CN106026970A - IIR (Infinite Impulse Response) digital filter construction method based on MATLAB - Google Patents
IIR (Infinite Impulse Response) digital filter construction method based on MATLAB Download PDFInfo
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- CN106026970A CN106026970A CN201610306888.0A CN201610306888A CN106026970A CN 106026970 A CN106026970 A CN 106026970A CN 201610306888 A CN201610306888 A CN 201610306888A CN 106026970 A CN106026970 A CN 106026970A
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- iir
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- impulse response
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H17/00—Networks using digital techniques
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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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Abstract
The invention discloses an IIR (Infinite Impulse Response) digital filter construction method based on MATLAB. In a modern digital communication system, most of original signals are complex mixed signals mixed with other signals, and thus, analysis on the original signals is carried out on the basis of a filter; and a digital filter generally completes analysis by numeric calculation, has no impedance matching problem, has high processing accuracy, is flexible, and can complete some special filtering functions which cannot be completed by an analog filter. Two types of digital filters, which respectively are an IIR filter and an FIR (Finite Impulse Response) filter, exist. According to the IIR digital filter construction method provided by the invention, the IIR digital filter can be simply, rapidly and conveniently produced; and moreover, the generated filter has high efficiency, high accuracy and a good filtering effect.
Description
Technical field
The present invention relates to wave filter building method, in particular it relates to a kind of iir digital filter based on MATLAB structure
Method.
Background technology
At present, in modern digital communication systems, mostly for being mixed with the complicated mixing of other signal in primary signal
Signal, so the analysis to primary signal is all based on wave filter and carries out.Digital signal actually uses Serial No. table
The signal shown, voice signal sampled and after quantifying the digital signal that obtains be an one-dimensional discrete time series, and image letter
Digital signal that is number sampled and that obtain after quantifying is a two-dimensional discrete spatial sequence.Digital Signal Processing is exactly to use numerical value meter
The method calculated carries out various process and signal is transformed into certain form suited the requirements Serial No..Such as: numeral is believed
Number through row filtering to limit his frequency band or filter noise and interference or they are separated with other signals, signal is carried out
Spectrum analysis or power spectrumanalysis, to understand the frequency spectrum composition of signal and then to be identified signal, carry out certain conversion to signal
It make it more appropriate to transmission storage and application encodes purpose reaching data compression etc. to signal.Digital filtering technique
It it is the important branch of Digital Signal Analysis, treatment technology.The either process of the acquisition of signal, transmission, or signal and exchange
All be unable to do without filtering technique, transmit its and efficient, flexible reliable to signals security it is critical that.In all of Department of Electronics
System uses the digital filter to be calculated that most technology is the most complicated.The good and bad quality directly determining product of digital filter.
Digital filter DF(Digital Filter) two classes can be divided into according to the time domain specification of its unit impulse response function: infinitely rush
Swash response IIR(Infinite Impulse Response) wave filter and finite impulse response FIR(Finite Impulse
Response) wave filter.Common iir filter structure is more complicated, and inefficient, filter effect is general.
Summary of the invention
It is an object of the invention to, for the problems referred to above, propose a kind of iir digital filter structure side based on MATLAB
Method, to realize structure efficiency height and the advantage of good wave filtering effect.
For achieving the above object, the technical solution used in the present invention is:
A kind of iir digital filter building method based on MATLAB, comprises the following steps:
The first step, provides yulewalk function in Calling MATLAB Matlab DSPToolBox, its call format is:
[b, a]=yulewalk(n, f, m)
Wherein n is the exponent number of given wave filter, and f is given Frequency point incremental vector, and m is the reason corresponding with frequency vector f
Thinking that amplitude is the most vectorial, m and f is identical dimension vector, and b, a are respectively molecule and the denominator polynomials system of filter
Number vector；
Second step, generates iir filter according to transmission function.
Further, the transmission function used in second step is:
, wherein h(n) and it is unit impulse response sequence, z is given number of planes
According to, b, a are respectively molecule and the denominator polynomials coefficient vector of filter, for transmission function.
Technical scheme has the advantages that
The structure filtered method of various embodiments of the present invention, by being then based on MATLAB and using specific function structured approach, permissible
More efficient stable structure wave filter.
Below by embodiment, technical scheme is described in further detail.
Detailed description of the invention
Hereinafter the preferred embodiments of the present invention are illustrated, it will be appreciated that preferred embodiment described herein is only used
In the description and interpretation present invention, it is not intended to limit the present invention.
A kind of iir digital filter building method based on MATLAB, comprises the following steps:
The first step, provides yulewalk function in Calling MATLAB Matlab DSPToolBox, its call format is:
[b, a]=yulewalk(n, f, m)
Wherein n is the exponent number of given wave filter, and f is given Frequency point incremental vector, and m is the reason corresponding with frequency vector f
Thinking that amplitude is the most vectorial, m and f is identical dimension vector, and b, a are respectively molecule and the denominator polynomials system of filter
Number vector；
Second step, generates iir filter according to transmission function.
Further, the transmission function used in second step is:
, wherein h(n) and it is unit impulse response sequence, z is given number of planes
According to, b, a are respectively molecule and the denominator polynomials coefficient vector of filter, for transmission function.
The general step designing digital filter in MATLAB has a lot, but the present invention is reduced to following two
Step: (1) changes the technical specification of the digital filter provided into the technology of simulation low-pass filter according to given well-behaved form
Index；(2) if its technical specification will be according to the technical specification after conversion when applying the exponent number of wave filter.
Using Impulse invariance procedure structure digital filter is a kind of feasible way, makes digital filtering specifically
Unit impulse response sequences h (n) of device imitates the unit impulse response ha(t of analog filter), it is necessary to systematic sampling its
The unit impulse response of analog filter, is the ha(t obtained) sample value just with h(n) equal, it may be assumed that
H(n)=ha(nT)
T is sampling period；
Relation between z-transform and the Laplace transform of analogue signal of the unit impulse response sequence obtained is:
This equation is a kind of by the method from s Planar Mapping to z-plane in system, is thus that we can allow numeral filter
The unit impulse response sequence of ripple device is run according to the impulse response sequence of analog filter.
It can be seen that analog filter is imitated in the unit impulse response that impulse response not political reform makes digital filter completely
Unit impulse response, namely time domain is approached well, and linear ω between analog frequency Ω and numerical frequency ω=
ΩT。
Use Bilinear transformation method efficient design can also go out iir digital filter, specifically comprise the following steps that
The design of the digital filter of z-plane is converted into the design of the equivalent simulation wave filter of s plane.Its relation is:
Bilinear transformation method overcomes the shortcoming of this multivalued mappings from s plane to z-plane of impulse response not political reform, and it can
To eliminate aliasing, let us is convenient to be used.The shortcoming that but he also has self, it is simply that can produce in conversion process
Give birth to nonlinear distortion, so we must carry out a certain degree of pre-corrected during design iir digital filter.
If the iir filter amplitude-frequency characteristic of design is more complicated, least square fitting can be used to give amplitude-frequency response,
The wave filter amplitude-frequency characteristic making design approaches desired frequency characteristic, and this method is referred to as the Direct Method of Design of iir filter.
Use this method then can to concretely comprise the following steps with the advantage of two kinds of methods of summary:
MATLAB Matlab DSPToolBox provide yulewalk function realize directly sending out design iir digital filter.It calls
Form is as follows:
[b, a]=yulewalk(n, f, m)
Wherein n is the exponent number of given wave filter, and f is given Frequency point incremental vector, and m is the reason corresponding with frequency vector f
Thinking that amplitude is the most vectorial, m and f is identical dimension vector, and b, a are respectively molecule and the denominator polynomials system of filter
Number vector.
The transmission the most following form of function of iir filter:
Wherein h(n) it is unit impulse response sequence, z is given panel data, and b, a are respectively the molecule of filter
With denominator polynomials coefficient vector, for transmission function.
Finally it is noted that the foregoing is only the preferred embodiments of the present invention, it is not limited to the present invention,
Although being described in detail the present invention with reference to previous embodiment, for a person skilled in the art, it still may be used
So that the technical scheme described in foregoing embodiments to be modified, or wherein portion of techniques feature is carried out equivalent.
All within the spirit and principles in the present invention, any modification, equivalent substitution and improvement etc. made, should be included in the present invention's
Within protection domain.
Claims (2)
1. an iir digital filter building method based on MATLAB, it is characterised in that comprise the following steps:
The first step, the yulewalk function provided in Calling MATLAB Matlab DSPToolBox, its call format is:
[b, a]=yulewalk(n, f, m)
Wherein n is the exponent number of given wave filter, and f is given Frequency point incremental vector, and m is the reason corresponding with frequency vector f
Thinking that amplitude is the most vectorial, m and f is identical dimension vector, and b, a are respectively molecule and the denominator polynomials system of filter
Number vector；Second step, generates iir filter according to transmission function.
Iir digital filter building method the most according to claim 1, the transmission function used in second step is:, wherein h(n) and it is unit impulse response sequence, z is given panel data, and b, a divide
Not Wei the molecule of filter and denominator polynomials coefficient vector, for transmission function.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN106921367A (en) * | 2017-03-03 | 2017-07-04 | 重庆湃芯微电子有限公司 | A kind of decimation filter of digital of sigma delta ADC |
| CN112866856A (en) * | 2020-12-31 | 2021-05-28 | 广州由我科技股份有限公司 | Design method, system and equipment of ANC noise reduction Bluetooth headset filter |
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|---|---|---|---|---|
| CN103777228A (en) * | 2014-02-26 | 2014-05-07 | 成都理工大学 | IIR filter-based Gaussian forming method for digital nuclear pulse signal |
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- 2016-05-11 CN CN201610306888.0A patent/CN106026970A/en active Pending
Patent Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103777228A (en) * | 2014-02-26 | 2014-05-07 | 成都理工大学 | IIR filter-based Gaussian forming method for digital nuclear pulse signal |
Non-Patent Citations (2)
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| 宗伟: "《信号与系统分析》", 1 November 2015 * |
| 栾颖: "《MATLAB R2013a基础与可视化编程》", 24 July 2014 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106921367A (en) * | 2017-03-03 | 2017-07-04 | 重庆湃芯微电子有限公司 | A kind of decimation filter of digital of sigma delta ADC |
| CN112866856A (en) * | 2020-12-31 | 2021-05-28 | 广州由我科技股份有限公司 | Design method, system and equipment of ANC noise reduction Bluetooth headset filter |
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Application publication date: 20161012 |