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Anti-aliasing filter used in monitoring systems of

electrical equipmentTopic number: .

Do not indicate authors' names!

Abstract - Anti-aliasing filters are an important element indata acquisition systems. Mounted upstream of the analogue digital converter, they serve to limit the frequency spectrum ofthe input signal, to avoid overlapping signal spectra of the signalresulting from sampling, known as the refolding The obtainedcircuit has advantages of modularization design, strongtransplantation, and has widely use value and applicationprospect.

I. GENERALNOTIONSOFDATAACQUISITIONSYSTEMS

Data acquisition is the process of sampling signals that

measure real world physical conditions and converting the

resulting samples into digital numeric values that can be

manipulated by a computer. Data acquisition systems

(abbreviated with the acronym DAS or DAQ) typically

convert analog waveforms into digital values for processing.

Therefore a data acquisition system, is designed to measure

or generate physical signals, and for this purpose contains in

its structure a data acquisition board.

Acquisition board is often considered the entire system.

These include in sensors that convert physical parameters to

electrical signals, their construction conditioning signalequipment to convert sensor signals into a form that can be

converted to digital values; analog to digital converters

(CAN) and Digital Analogue (CNA), inputs and outputs (I /

O) Analog and Digital, count (count, time clock generators)

and DMA (Direct memory Access) memory units to transmit

data directly to the computer without using microprocessor.

The most important operation is the analog digital

conversion, made with one or more circuits, depending on the

type of application). Another often encountered operations in

such systems are sampling and temporary storing of taken

samples.

The sampling frequency is determined by: the frequencyspectrum of the input signals; speed of the A / D converter;

accuracy of required processing.

Information processing may consist of simple operations

(comparisons) to complicated mathematical processing

(integration, differentiation, mediation, Fourier transform

calculation, etc..).

II. THE SHANNONSAMPLINGTHEOREM

To analyze and synthesize a signal in the digital domain,

analog signals must be converted into digital signals through

the acquisition of "samples" at certain regular intervals.

This process, called sampling is accomplished by

"questioning" the analog signal at regular periods of time,

denoted Te (where Te is called the sampling period is theinverse of the sampling frequency, fe (fe = 1/Te)).

In mathematical form, a sample of a signal is obtained by

multiplying the signal with a unit step pulse.

To avoid loss of information in the process of sampling an

analog signal, the sampling frequency must be at least two

times the maximum frequency of the sampled signal.The consequences of sampling at a lower frequency that the

highest frequency of the signal, generates a phenomena

known as refolding (aliasing). This concept results from

misidentification of the required frequency for signal

reconstruction.

The Shannon sampling theorem introduced restrictions on

the frequency of sampled signal in time, f (t) as follows: To

reconstruct a signal f (t), it is necessary sampling at a rate

twice as high as the maximum signal frequency.

If Shannon's theorem is not respected, it may cause

interference with other frequencies that are not in the band of

interest regarding the analyzed signal(aliasing, mentionedabove).

The same unwanted phenomenon is met if a digital signal

contains frequencies higher than the Nyquist frequency

(where the Nyquist frequency is half the sampling frequency

fN=fe/2 ).In fact, the spectrum of an acquired signal is infinite width.

Although Shannon's sampling theorem respects, the

phenomenon of aliasing occurs (overlapping power spectrum

of the signal). For this it is necessary to filter the source

signal by placing a low-pass filter (filter guard) upstream of

the sampling device.

III. THEORETICALCONCEPTSABOUTFILTERS

In signal processing, a filter is a device or process that

removes from asignalsome unwanted component or feature,

this means removing somefrequenciesand not others in order

to suppress interfering signals and reduce background noise.

The main specific size filters are cut off frequency - the

frequency at which the amplitude of the output signal

represents 0.707 of the input signal amplitude, and band pass

- band between zero and cutoff frequency.

http://en.wikipedia.org/wiki/Signal_processinghttp://en.wikipedia.org/wiki/Signal_processinghttp://en.wikipedia.org/wiki/Signal_(electronics)http://en.wikipedia.org/wiki/Signal_(electronics)http://en.wikipedia.org/wiki/Signal_(electronics)http://en.wikipedia.org/wiki/Frequencyhttp://en.wikipedia.org/wiki/Frequencyhttp://en.wikipedia.org/wiki/Frequencyhttp://en.wikipedia.org/wiki/Signal_noisehttp://en.wikipedia.org/wiki/Signal_processinghttp://en.wikipedia.org/wiki/Signal_(electronics)http://en.wikipedia.org/wiki/Frequencyhttp://en.wikipedia.org/wiki/Signal_noise

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The frequency response can be classified into a number ofdifferentbandformsdescribing which frequencies the filter

passes (thepassband) and which it rejects (thestopband):

low-pass filter low frequencies are passed, high frequencies

are attenuated.High-pass filter high frequencies are passed,

low frequencies are attenuated. Band-pass filter only

frequencies in a frequency band are passed. Band-stop

filteror band-reject filter only frequencies in a frequencyband are attenuated. Notch filter rejects just one specific

frequency - an extreme band-stop filter. Comb filter has

multiple regularly spaced narrow passbands giving the

bandform the appearance of a comb.All-pass filter all

frequencies are passed, but the phase of the output is

modified.

Depending on the design of analog filters, they can be

classified: Passive filters consisting only of passive circuit

elements (resistors, coils, capacitors). The consequence of

such structures is that the amplitude of the signal at the output

of the filter may be greater than the amplitude of the input

signal (maximum value of the transfer function can not be

over-unit).Active filterwhich is a combination of passive andactive elements of the filter circuit (most of the time, the

operational amplifiers). The presence of active elements

ensure amplification of signals with frequencies in the

passband and improved filter characteristics.

Order filter is important for several reasons. It is directly

related to the number of components of the filter, and thus the

cost, size and complexity of the filter. Therefore, higher order

filters are more expensive, take up more space and are more

difficult to create. The main advantage of a high order filter is

that it will have greater attenuation slope from lower order

filters.

First and second order filters are building floors for higherorder filters.Even order filters contain two floors of the order

and odd order filters contain a floor plus first order.

Usually the amount of attenuation is expressed in dB. The

most common measure of attenuation is "dB / decade."

Maximum attenuation rate is 20 dB / decade for all pole filter,

low-pass filters and high-pass.

IV. MONITORINGELECTRICALDRIVESUSING PC DATAACQUISITIONSYSTEMSWITHANTIALISINGFILTERS

Real signals of voltage or current may contain higher

frequency spectral components that the Nyquist frequency,known as refolding effect, usually causing inaccurate

measurements.

The most simple and effective way of avoiding this

phenomena is to filter the original signal using a low-pass

type filter characterized by a cut off frequency equal to the

Nyquist frequency.This filter is called antialiasing filter and it

requires its attenuation outside the pass band more than

50dB.

An anti-aliasing filter has two properties defining it. One is

the cutoff frequency, the point at which frequencies above it

are attenuated, the other attribute of a filter is its slope,

measured in dB per octave.

One more notable aspect of anti-aliasing filters is that the

steeper their slope, the more distortion is present near the

cutoff frequency. This is due to a property of physics that

applies only to analog filters. Thus it is better to increase your

sampling rate to allow for a higher Nyquist frequency so that

your anti-aliasing filter's slope can be shallower.The problem which arises in the implementation of this

kind of filter is that the data acquisition interface allows

software selection of the sampling frequency in a wide range

of values. So the cutoff frequency of antialiasing filter should

modify in order to eliminate higher frequencies.

One of the techniques used to prevent the refolding is

oversampling and analog-to-digital conversion in

combination with anti aliasing analog filter. It is additionally

used digital filters and decimation operations along with

keeping requirements sampling theorem.

In order to determine corrective action, we must directly

address the two conditions necessary for exact signal

reconstruction. The first solution calls for low-pass filteringbefore sampling.This method, known as prefiltering,

bandlimits the signal to levels below fmax, thereby eliminating

the offending high frequencies. Notice that the frequency at

which the signal is to be sampled imposes limits on the

allowable bandwidth.

The second solution is to point-sample at a higher

frequency. In doing so, the replicated spectra are spaced

farther apart, thereby separating the overlapping spectra tails.

This approach theoretically implies sampling at a resolution

determined by the highest frequencies present in the signal.

In practice, antialiasing is performed through a

combination of these two approaches. That is, the samplingfrequency is increased so as to reduce the amount of

bandlimiting to a minimum.

http://en.wikipedia.org/wiki/File:Bandform_template.svghttp://en.wikipedia.org/wiki/File:Bandform_template.svghttp://en.wikipedia.org/wiki/File:Bandform_template.svghttp://en.wikipedia.org/wiki/Passbandhttp://en.wikipedia.org/wiki/Stopbandhttp://en.wikipedia.org/wiki/Stopbandhttp://en.wikipedia.org/wiki/Low-pass_filterhttp://en.wikipedia.org/wiki/Low-pass_filterhttp://en.wikipedia.org/wiki/High-pass_filterhttp://en.wikipedia.org/wiki/Band-pass_filterhttp://en.wikipedia.org/wiki/Band-pass_filterhttp://en.wikipedia.org/wiki/Band-stop_filterhttp://en.wikipedia.org/wiki/Band-stop_filterhttp://en.wikipedia.org/wiki/Notch_filterhttp://en.wikipedia.org/wiki/Notch_filterhttp://en.wikipedia.org/wiki/Comb_filterhttp://en.wikipedia.org/wiki/Comb_filterhttp://en.wikipedia.org/wiki/All-pass_filterhttp://en.wikipedia.org/wiki/All-pass_filterhttp://en.wikipedia.org/wiki/All-pass_filterhttp://en.wikipedia.org/wiki/File:Bandform_template.svghttp://en.wikipedia.org/wiki/Passbandhttp://en.wikipedia.org/wiki/Stopbandhttp://en.wikipedia.org/wiki/Low-pass_filterhttp://en.wikipedia.org/wiki/High-pass_filterhttp://en.wikipedia.org/wiki/Band-pass_filterhttp://en.wikipedia.org/wiki/Band-stop_filterhttp://en.wikipedia.org/wiki/Band-stop_filterhttp://en.wikipedia.org/wiki/Notch_filterhttp://en.wikipedia.org/wiki/Comb_filterhttp://en.wikipedia.org/wiki/All-pass_filter

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V. NUMERICALSIMULATIONSANDRESULTS

ACKNOWLEDGMENT

The preferred spelling of the word acknowledgment in

America is without an e after the g. Try to avoid the

stilted expression, One of us (R. B. G.) thanks Instead,

try R.B.G. thanks

REFERENCES

[1] G. Eason, B. Noble, and I.N. Sneddon, On certain integrals ofLipschitz-Hankel type involving products of Bessel functions, Phil.Trans. Roy. Soc. London, vol. A247, pp. 529-551, April 1955.

[2] J. Clerk Maxwell,A Treatise on Electricity and Magnetism, 3rd ed., vol.2. Oxford: Clarendon, 1892, pp.68-73.

[3] I.S. Jacobs and C.P. Bean, Fine particles, thin films and exchangeanisotropy, in Magnetism, vol. III, G.T. Rado and H. Suhl, Eds. NewYork: Academic, 1963, pp. 271-350.

[4] K. Elissa, Title of paper if known, unpublished.[5] R. Nicole, Title of paper with only first word capitalized, J. Name

Stand. Abbrev., in press.[6] Y. Yorozu, M. Hirano, K. Oka, and Y. Tagawa, Electron spectroscopy

studies on magneto-optical media and plastic substrate interface,IEEETransl. J. Magn. Japan, vol. 2, pp. 740-741, August 1987 [Digests 9th

Annual Conf. Magnetics Japan, p. 301, 1982].

[7] M. Young, The Technical Writers Handbook. Mill Valley, CA:University Science, 1989.