phase-sensitive signal processing.
In some embodiments, when the first filter is a low pass filter, the second filter may be a low pass filter or an all pass filter.
In one implementation of this embodiment, the first filter is a low-pass filter, and the second filter is a low-pass filter; the first filter and the second filter allow low-frequency or direct-current components in the signal to pass through, and suppress high-frequency components or interference and noise to play a role in filtering.
In another implementation manner of this embodiment, the first filter is a low-pass filter, and the second filter is an all-pass filter, because the first filter allows low-frequency or direct-current components in the signal to pass through, high-frequency components or interference and noise are suppressed; the second filter has no change in the amplitude of the signal over the full frequency band, i.e. the gain of the amplitude is constant equal to 1 over the full frequency band. Generally, an all-pass filter is used to shift the phase, i.e. to change the phase of the input signal, ideally with a corresponding change in phase shift and frequency exactly symmetrical to the phase shift of the first filter on the X-axis. After the continuous signal passes through the first filter to filter out the high-frequency component of the signal, the low frequency or direct current in the residual signal is only subjected to phase shifting through the second filter.
In some embodiments, when the first filter is a high pass filter, the second filter may be a high pass filter or an all pass filter.
In one implementation of this embodiment, the first filter is a high-pass filter, and the second filter is a high-pass filter; the first filter and the second filter allow high-frequency components in the signal to pass through and suppress low-frequency or direct-current components.
In another implementation manner of this embodiment, the first filter is a high-pass filter, and the second filter is an all-pass filter, since the first filter allows the high-frequency component in the allowed signal in the signal to pass through, and suppresses the low-frequency or direct-current component; the second filter has no change in the amplitude of the signal over the full frequency band, i.e. the gain of the amplitude is constant equal to 1 over the full frequency band. Generally, an all-pass filter is used to shift the phase, i.e. to change the phase of the input signal, ideally with a corresponding change in phase shift and frequency exactly symmetrical to the phase shift of the first filter on the X-axis. After the continuous signal passes through the first filter to filter out the low-frequency or direct-current component of the signal, the high-frequency component in the residual signal is only subjected to phase shifting through the second filter.
In some embodiments, referring to fig. 2, the first filter and the second filter comprise at least one addition operation, at least one amplification operation, and at least one delay operation.
In an implementation manner of this embodiment, the first filter and the second filter have the same structure, and the same structure adopts different coefficients; in this embodiment, the structure of the first filter and the second filter includes 4 adders, 2 retarders, and 5 amplifiers, and the connection relationship of the adders, the retarders, and the amplifiers is as shown in fig. 2.
In some embodiments, the transfer function of the first filter is:
wherein a1, a2, b0, b1 and b2 are coefficients of the first filter.
In one embodiment of the present embodiment, the adder, the delay and the amplifier are connected as shown in fig. 2; the structure of the first filter comprises 4 adders, 2 delayers and 5 amplifiers; the coefficients a1, a2, b0, b1 and b2 not only affect the phase, but also affect the amplitude, and also affect the filter properties, such as low-pass, high-pass, band-pass, all-pass, band-stop and so on; are important components of the filter.
In some embodiments, the transfer function of the second filter is:
wherein c1, c2, d0, d1 and d2 are coefficients of the second filter.
In one embodiment of the present embodiment, the adder, the delay and the amplifier are connected as shown in fig. 2; the structure of the second filter comprises 4 adders, 2 delayers and 5 amplifiers; the coefficients c1, c2, d0, d1 and d2 not only affect the phase, but also affect the amplitude, and also affect the filter properties, such as low-pass, high-pass, band-pass, all-pass, band-stop and so on; are important components of the filter.
In one implementation of the above embodiment, the first filter is a low-pass filter, and the second filter is a low-pass filter with a "mirror phase" corresponding to the first filter, where the mirror phase is a mirror plane of the first filter and the second filter with a zero degree phase X-axis, and the first filter and the second filter are vertically symmetrical, that is, the phases of the first filter and the second filter are vertically symmetrical along the X-axis.
In the present embodiment, the calculation formula of the coefficients of the first-order low-pass filter F1 and the first-order low-pass mirror phase filter F2 is:
a 1 = -(1-sinω0+cosω0) / (1+sinω0+cosω0);
a 2 = 0;
b 0 = sinω0 / (1+sinω0+cosω0) ;
b 1 = sinω0 / (1+sinω0+cosω0);
b 2 = 0;
c 1 = -(1+sinω0+cosω0) / (1-sinω0+cosω0);
c 2 = 0;
d 0 = -sinω0 / (1-sinω0+cosω0);
d 1 = -sinω0 / (1-sinω0+cosω0);
d 2 = 0;
wherein ,ω 0 is the cut-off angle frequency, f0 is the cut-off frequency, and Fs is the sampling frequency.
In this embodiment, in the first filter of the first-order low pass with a cutoff frequency of 1000Hz, when the sampling frequency Fs =48kHz, the coefficients of the first filter are:
a 1 = -0.876976462993;
a 2 = 0;
b 0 = 0.061511768504;
b 1 = 0.061511768504;
b 2 = 0;
coefficient of F2:
c 1 = -1.140281458168;
c 2 = 0;
d 0 = -0.070140729084;
d 1 = -0.070140729084;
d 2 = 0;
the bode plot of the first filter, fig. 3, the bode plot of the second filter, fig. 4, and the bode plot of the final signal output, fig. 5.
As shown in fig. 5, the amplitude-frequency characteristic of the output signal is a characteristic of a second-order low-pass filter, and is a superposition effect of two first-order low-pass filters, and the phase-frequency characteristic is a straight line with a zero-degree phase; from this embodiment can prove that this application has solved the problem that IIR filter nonlinear phase arouses phase distortion, has solved stereo set frequency divider phase distortion problem, has solved audio and video signal processing's phase distortion problem. The accuracy and the calculation efficiency of the zero phase shift filter are improved, the effective bandwidth of the zero phase shift filter is improved, and zero phase shift exists in the effective bandwidth of signals. This application simple structure, it is convenient to implement, the hardware requirement can support direct II type's IIR filter can, low time delay, continuous signal can real-time response, the accurate compensation of phase place, zero phase shift effect ideal. The method and the device have the advantages that the added calculation amount is small, and compared with the existing DSP digital signal frequency divider, the calculation amount of a second-order IIR filter is increased at most, and the calculation amount is extremely low. The method and the device can also be used for audio and video signal processing and other phase-sensitive signal processing.
In one implementation of the above embodiment, the first filter is a low-pass filter, and the second filter is a low-pass filter with a "mirror phase" corresponding to the first filter, where the mirror phase is a mirror plane of the first filter and the second filter with a zero degree phase X-axis, and the first filter and the second filter are vertically symmetrical, that is, the phases of the first filter and the second filter are vertically symmetrical along the X-axis.
The coefficients for the second-order low-pass filter F1 and the second-order low-pass mirror phase filter F2, a2, b2, c2, d2, are not zero; the higher order filters are implemented using a cascade of second order IIR filters.
In one implementation of the above embodiment, the first filter is a high-pass filter, and the second filter is a high-pass filter with a "mirror phase" corresponding to the first filter, where the mirror phase is a mirror plane of the first filter and the second filter with a zero degree phase X-axis, and the first filter and the second filter are vertically phase-symmetric, that is, the phases of the first filter and the second filter are vertically symmetric along the X-axis.
In the present embodiment, the calculation formula of the coefficients of the first-order high-pass filter F1 and the first-order high-pass mirror phase filter F2 is:
a 1 = -(1-sinω0+cosω0) / (1+sinω0+cosω0);
a 2 = 0;
b 0 = (1+ cosω0) / (1+sinω0+cosω0) ;
b 1 = -(1+ cosω0) / (1+sinω0+cosω0);
b 2 = 0;
c 1 = -(1+sinω0+cosω0) / (1-sinω0+cosω0);
c 2 = 0;
d 0 = (1+ cosω0) / (1-sinω0+cosω0);
d 1 = -(1+ cosω0) / (1-sinω0+cosω0);
d 2 = 0;
wherein ,ω 0 is the cut-off angle frequency, f0 is the cut-off frequency, and Fs is the sampling frequency.
In this embodiment, the first filter and the second filter of the high-pass filter are used, and the phase-frequency characteristics of the first filter and the second filter form a straight line with a zero-degree phase after passing through the first filter and the second filter. From this embodiment can prove that this application has solved the problem that IIR filter nonlinear phase arouses phase distortion, has solved stereo set frequency divider phase distortion problem, has solved audio and video signal processing's phase distortion problem. The accuracy and the calculation efficiency of the zero phase shift filter are improved, the effective bandwidth of the zero phase shift filter is improved, and zero phase shift exists in the effective bandwidth of signals. This application simple structure, it is convenient to implement, the hardware requirement can support direct II type's IIR filter can, low time delay, continuous signal can real-time response, the accurate compensation of phase place, zero phase shift effect ideal. The method and the device have the advantages that the added calculation amount is small, and compared with the existing DSP digital signal frequency divider, the calculation amount of a second-order IIR filter is increased at most, and the calculation amount is extremely low. The method and the device can also be used for audio and video signal processing and other phase-sensitive signal processing.
In some embodiments, the first filter and the second filter are IIR filters; in the present embodiment, the IIR filter is a recursive filter with feedback. The system function of the IIR filter may be a closed function, in this embodiment, the structure of the IIR filter is composed of basic operations such as a delay, an adder, and an amplifier, and the IIR filter may be combined into four structural forms of direct type, normal type, cascade type, and parallel type, and all have feedback loops.
In some embodiments, referring to fig. 1, the present application further provides an apparatus for an IIR filter to implement zero phase, comprising a first filter and a second filter, the apparatus configured to: transmitting an input signal into a first filter for filtering to generate a first signal; and transmitting the first signal into a second filter for filtering to generate a second signal. The first filter and the second filter each comprise at least one adder, at least one amplifier and at least one delayer. In this embodiment, the structure of the first filter and the second filter includes 4 adders, 2 retarders, and 5 amplifiers, and the connection relationship of the adders, the retarders, and the amplifiers is as shown in fig. 2. From this embodiment can prove that this application has solved the problem that IIR filter nonlinear phase arouses phase distortion, has solved stereo set frequency divider phase distortion problem, has solved audio and video signal processing's phase distortion problem. The accuracy and the calculation efficiency of the zero phase shift filter are improved, the effective bandwidth of the zero phase shift filter is improved, and zero phase shift exists in the effective bandwidth of signals. This application simple structure, it is convenient to implement, the hardware requirement can support direct II type's IIR filter can, low time delay, continuous signal can real-time response, the accurate compensation of phase place, zero phase shift effect ideal. The method and the device have the advantages that the added calculation amount is small, and compared with the existing DSP digital signal frequency divider, the calculation amount of a second-order IIR filter is increased at most, and the calculation amount is extremely low. The method and the device can also be used for audio and video signal processing and other phase-sensitive signal processing.
Finally, it should be noted that: the above-mentioned embodiments are only specific embodiments of the present application, and are used for illustrating the technical solutions of the present application, but not limiting the same, and the scope of the present application is not limited thereto, and although the present application is described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: any person skilled in the art can modify or easily conceive the technical solutions described in the foregoing embodiments or equivalent substitutes for some technical features within the technical scope disclosed in the present application; such modifications, changes or substitutions do not depart from the spirit and scope of the exemplary embodiments of the present application, and are intended to be covered by the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.
Claims (9)
1. A method for realizing zero phase by an IIR filter, which is applied to a device provided with a first filter and a second filter, the method comprising:
inputting the continuous signal into the first filter for filtering to generate a first filtered signal;
inputting the first filtering signal into the second filter for filtering, and generating and outputting a second filtering signal with a zero phase;
wherein the phases of the first and second filters are symmetric up and down along the X-axis.
2. The IIR filter implementation of claim 1, wherein when said first filter is a low pass filter, said second filter is a low pass filter or an all pass filter.
3. The IIR filter zero-phase method of claim 1, wherein when said first filter is a high-pass filter, said second filter is a high-pass filter or an all-pass filter.
4. The IIR filter of claim 1, wherein said first filter and said second filter operations include at least one addition operation, at least one amplification operation, and at least one delay operation.
5. The IIR filter zero-phase implementation method of claim 1, wherein the transfer function of said first filter is:
wherein a1, a2, b0, b1 and b2 are coefficients of the first filter.
6. The IIR filter zero-phase implementation method of claim 1, wherein said second filter has a transfer function of:
wherein c1, c2, d0, d1 and d2 are coefficients of the second filter.
7. The IIR filter zero-phase implementation method of claim 1, wherein said first filter and said second filter are IIR filters.
8. An apparatus for an IIR filter to achieve zero phase, comprising a first filter and a second filter, the apparatus configured to: transmitting an input signal into the first filter for filtering to generate a first signal; and transmitting the first signal into the second filter for filtering to generate a second signal.
9. The IIR filter zero-phase apparatus of claim 8, wherein said first and second filters each comprise at least one adder, at least one amplifier, and at least one delay.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN112244835A (en) * | 2020-09-16 | 2021-01-22 | 深圳数联天下智能科技有限公司 | Signal processing method and related device |
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| US5089981A (en) * | 1989-04-24 | 1992-02-18 | Audio Precision, Inc. | Hybrid form digital filter |
| US20040148322A1 (en) * | 2001-03-13 | 2004-07-29 | Eric Hertz | Radio reveiver |
| US20050168361A1 (en) * | 2003-12-18 | 2005-08-04 | Azizi Seyed A. | Sample rate converter |
| CN101361650A (en) * | 2007-08-07 | 2009-02-11 | 深圳市理邦精密仪器有限公司 | Zero phase implementation method of IIR filter and zero phase IIR fiter |
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- 2019-08-31 CN CN201910819813.6A patent/CN110601678B/en active Active
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5089981A (en) * | 1989-04-24 | 1992-02-18 | Audio Precision, Inc. | Hybrid form digital filter |
| US20040148322A1 (en) * | 2001-03-13 | 2004-07-29 | Eric Hertz | Radio reveiver |
| US20050168361A1 (en) * | 2003-12-18 | 2005-08-04 | Azizi Seyed A. | Sample rate converter |
| CN101361650A (en) * | 2007-08-07 | 2009-02-11 | 深圳市理邦精密仪器有限公司 | Zero phase implementation method of IIR filter and zero phase IIR fiter |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN112244835A (en) * | 2020-09-16 | 2021-01-22 | 深圳数联天下智能科技有限公司 | Signal processing method and related device |
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