Advantages and Disadvantages of UsingDSP Filtering on Oscilloscope Waveforms

Application Note 1494

Introduction

All of today’s high-speed real-timesampling oscilloscopes use variousforms of digital signal processing(DSP) on digitized oscilloscopewaveforms. Some engineers areconcerned that filtering digitizeddata with software may alter thetrue nature of a captured signal.However, the captured waveform isonly a representation of the actualinput signal, and “raw” digitizeddata captured by an oscilloscopeincludes altered/distorted results

Table of Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . . . 1

Waveform-reconstruction filtering. . . . 3

Magnitude-flattening filtering. . . . . . . . 6

Phase-correction filtering . . . . . . . . . . . 7

Noise-reduction filtering . . . . . . . . . . . . 9

Bandwidth-enhancement filtering . . . 10

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 12

Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Support, Services, and Assistance . . . 14

contributed by the scope’sfront-end hardware filtering. In a perfect world, real-timeoscilloscopes would have infinitelyfast sample rates, perfectly flatfrequency responses, linear phaseresponses, no noise, and infinitebandwidth. But in the real world,oscilloscopes have hardwarelimitations that produce errors.DSP filtering ultimately can correctfor hardware-induced errors toimprove measurement accuracyand enhance display quality.

2

There are five different characteristics of DSP filtering commonlyemployed in today’s higher-performance real-time scopes:

DSP filtering Corrects for

Waveform reconstruction Limited sample rate

Magnitude flattening Non-flat frequency response

Phase correction Non-linear phase response

Noise reduction Instrument’s noise floor

Bandwidth enhancement Limited bandwidth

Each of these filter characteristics can be implemented in a singlefinite-impulse response (FIR) software filter in real-time samplingoscilloscopes. This application note explores the purposes of thesedifferent characteristics of DSP filters, and discusses the benefits andpossible tradeoffs associated with each one. This application note doesnot provide information about the actual software implementation ofthe various DSP filters.

3

Waveform-reconstruction filtering

The purpose of waveformreconstruction filtering is to“fill-in” the waveform data recordbetween discrete and evenlysampled real-time acquired datapoints. Filling-in the data pointsenhances both the measurementaccuracy and the viewability ofdigitized waveforms on fastertimebase ranges. You can useequivalent-time/repetitivesampling to fill in the data, but for real-time applications,repetitive sampling is not anoption. The waveform must be captured in a single-shotacquisition. Software waveformreconstruction filtering is theonly other possibility.

The simplest type of waveformreconstruction uses alinear-interpolation filter.Although this type of filter will improve measurementresolution, accuracy, and displayquality, a more accurate type of interpolation is sin(x)/xreconstruction filtering, which is a symmetrical filter. Figure 1shows an example of a 3-GHz sinewave captured and filtered withlinear reconstruction (top/bluetrace) and sin(x)/x reconstruction(bottom/yellow trace). With linearreconstruction, we can clearly see the discreetly spaced 50-pssample points generated by this20-GSa/s oscilloscope.

Sin(x)/x filtering will almostalways provide a more accuraterepresentation of the input signalwith a few caveats. First of all, forsin(x)/x reconstruction filteringto be absolutely accurate, thedigitized input signal must notpossess any frequency componentsbeyond the Nyquist frequency (fN).The Nyquist frequency is defined

to be 1/2 of the sample frequency(fS). For a scope that can sampleat 20 GSa/s, the Nyquist frequencyis 10 GHz. To provide maximumbandwidth while guaranteeingthat no frequency componentsbeyond 10 GHz are ever sampled,the oscilloscope theoreticallymust have a hardware brickwallfilter at 10 GHz or lower.

Unfortunately, brickwall filtersare not physically realizable inhardware. The red trace in Figure 2represents the characteristics of abrickwall filter; all frequencycomponents below the Nyquistfrequency are perfectly passed,and all frequency componentsabove the Nyquist frequency areperfectly eliminated.

Figure 1. Linear vs sin(x)/x reconstruction

0 dB

-9 dB

-6 dB

-3 dB

Frequency

0 Hz 25 GHz20 GHz15 GHz10 GHz5 GHz

-3 dB BW point

Nyquist frequency (fN)

Sample frequency (fS)

V (Brickwall response)V (Maximally-flat response)V (Gaussian response)

Figure 2. Various hardware filter responses

4

Waveform-reconstruction filtering (continued)

In the past, lower-bandwidthscopes typically have hadGaussian-type roll-offcharacteristics, as represented by the green trace (bottom) inFigure 2. If you are digitizing veryfast signals using this slow roll-offcharacteristic, there often will besignificant components of thesignal above the –3dB bandwidthpoint. Frequency componentsbeyond the Nyquist frequency(represented by the hashed areain this graph) will be aliased. If adigitized signal is grossly aliasedwhere the fundamental inputfrequency is beyond the Nyquistfrequency, the displayedwaveform will appear to beuntriggered when you are viewingrepetitive real-time acquisitions,and measurements of digitizedpoints may be in error by ordersof magnitude. When the inputsignal’s fundamental inputfrequency is below the Nyquistfrequency, but harmonics of thesignal are beyond the Nyquistfrequency, you may observe awaveform on the oscilloscope’sdisplay with edges that “wobble.”For this reason, AgilentTechnologies traditionally has limited the bandwidth oflower-bandwidth real-time scopesthat have Gaussian roll-offcharacteristics to 1/4 the samplerate, which is 1/2 the Nyquistfrequency. This significantlylimits the captured energy ofsignals with harmonic-frequencycontent beyond the Nyquistfrequency.

For some of the newerhigher-bandwidth, real-timescopes with bandwidths from2 GHz to 6 GHz, the hardwareroll-off characteristic begins toapproach a theoretical brickwallfilter. In most oscilloscopemeasurement cases, this is adesirable characteristic. This type of hardware filter, called ahigh-order maximally flat filter, is illustrated by the blue trace(middle) in Figure 2. With thistype of hardware filter, most ofthe in-band frequencies arepassed with minimal attenuation,and most of the out-of-bandfrequencies are significantlyattenuated. With a high-ordermaximally flat response, thescope’s bandwidth can then begin to approach the Nyquistlimit. Agilent recommends that for scopes with a high-ordermaximally flat response, thebandwidth of the scope should belimited to no more than 0.4 timesthe sample rate. In other words,for waveform reconstructionusing sin(x)/x filtering to beeffective and accurate, thebandwidth of a scope thatsamples at 20 GSa/s should notexceed 8 GHz.

What are the tradeoffs inemploying a sin(x)/x softwarereconstruction filter in anoscilloscope? If the input signal isinitially band-limited, or if thehardware of the oscilloscopeproperly limits the sampledfrequency components beyond

the Nyquist frequency, thetradeoffs are minimal. But if the input signal has significanthigh-frequency componentsbeyond the system bandwidth,one artifact of sin(x)/x filtering is the possibility ofsoftware-created pre-shoot andover-shoot of the reconstructedwaveform. This effect isessentially Gibbs phenomena. The software-created over-shootis often hidden by inherentover-shoot in the actual inputsignal, as well as over-shootcreated by the scope’s hardwarefiltering. Because pre-shoot isusually not actually present in thesignal, oscilloscope users oftenquestion the validity of sin(x)/xfiltering. But software-inducederrors such as pre-shoot can palein comparison to uncorrectedhardware-induced errors when you are measuringout-of-band signals.

Remember, measuring anout-of-band signal simply meansthat you are attempting to capturea signal which has frequencycomponents beyond the specifiedbandwidth capability of theoscilloscope. This means thatmeasured results can includesignificant components of errordue to hardware limitations. For example, if you attempt tomeasure an input signal with anedge speed of 20 ps (10% to 90%),a 6-GHz oscilloscope will producemeasured edge speeds in therange of 70 ps, which is a

5

Waveform-reconstruction filtering (continued)

250 percent error. Althoughpre-shoot and over-shootproduced by software filteringmay be intuitively disturbing,these phenomena are minorsources of error compared tohardware-induced over-shoot andedge-speed errors, which areoften overlooked.

To reduce software-inducedpre-shoot, oscilloscope designers could employ sin(x)/xreconstruction filtering withoutphase correction to the acquiredout-of-band waveform. (Seepage 7 for more information on phase-correction filtering.)Although the resultant filteredwaveform that exhibits lots ofover-shoot with minimal pre-shootmay feel more comfortable,accuracy of amplitude andedge-speed measurements will bedegraded. Proper DSP filteringwith linear phase correction will produce the most accuratemeasurements on fast rising andfalling edges.

The best approach is to try toignore the pre-shoot artifact andtake this unintuitive “wiggle” atthe beginning of fast-edge pulsesas a sign that the real-timeoscilloscope is employing a DSP filter that most accuratelyrepresents the overallcharacteristics of the out-of-bandinput signal. You also can take thepre-shoot artifact as a sign thatyou are pushing the real-timeoscilloscope beyond its intended

bandwidth measurementcapabilities. You may want to consider using ahigher-bandwidth samplingoscilloscope, such as Agilent’s86100C, for your measurementapplication. If repetitive samplingis not a possibility, then you mayneed to just accept the real-timemeasurement results as the bestthat is possible with today’sreal-time sampling and filtering technology.

As previously mentioned, sin(x)/xDSP filtering will significantlyimprove measurement resolutionand accuracy to well beyond the real-time sample interval(1/sample-rate). With Agilent’s20-GSa/s 54855A oscilloscope,delta-time measurement accuracycan be improved to less than±1 ps with the use of sin(x)/xfiltering on single-shotacquisitions. In some cases thereare also throughput tradeoffswhen you use sin(x)/x filtering.In other words, the filter causesyour scope display to updatemore slowly. However, theenhanced accuracy advantages ofusing sin(x)/x filtering typicallyfar outweigh all disadvantages.

All major real-time scope vendorstoday allow you to decide if youwant to use sin(x)/x filtering.This mode of operation is adefault selection in Agilentoscilloscopes, but you canoverride this selection if you choose.

6

Magnitude-flattening filtering

The purpose of magnitude-flattening filtering is to correctfor a non-flat frequency responseof the hardware characteristics of the oscilloscope. Ideally,oscilloscopes would have aperfectly flat hardware responseall the way out to the naturalbandwidth roll-off characteristicsof the oscilloscope, as shown bythe traces in Figure 2. This meansthat if you measure a sine wavewith constant amplitude, but varythe frequency, you would alwaysmeasure the same amplitude until reaching the upper roll-offfrequencies. Unfortunately, as youapproach the bandwidth limit ofa scope, flatness-of-responsetends to degrade. Often, there can be a combination ofhardware-induced attenuationand peaking at particularfrequencies. In fact, oscilloscopedesign engineers will oftenintentionally induce peaking inthe scope’s hardware responsenear the bandwidth limit in order to compensate for minorfrequency-dependent attenuationand to push the scope’s frequencyresponse to a higher bandwidth.

Channel 1, 100 mV/div, magnitude

Res

pons

e (d

B)

5

4

3

2

1

0

-1

-2

-3

-4

-50.1 1 10

Frequency (GHz)

Figure 3. Magnitude-flattening filter response

The red trace (top) in Figure 3shows the typical hardware/analogfrequency response of Agilent’s54855A real-time 6-GHzoscilloscope. As you can see, the hardware response of thisscope meets the –3 dB hardwarebandwidth criteria of 6 GHz, butthe response also shows about+1 dB of peaking at approximately3.5 GHz, and nearly +2 dB ofpeaking at approximately 5.5 GHz.Oscilloscope manufacturers todaydo not specify the flatness oftheir scope’s frequency response.The only point in the frequencydomain scope makers specify isthe –3 dB bandwidth point. Evenif a scope had +6 dB of peaking,which would translate into 60percent amplitude error at aparticular in-band frequency, aslong as the –3 dB point is higherthan the specified bandwidth, the scope is considered to bewithin specification. But just asattenuation at higher frequenciescan degrade the accuracy of measurements, so canamplification/peaking degrademeasurement accuracy.

The blue trace (bottom) in Figure 3shows the corrected magnitudefrequency response of the 54855Ausing magnitude-flatteningfiltering. With this DSP/softwarefilter, the corrected frequencyresponse of the oscilloscopetypically does not deviate morethan ±0.5 dB until the responsenaturally rolls off near thespecified 6 GHz bandwidth. This particular characteristic of the scope’s FIR filter is notuser-selectable — it always runswhen you are sampling at thescope’s maximum sample rate tocorrect for always-presenthardware filtering errors. Thecombination of the software andhardware filter produces moreaccurate data than data producedby the hardware filter alone.

7

Phase-correction filtering

High-speed digital signals arecomposed of multiple frequencycomponents including thefundamental and harmonics.Ideally, the fundamental andharmonics of a digital signalshould all be in-phase and haveno delay between the variousfrequency components, as shownin Figure 4. Unfortunately, theoscilloscope’s hardware addsunwanted phase shift to thehigher-order components ofhigh-speed signals that can only be eliminated by eithersignificantly increasing theinstrument’s bandwidth, or bycorrecting with phase-correctionDSP filtering. Figure 5 shows anexample where the 5th harmonic(green trace) is delayed from both the fundamental and 3rdharmonic. The result will be adistorted digital waveform on theoscilloscope’s display. Withoutphase correction, this distortionusually manifests as excessiveover-shoot in the digitizedwaveform, along with reducededge speeds. High-speed digitaldesigners often overlook theover-shoot component ofdistortion, thinking that themeasured over-shoot is actuallypresent on the input signal. But itmay not be, and may actually bean artifact of the inadequacy ofthe hardware to “keep-up” at allinput frequencies.

1.0

0.5

0.0

-0.5

-1.0

0.9 1.0 1.1 1.2 1.3 1.91.81.71.61.51.4

time, nsec

VH5

VH3

VH1

Figure 4. In-phase harmonics

Delayed

1.0

0.5

0.0

-0.5

-1.0

VH5

VH3

VH1

0.9 1.0 1.1 1.2 1.3 1.91.81.71.61.51.4

time, nsec

Figure 5. 5th harmonic delayed

8

Phase-correction filtering (continued)

200

150

100

50

-50

-100

-150

-20010.1 10

Frequency (GHz)

Phas

e (d

egre

es)

Channel 1, 100 mV/div, phase response

Hardware phase response

DSP corrected phase response

0

Figure 6. Correct and uncorrected phase response

V (max-flat, uncorrected ), tr =82 ps (0.49/BW)

V (max-flat, corrected ), tr =71 ps (0.43/BW)1.2

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

-700 600500300100-100-300-500

time, psec

Figure 7. Pulse response with and without phase correction

The red trace in Figure 6 showsthe typical frequency-dependentphase error induced by the54855A hardware at higher inputfrequencies. The blue trace in thisgraph shows the corrected phaseresponse using phase-correctionDSP/software filtering. As youcan see, this software filtercorrects for all phase errors to well beyond the bandwidthspecification of the instrument.

Figure 7 shows a simulation of adigitized fast-edge signal, withand without phase-correction, for a 6-GHz hardware systembased on a high-order maximallyflat response. The one artifactthat you will note in thephase-corrected waveform(left/red trace) is the presence ofminimal pre-shoot and over-shooton the waveform. Again, neitherthe pre-shoot nor the over-shootare actually present in thesimulated input signal, which hadan infinitely fast rise time, butare artifacts of the linear-phasesystem response and signalcontent beyond the –3 dBfrequency. But don’t overlook the excessive over-shoot on thenon-phase corrected waveform(right/blue trace). Withphase-correction, the overallperturbation errors on both thetop and base of this waveformhave been improved. Mostimportantly though, timingmeasurements such as the risetimes and fall times are muchmore accurate when phasecorrection is applied on eitherin-band or out-of-band signals.Again, phase-correction filteringis not user-selectable in Agilent’s54855A oscilloscope; it is alwaysrunning to correct for addedhardware phase errors.

9

Noise-reduction filtering

As you would expect,noise-reduction filtering reducesthe effect of the oscilloscope’snoise floor. Oscilloscopes arebroadband instruments and thehigher the bandwidth the higherthe noise floor will be. Thishardware-induced errorcomponent is unavoidable inbroadband instruments. WithAgilent’s 54855A oscilloscope,you can selectively usenoise-reduction filtering toimprove measurement accuracy,but there is a big tradeoff. Whenthe scope’s FIR filter includesnoise-reduction filteringcharacteristics, the bandwidth of the instrument is reduced.

Figure 8 shows an example ofcapturing a 1-GHz sine waveusing the 6-GHz bandwidth54855A oscilloscope without theuse of noise-reduction filtering.Using the infinite-persistencedisplay mode, after 1000accumulated acquisitions we seea band of noise on this capturedsine wave that is induced by theoscilloscope’s hardware noise

floor. At this setting, theinstrument-induced noisemeasured approximately2.8 mV RMS. The upper/yellowtrace shows the input signalscaled to near full-scale at100 mV/div. The lower/greentrace shows a 10X waveformexpansion of this waveform near its peak.

Figure 9 shows the same 1-GHzsine wave, but now capturedusing 2-GHz bandwidthnoise-reduction filtering. After1000 accumulated acquisitions,we see a much cleaner waveformdue to a nearly 2:1 reduction inthe system’s noise floor. Again,the upper/yellow trace shows theinput signal scaled at 100 mV/divand the lower/green trace showsan expansion of the waveformnear its peak allowing us to seemore clearly the effects of thescope’s reduced noise floor usingnoise-reduction filtering.

When testing lower-bandwidthsignals, or signals with relatively

slow edge speeds, engagingnoise-reduction filtering willoften enhance accuracy of both amplitude and timingmeasurements. One exampleinvolves measuring jitter. One ofthe largest, but often overlooked,components of error in jitter measurements isjitter/timing-error contributed byvertical noise. There is a directrelationship between verticalnoise and timing error as afunction of the slew rate of the signal. Although it may becounter-intuitive, reducing thebandwidth of your measurementsystem may actually improve theaccuracy of jitter measurementswhen you are measuring in-band signals. Turning onnoise-reduction filtering will automatically reduceinstrument-induced jitter due toan excessive instrument noisefloor. Because of the obvioustrade-offs (bandwidth versusnoise), use of noise-reductionfiltering is user-selectable inAgilent’s 54855A oscilloscope.

Figure 8. Default 6-GHz bandwidth mode with 2.8 mV RMSscope noise floor

Figure 9. 2-GHz noise-reduction mode with 1.6 mV RMSscope noise floor

10

Bandwidth-enhancement filtering

Bandwidth-enhancementfiltering, sometimes referred to as“bandwidth boosting,” is probablythe least intuitive type of DSPfiltering. It is employed today insome high-bandwidth real-timeoscilloscopes. How can youenhance the bandwidth of asystem once the hardware hasattenuated the signal? The simpleanswer is, pump it back up withsoftware. Once you break adigitized signal down into itsvarious sine wave frequencycomponents, you can usesoftware to selectively “amplify” the various frequencycomponents that are attenuatedbased on software filteringcharacteristics that are a mirrorimage (up to the boosted –3 dBpoint) of the hardware roll-offcharacteristic of the scope, asshown in Figure 10. The red trace (bottom) in this graphshows a typical hardwarefrequency response. The green

trace (top) represents thebandwidth-enhancement filter,and the blue trace (middle)represents the improvedbandwidth response of thesystem, which you can see hasbeen “boosted” to a higherfrequency. In addition toincreasing the bandwidth, thisparticular filter also generates asharper roll-off characteristic forthe oscilloscope to help reducehigh-frequency noise and to helpeliminate aliasing when testingout-of-band input signals.

Again, there is one big tradeoff.As we mentioned, an oscilloscopeis a broadband instrument, andthe noise floor of the instrumentcan significantly degrademeasurement results. Withbandwidth-enhancement filtering,the noise floor of the instrumentalso is selectively amplified. So, there is a signal-to-noise

tradeoff when you use these bandwidth-enhancingcharacteristics of the scope’s FIR DSP filter.

Although bandwidthenhancement filtering may be a fairly new capability in some of today’s higher-bandwidthreal-time oscilloscopes, this is not a new technique in thetest-and-measurement industry.Agilent has been usingbandwidth-enhancementtechniques for years in networkanalyzers and spectrumanalyzers. In fact, Agilent first used this technique in anoscilloscope to simulate fasteredge speeds when performingTDR measurements with a20-GHz sampling oscilloscope.This technique is known as“normalization” in today’ssampling oscilloscopes with TDRmeasurement capability.

-3 dB

0 dB

Response vs frequency

Res

pons

e

Frequency

Filter

Standard bandwidthIncreased bandwidth

Figure 10. Bandwidth-enhancement filtering

11

Bandwidth-enhancement filtering (continued)

Figure 11 shows an example ofmeasuring an out-of-band signalusing a 6-GHz oscilloscope. Theinput signal has an approximaterisetime of 50 ps (based on a 10% to 90% measurementcriteria). But since the basichardware of the oscilloscope has a risetime specification of70 ps, we measure a risetime of just 74 ps. With the use of7-GHz bandwidth-enhancementfiltering, we can now make amore accurate measurement onthis signal of approximately66 ps, as shown in Figure 12.However, you can see that thebaseline noise on both the topand base of this waveform has

Figure 11. Risetime measurement withoutbandwidth-enhancement

Figure 12. Risetime measurement with 7-GHzbandwidth-enhancement

increased. In the standard 6-GHzbandwidth mode, the noise floor of the scope measuresapproximately 3 mV RMS at the100 mV/div setting. The noisefloor increases to approximately6 mV RMS when using 7-GHzbandwidth-enhancement filtering.

Another benefit of DSP filteringwith bandwidth-enhancement onAgilent’s 54855A oscilloscopes ishigh-impedance active probingmeasurements can be performedup to 7-GHz system bandwidth.No longer is the differential activeprobe the weakest link in theoscilloscope measurement chain.

12

Product Web site

For copies of this literature,contact your Agilentrepresentative or visit ourproduct Web site at: www.agilent.com/find/infiniimax

Conclusion

Many engineers today tend totrust hardware filtering, but areskeptical of DSP filtering becauseit is based on software. As weillustrated in this applicationnote, DSP filtering onoscilloscope waveforms isemployed for the purpose ofcorrecting hardware filteringerrors. Instead of thinking ofsoftware filtering as a form ofdata manipulation, it is moreappropriate to think of it as dataun-manipulation. Software hasbeen used for years to correct forhardware errors in oscilloscopes,including gain/offset calibrationand de-skewing delay betweenchannels. It makes sense to usesoftware also to correct for morecomplex frequency-dependentsources of hardware errors usingDSP filtering.

Some of the filter characteristicsdiscussed in this application notehave minimal or no disadvantages,such as magnitude-flattening andphase-correction filtering. Forthese reasons, these particularfilter characteristics are notuser-selectable but run as adefault operation when the

Agilent 54855A oscilloscope is sampling at the maximumspecified sample rate (20 GSa/s).Because we believe that sin(x)/xwaveform-reconstruction filteringalso improves measurementaccuracy and display quality, thecharacteristics of this particularfilter runs as a default operatingmode of the oscilloscope, but you can easily disabled it. Thetradeoffs using sin(x)/x filteringare primarily associated withthroughput, not accuracy.

Other characteristics of the scope’s FIR DSP filter,including noise-reduction andbandwidth-enhancement filteringhave very definite tradeoffs interms of bandwidth and noise.For this reason, neither of thesefilter characteristics run as adefault mode of operation of theoscilloscope; you must turn themon to use them.

As long as you are aware of the tradeoffs inherent in somefiltering types, it makes sense to use DSP filtering to improvethe accuracy and resolution oftoday’s real-time oscilloscopes.

Related Literature

Publication Title Publication Type Publication Number

Infiniium 54850 Series Oscilloscope, Data sheet 5988-7976EN/ENUSInfiniiMax 1130

Understanding Oscilloscope Frequency Application Note 1420 5988-8008ENResponse and its Effect on Rise Time Accuracy

Time-Domain Response of Agilent InfiniiMax Application Note 1461 5988-9608ENProbes and 54850 Series Infiniium Oscilloscope

Improving TDR/TDT Measurements Application Note 1304-5 5988-2490ENUsing Normalization

Agilent Technologies Option 008 Data sheet 5989-1066ENEnhanced Bandwidth Software for the 54855A Infiniium Oscilloscope

13

Glossary

DSP digital signal processing

Brickwall filter a theoretical but unrealizable filter that perfectly passesall frequency components of the signal below a particular cut-offfrequency, and rejects all frequency components of the signal above thecut-off frequency

Equivalent-time sampling digitizing an input signal repetitively usingmultiple acquisition cycles

Finite-impulse response (FIR) filter a software filter whose output is aweighted sum of the input data

Gaussian filter a filter that exhibits relatively slow roll-offcharacteristics

Gibbs phenomena symmetrical filter-induced pre-shoot and over-shootdue to truncation of Fourier series beyond a given frequency

High-order maximally flat filter a filter that approaches the sharp roll-offcharacteristics of a brickwall filter

In-band frequency components of signals that are less than thespecified bandwidth frequency

Infinite persistence a display mode in oscilloscopes that accumulatesmultiple acquisitions on the scope’s display to show worst-casedeviations

Jitter any time deviation (error) from the ideal instance in time when asignal edge/transition should occur

Nyquist frequency (fN) which is the frequency that is equal to 1/2 thesampling frequency (fS)

Out-of-band frequency components of signals that are greater than thespecified bandwidth frequency

Real-time sampling digitizing an input signal from a single-shotacquisition using a high rate of sampling

Sin(x)/x filtering characteristics of software filtering that reconstructsa sampled waveform to provide higher data resolution that will moreaccurately represent the original un-sampled input signal whenNyquist’s rules are observed

Agilent Technologies’ Test and Measurement Support, Services, and AssistanceAgilent Technologies aims to maximize the value you receive, while minimizing your risk andproblems. We strive to ensure that you get the test and measurement capabilities you paidfor and obtain the support you need. Our extensive support resources and services can helpyou choose the right Agilent products for your applications and apply them successfully.Every instrument and system we sell has a global warranty. Support is available for at leastfive years beyond the production life of the product. Two concepts underlie Agilent's overallsupport policy: "Our Promise" and "Your Advantage."

Our PromiseOur Promise means your Agilent test and measurement equipment will meet its advertisedperformance and functionality. When you are choosing new equipment, we will help youwith product information, including realistic performance specifications and practicalrecommendations from experienced test engineers. When you use Agilent equipment, wecan verify that it works properly, help with product operation, and provide basic measurementassistance for the use of specified capabilities, at no extra cost upon request. Many self-helptools are available.

Your AdvantageYour Advantage means that Agilent offers a wide range of additional expert test andmeasurement services, which you can purchase according to your unique technical andbusiness needs. Solve problems efficiently and gain a competitive edge by contracting withus for calibration, extra-cost upgrades, out-of-warranty repairs, and on-site education andtraining, as well as design, system integration, project management, and other professionalengineering services. Experienced Agilent engineers and technicians worldwide can helpyou maximize your productivity, optimize the return on investment of your Agilentinstruments and systems, and obtain dependable measurement accuracy for the life ofthose products.

By internet, phone, or fax, get assistance withall your test & measurement needs

Online assistance:www.agilent.com/find/assist

Phone or FaxUnited States:(tel) 800 829 4444

Canada:(tel) 877 894 4414(fax) 905 282 6495

China:(tel) 800 810 0189(fax) 800 820 2816

Europe:(tel) (31 20) 547 2323(fax) (31 20) 547 2390

Japan:(tel) (81) 426 56 7832(fax) (81) 426 56 7840

Korea:(tel) (82 2) 2004 5004(fax) (82 2) 2004 5115

Latin America:(tel) (305) 269 7500(fax) (305) 269 7599

Taiwan:(tel) 0800 047 866(fax) 0800 286 331

Other Asia Pacific Countries:(tel) (65) 6375 8100(fax) (65) 6836 0252Email: tm_asia@agilent.com

Product specifications and descriptions in thisdocument subject to change without notice.

© Agilent Technologies, Inc. 2004Printed in USA May 24, 2004

5989-1145EN

www.agilent.com/find/emailupdatesGet the latest information on the products and applications you select.

Agilent T&M Software and ConnectivityAgilent's Test and Measurement software and connectivity products, solutions anddeveloper network allows you to take time out of connecting your instruments to yourcomputer with tools based on PC standards, so you can focus on your tasks, not on yourconnections. Visit www.agilent.com/find/connectivity for more information.

www.agilent.com

www.agilent.com/find/agilentdirectQuickly choose and use your test equipment solutions with confidence.

Agilent Email Updates

Agilent Direct