Bewise Inc. www.tool-tool.com Reference source from the internet.
Jump to: navigation, search
An FIR filter
In electronics, computer science and mathematics, a digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal. This is in contrast to the other major type of electronic filter, the analog filter, which is an electronic circuit operating on continuous-time analog signals. An analog signal may be processed by a digital filter by first being digitized and represented as a sequence of numbers, then manipulated mathematically, and then reconstructed as a new analog signal (see digital signal processing). In an analog filter, the input signal is "directly" manipulated by the circuit.
A digital filter system usually consists of an analog-to-digital converter (to sample the input signal), a microprocessor (often a specialized digital signal processor), and a digital-to-analog converter. Software running on the microprocessor can implement the digital filter by performing the necessary mathematical operations on the numbers received from the ADC. In some high performance applications, an FPGA or ASIC is used instead of a general purpose microprocessor.
Digital filters may be more expensive than an equivalent analog filter due to their increased complexity, but they make practical many designs that are impractical or impossible as analog filters. Since digital filters use a sampling process and discrete-time processing, they experience latency (the difference in time between the input and the response), which is almost irrelevant in analog filters.
Digital filters are commonplace and an essential element of everyday electronics such as radios, cellphones, and stereo receivers.
Contents
[hide]
[edit] Characterization of digital filters
A digital filter is characterized by its transfer function, or equivalently, its difference equation. Mathematical analysis of the transfer function can describe how it will respond to any input. As such, designing a filter consists of developing specifications appropriate to the problem (for example, a second-order lowpass filter with a specific cut-off frequency), and then producing a transfer function which meets the specifications.
The transfer function for a linear, time-invariant, digital filter can be expressed as a transfer function in the Z-domain; if it is causal, then it has the form:
where the order of the filter is the greater of N or M. See Z-transform's LCCD equation for further discussion of this transfer function.
This form is for a recursive filter, which typically leads to infinite impulse response behaviour, but if the denominator is unity, then this is the form for a finite impulse response filter.
[edit] Analysis techniques
A variety of mathematical techniques may be employed to analyze the behaviour of a given digital filter. Many of these analysis techniques may also be employed in designs, and often form the basis of a filter specification.
Typically, one analyzes filters by calculating how the filter will respond to a simple input. One can then extend this information to visualize the filter's response to more complex signals.
[edit] Impulse response
The impulse response, often denoted H(z) or h(n) is a measurement of how a filter will respond to the Kronecker delta function. For example, given a difference equation, one would set x(0) = 1 and x(n) = 0 for n > 0 and evaluate. In the case of linear time-invariant FIR filters, the impulse response is exactly equal to the sequence of filter coefficients h(n) = bn. In general, the impulse response is a characterization of the filter's behaviour.
A plot of the impulse response will help to reveal how a filter will respond to a sudden, momentary disturbance.
[edit] Filter design
The design of digital filters is a deceptively complex topic[1]. Although filters are easily understood and calculated, the practical challenges of their design and implementation are significant and are the subject of much advanced research.
There are two categories of digital filter: the recursive filter and the nonrecursive filter. These are often referred to as infinite impulse response (IIR) filters and finite impulse response (FIR) filters, respectively[2].
[edit] Filter realization
After a filter is designed, it must be realized by developing a signal flow diagram that describes the filter in terms of operations on sample sequences.
A given transfer function may be realized in many ways. Consider how a simple expression such as ax + bx + c could be evaluated – one could also compute the equivalent x(a + b) + c. In the same way, all realizations may be seen as "factorizations" of the same transfer function, but different realizations will have different numerical properties. Specifically, some realizations are more efficient in terms of the number of operations or storage elements required for their implementation, and others provide advantages such as improved numerical stability and reduced round-off error. Some structures are more optimal for fixed-point arithmetic and others may be more optimal for floating-point arithmetic.
[edit] Direct Form I
A straightforward approach for IIR filter realization is Direct Form I, where the difference equation is evaluated directly. This form is practical for small filters, but may be inefficient and impractical (numerically unstable) for complex designs[3]. In general, this form requires 2N delay elements (for both input and output signals) for a filter of order N.
[edit] Direct Form II
The alternate Direct Form II only needs N delay units, where N is the order of the filter – potentially half as much as Direct Form I. The disadvantage is that Direct Form II increases the possibility of arithmetic overflow for filters of high Q or resonance.[4] It has been shown that as Q increases, the round-off noise of both direct form topologies increases without bounds.[5] This is because, conceptually, the signal is first passed through an all-pole filter (which normally boosts gain at the resonant frequencies) before the result of that is saturated, then passed through an all-zero filter (which often attenuates much of what the all-pole half amplifies).
[edit] Cascaded second-order sections
A common strategy is to realize a higher-order (greater than 2) digital filter as a cascaded series of second-order "biquadratric" (or "biquad") sections[6] (see digital biquad filter). Advantages of this strategy is that the coefficient range is limited. Cascading direct form II sections result in N delay elements for filter order of N. Cascading direct form I sections result in N+2 delay elements since the delay elements of the input of any section (except the first section) are a redundant with the delay elements of the output of the preceding section.
[edit] Difference equation
In discrete-time systems, the digital filter is often implemented by converting the transfer function to a linear constant-coefficient difference equation (LCCD) via the Z-transform. The discrete frequency-domain transfer function is written as the ratio of two polynomials. For example:
This is expanded:
and divided by the highest order of z:
The coefficients of the denominator, ak, are the 'feed-backward' coefficients and the coefficients of the numerator are the 'feed-forward' coefficients, bk. The resultant linear difference equation is:
![y[n] = -\sum_{k=1}^{N} a_{k} y[n-k] + \sum_{k=0}^{M} b_{k} x[n-k]](https://imageproxy.pixnet.cc/imgproxy?url=https://upload.wikimedia.org/math/7/5/5/7550fd7e8b5e1aa43d587ff986ef5238.png)
or, for the example:
![y[n] = x[n] + 2x[n-1] + x[n-2] - \frac{1}{4} y[n-1] + \frac{3}{8} y[n-2]](https://imageproxy.pixnet.cc/imgproxy?url=https://upload.wikimedia.org/math/9/9/7/997debf289db57393e914bf7af07674a.png)
This equation shows how to compute the next output sample, y[n], in terms of the past outputs, y[n − p], the present input, x[n], and the past inputs, x[n − p]. In this form, the filter is amenable to numerical simulation via straightforward iteration.
[edit] Other Forms
This section requires expansion.
Other forms include:
- Series/cascade[7]
- Parallel[7]
- Ladder form[7]
- Lattice form[7]
- Coupled normal form
- Multifeedback
- Analog-inspired forms such as Sallen-key and state variable filters
- Systolic arrays
[edit] Comparison of analog and digital filters
Digital filters are not subject to the component non-linearities that greatly complicate the design of analog filters. Analog filters consist of imperfect electronic components, whose values are specified to a limit tolerance (e.g. resistor values often have a tolerance of +/- 5%) and which may also change with temperature and drift with time. As the order of an analog filter increases, and thus its component count, the effect of variable component errors is greatly magnified. In digital filters, the coefficient values are stored in computer memory, making them far more stable and predictable.[8]
Because the coefficients of digital filters are definite, they can be used to achieve much more complex and selective designs – specifically with digital filters, one can achieve a lower passband ripple, faster transition, and higher stopband attenuation than is practical with analog filters. Even if the design could be achieved using analog filters, the engineering cost of designing an equivalent digital filter would likely be much lower. Furthermore, one can readily modify the coefficients of a digital filter to make an adaptive filter or a user-controllable parametric filter. While these techniques are possible in an analog filter, they are again considerably more difficult.
Digital filters can be used in the design of finite impulse response filters. Analog filters do not have the same capability, because finite impulse response filters require delay elements.
Digital filters rely less on analog circuitry, potentially allowing for a better signal-to-noise ratio. A digital filter will introduce noise to a signal during analog low pass filtering, analog to digital conversion, digital to analog conversion and may introduce digital noise due to quantization. With analog filters, every component is a source of thermal noise (such as Johnson noise), so as the filter complexity grows, so does the noise.
However, digital filters do introduce a higher fundamental latency to the system. In an analog filter, latency is often negligible; strictly speaking it is the time for an electrical signal to propagate through the filter circuit. In digital filters, latency is a function of the number of delay elements in the system.
Digital filters also tend to be more limited in bandwidth than analog filters. High bandwidth digital filters require expensive ADC/DACs and fast computer hardware for processing.
In very simple cases, it is more cost effective to use an analog filter. Introducing a digital filter requires considerable overhead circuitry, as previously discussed, including two low pass analog filters.
[edit] Types of digital filters
Many digital filters are based on the Fast Fourier transform, a mathematical algorithm that quickly extracts the frequency spectrum of a signal, allowing the spectrum to be manipulated (such as to create band-pass filters) before converting the modified spectrum back into a time-series signal.
Another form of a digital filter is that of a state-space model. A well used state-space filter is the Kalman filter published by Rudolf Kalman in 1960.
[edit] References
[edit] General
- A. Antoniou, Digital Filters: Analysis, Design, and Applications, New York, NY: McGraw-Hill, 1993.
- J. O. Smith III, Introduction to Digital Filters with Audio Applications, Center for Computer Research in Music and Acoustics (CCRMA), Stanford University, September 2007 Edition.
- S.K. Mitra, Digital Signal Processing: A Computer-Based Approach, New York, NY: McGraw-Hill, 1998.
- A.V. Oppenheim and R.W. Schafer, Discrete-Time Signal Processing, Upper Saddle River, NJ: Prentice-Hall, 1999.
- J.F. Kaiser, Nonrecursive Digital Filter Design Using the Io-sinh Window Function, Proc. 1974 IEEE Int. Symp. Circuit Theory, pp. 20-23, 1974.
- S.W.A. Bergen and A. Antoniou, Design of Nonrecursive Digital Filters Using the Ultraspherical Window Function, EURASIP Journal on Applied Signal Processing, vol. 2005, no. 12, pp. 1910-1922, 2005.
- T.W. Parks and J.H. McClellan, Chebyshev Approximation for Nonrecursive Digital Filters with Linear Phase, IEEE Trans. Circuit Theory, vol. CT-19, pp. 189-194, Mar. 1972.
- L. R. Rabiner, J.H. McClellan, and T.W. Parks, FIR Digital Filter Design Techniques Using Weighted Chebyshev Approximation, Proc. IEEE, vol. 63, pp. 595-610, Apr. 1975.
- A.G. Deczky, Synthesis of Recursive Digital Filters Using the Minimum p-Error Criterion, IEEE Trans. Audio Electroacoust., vol. AU-20, pp. 257-263, Oct. 1972.
- ^ M. E. Valdez, Digital Filters, 2001.
- ^ A. Antoniou, chapter 1
- ^ J. O. Smith III, Direct Form I
- ^ J. O. Smith III, Direct Form II
- ^ L. B. Jackson, "On the Interaction of Roundoff Noise and Dynamic Range in Digital Filters," Bell Sys. Tech. J., vol. 49 (1970 Feb.), reprinted in Digital Signal Process, L. R. Rabiner and C. M. Rader, Eds. (IEEE Press, New York, 1972).
- ^ J. O. Smith III, Series Second Order Sections
- ^ a b c d A. Antoniou
- ^ http://www.dspguide.com/ch21/1.htm
[edit] See also
[edit] External links
歡迎來到Bewise Inc.的世界，首先恭喜您來到這接受新的資訊讓產業更有競爭力，我們是提供專業刀具製造商，應對客戶高品質的刀具需求，我們可以協助客戶滿足您對產業的不同要求，我們有能力達到非常卓越的客戶需求品質，這是現有相關技術無法比擬的，我們成功的滿足了各行各業的要求，包括：精密HSS DIN切削刀具、協助客戶設計刀具流程、DIN or JIS 鎢鋼切削刀具設計、NAS986 NAS965 NAS897 NAS937orNAS907 航太切削刀具,NAS航太刀具設計、超高硬度的切削刀具、醫療配件刀具設計、複合式再研磨機、PCD地板專用企口鑽石組合刀具、NSK高數主軸與馬達、專業模具修補工具-氣動與電動、粉末造粒成型機、主機版專用頂級電桿、PCD V-Cut刀、捨棄式圓鋸片組、粉末成型機、主機版專用頂級電感、’汽車業刀具設計、電子產業鑽石刀具、木工產業鑽石刀具、銑刀與切斷複合再研磨機、銑刀與鑽頭複合再研磨機、銑刀與螺絲攻複合再研磨機等等。我們的產品涵蓋了從民生刀具到工業級的刀具設計；從微細刀具到大型刀具；從小型生產到大型量產；全自動整合；我們的技術可提供您連續生產的效能，我們整體的服務及卓越的技術，恭迎您親自體驗！！
BW Bewise Inc. Willy Chen willy@tool-tool.com bw@tool-tool.com www.tool-tool.com skype:willy_chen_bw mobile:0937-618-190 Head &Administration Office No.13,Shiang Shang 2nd St., West Chiu Taichung,Taiwan 40356 http://www.tool-tool.com / FAX:+886 4 2471 4839 N.Branch 5F,No.460,Fu Shin North Rd.,Taipei,Taiwan S.Branch No.24,Sec.1,Chia Pu East Rd.,Taipao City,Chiayi Hsien,Taiwan
Welcome to BW tool world! We are an experienced tool maker specialized in cutting tools. We focus on what you need and endeavor to research the best cutter to satisfy users’ demand. Our customers involve wide range of industries, like mold & die, aerospace, electronic, machinery, etc. We are professional expert in cutting field. We would like to solve every problem from you. Please feel free to contact us, its our pleasure to serve for you. BW product including: cutting tool、aerospace tool .HSS DIN Cutting tool、Carbide end mills、Carbide cutting tool、NAS Cutting tool、NAS986 NAS965 NAS897 NAS937orNAS907 Cutting Tools,Carbide end mill、disc milling cutter,Aerospace cutting tool、hss drill’Фрезеры’Carbide drill、High speed steel、Compound Sharpener’Milling cutter、INDUCTORS FOR PCD’CVDD(Chemical Vapor Deposition Diamond )’PCBN (Polycrystalline Cubic Boron Nitride) ’Core drill、Tapered end mills、CVD Diamond Tools Inserts’PCD Edge-Beveling Cutter(Golden Finger’PCD V-Cutter’PCD Wood tools’PCD Cutting tools’PCD Circular Saw Blade’PVDD End Mills’diamond tool. INDUCTORS FOR PCD . POWDER FORMING MACHINE ‘Single Crystal Diamond ‘Metric end mills、Miniature end mills、Специальные режущие инструменты ‘Пустотелое сверло ‘Pilot reamer、Fraises’Fresas con mango’ PCD (Polycrystalline diamond) ‘Frese’POWDER FORMING MACHINE’Electronics cutter、Step drill、Metal cutting saw、Double margin drill、Gun barrel、Angle milling cutter、Carbide burrs、Carbide tipped cutter、Chamfering tool、IC card engraving cutter、Side cutter、Staple Cutter’PCD diamond cutter specialized in grooving floors’V-Cut PCD Circular Diamond Tipped Saw Blade with Indexable Insert’ PCD Diamond Tool’ Saw Blade with Indexable Insert’NAS tool、DIN or JIS tool、Special tool、Metal slitting saws、Shell end mills、Side and face milling cutters、Side chip clearance saws、Long end mills’end mill grinder’drill grinder’sharpener、Stub roughing end mills、Dovetail milling cutters、Carbide slot drills、Carbide torus cutters、Angel carbide end mills、Carbide torus cutters、Carbide ball-nosed slot drills、Mould cutter、Tool manufacturer.
Bewise Inc. www.tool-tool.com
ようこそＢｅｗｉｓｅ Ｉｎｃ.の世界へお越し下さいませ、先ず御目出度たいのは新たな
情報を受け取って頂き、もっと各産業に競争力プラス展開。
弊社は専門なエンド・ミルの製造メーカーで、客先に色んな分野のニーズ、
豊富なパリエーションを満足させ、特にハイテク品質要求にサポート致します。
弊社は各領域に供給できる内容は：
（１）精密ＨＳＳエンド・ミルのＲ＆Ｄ
（２）Carbide Cutting tools設計
（３）鎢鋼エンド・ミル設計
（４）航空エンド・ミル設計
（５）超高硬度エンド・ミル
（６）ダイヤモンド・エンド・ミル
（７）医療用品エンド・ミル設計
（８）自動車部品＆材料加工向けエンド・ミル設計
弊社の製品の供給調達機能は：
（１）生活産業～ハイテク工業までのエンド・ミル設計
（２）ミクロ・エンド・ミル～大型エンド・ミル供給
（３）小Ｌｏｔ生産～大量発注対応供給
（４）オートメーション整備調達
（５）スポット対応～流れ生産対応
弊社の全般供給体制及び技術自慢の総合専門製造メーカーに貴方のご体験を御待ちしております。
Bewise Inc. talaşlı imalat sanayinde en fazla kullanılan ve üç eksende (x,y,z) talaş kaldırabilen freze takımlarından olan Parmak Freze imalatçısıdır. Çok geniş ürün yelpazesine sahip olan firmanın başlıca ürünlerini Karbür Parmak Frezeler, Kalıpçı Frezeleri, Kaba Talaş Frezeleri, Konik Alın Frezeler, Köşe Radyüs Frezeler, İki Ağızlı Kısa ve Uzun Küresel Frezeler, İç Bükey Frezeler vb. şeklinde sıralayabiliriz.
BW специализируется в научных исследованиях и разработках, и снабжаем самым высокотехнологичным карбидовым материалом для поставки режущих / фрезеровочных инструментов для почвы, воздушного пространства и электронной индустрии. В нашу основную продукцию входит твердый карбид / быстрорежущая сталь, а также двигатели, микроэлектрические дрели, IC картонорезальные машины, фрезы для гравирования, режущие пилы, фрезеры-расширители, фрезеры-расширители с резцом, дрели, резаки форм для шлицевого вала / звездочки роликовой цепи, и специальные нано инструменты. Пожалуйста, посетите сайт www.tool-tool.com для получения большей информации.
BW is specialized in R&D and sourcing the most advanced carbide material with high-tech coating to supply cutting / milling tool for mould & die, aero space and electronic industry. Our main products include solid carbide / HSS end mills, micro electronic drill, IC card cutter, engraving cutter, shell end mills, cutting saw, reamer, thread reamer, leading drill, involute gear cutter for spur wheel, rack and worm milling cutter, thread milling cutter, form cutters for spline shaft/roller chain sprocket, and special tool, with nano grade. Please visit our web www.tool-tool.com for more info.
![y[n] = {\sum_{k=0}^N} b_k \cdot x[n-k] - {\sum_{k=1}^M} a_k \cdot y[n-k]](https://imageproxy.pixnet.cc/imgproxy?url=https://upload.wikimedia.org/math/2/4/6/2464d0b9c1beb3b25b5359ccd12116e6.png)
![y[n] = b_0 \cdot x[n] + b_1 \cdot x[n-1] + b_2 \cdot x[n-2] + .... + b_N \cdot x[n-N] - a_1 \cdot y[n-1] - a_2 \cdot y[n-2] + .... + a_M \cdot y[n-M]](https://imageproxy.pixnet.cc/imgproxy?url=https://upload.wikimedia.org/math/5/2/8/5289f1a5e6d91364692acf470ef34bb1.png&width=597&height=15){kind=small}
ja 
kautta. Tärkeä erikoistapaus on se, jossa kertoimet 
LI2
[例題4-1]某電感器之電感量為15亨利,電流為4安培,
15
42=120(J)
:磁通量,韋伯(Wb)
:導磁係數, = o r
o=4
