DigitalSignalProcessing(DSP)FundamentalsOverviewWhatisDSP?ConvertingAnalogintoDigitalElectronicallyComputationallyHowDoesItWork?FaithfulDuplicationResolutionTrade-offsWhatisDSP?Convertingacontinuouslychangingwaveform(analog)intoaseriesofdiscretelevels(digital)WhatisDSP?TheanalogwaveformisslicedintoequalsegmentsandthewaveformamplitudeismeasuredinthemiddleofeachsegmentThecollectionofmeasurementsmakeupthedigitalrepresentationofthewaveformWhatisDSP?ConvertingAnalogintoDigitalElectronicallyThedevicethatdoestheconversioniscalledanAnalogtoDigitalConverter(ADC)ThereisadevicethatconvertsdigitaltoanalogthatiscalledaDigitaltoAnalogConverter(DAC)ConvertingAnalogintoDigitalElectronicallyThesimplestformofADCusesaresistanceladdertoswitchintheappropriatenumberofresistorsinseriestocreatethedesiredvoltagethatiscomparedtotheinput(unknown)voltageConvertingAnalogintoDigitalElectronicallyTheoutputoftheresistanceladderiscomparedtotheanalogvoltageinacomparatorWhenthereisamatch,thedigitalequivalent(switchconfiguration)iscapturedConvertingAnalogintoDigitalComputationallyTheanalogvoltagecannowbecomparedwiththedigitallygeneratedvoltageinthecomparatorThroughatechniquecalledbinarysearch,thedigitallygeneratedvoltageisadjustedinstepsuntilitisequal(withintolerances)totheanalogvoltageWhenthetwoareequal,thedigitalvalueofthevoltageistheoutcomeConvertingAnalogintoDigitalComputationallyThebinarysearchisamathematicaltechniquethatusesaninitialguess,theexpectedhigh,andtheexpectedlowinasimplecomputationtorefineanewguessThecomputationcontinuesuntiltherefinedguessmatchestheactualvalue(oruntilthemaximumnumberofcalculationsisreached)ThefollowingsequencetakesyouthroughabinarysearchcomputationBinarySearchInitialconditionsExpectedhigh5-voltsExpectedlow0-volts5-volts256-binary0-volts0-binaryVoltagetobeconverted3.42-voltsEquatesto175binaryAnalogDigital5-volts2560-volts02.5-volts1283.42-voltsUnknown(175)BinarySearchBinarysearchalgorithm:FirstGuess:AnalogDigital5-volts2560-volts01283.42-voltsunknownGuessisLowBinarySearchNewGuess(2):AnalogDigital5-volts2560-volts01923.42-voltsunknownGuessisHighBinarySearchNewGuess(3):AnalogDigital5-volts2560-volts01603.42-voltsunknownGuessisLowBinarySearchNewGuess(4):AnalogDigital5-volts2560-volts01763.42-voltsunknownGuessisHighBinarySearchNewGuess(5):AnalogDigital5-volts2560-volts01683.42-voltsunknownGuessisLowBinarySearchNewGuess(6):AnalogDigital5-volts2560-volts01723.42-voltsunknownGuessisLow(butgettingclose)BinarySearchNewGuess(7):AnalogDigital5-volts2560-volts01743.42-voltsunknownGuessisLow(butgettingreally,really,close)BinarySearchNewGuess(8):AnalogDigital5-volts2560-volts03.42-volts175!GuessisRightOnBinarySearchThespeedthebinarysearchisaccomplisheddependson:TheclockspeedoftheADCThenumberofbitsresolutionCanbeshortenedbyagoodguess(butusuallyisnotworththeeffort)HowDoesItWork?FaithfulDuplicationNowthatwecansliceupawaveformandconvertitintodigitalform,letstakealookathowitisusedinDSPDrawasimplewaveformongraphpaperScaleappropriately“Gather”digitaldatapointstorepresentthewaveformStartingWaveformUsedtoCreateDigitalDataHowDoesItWork?FaithfulDuplicationSwapyourwaveformdatawithapartnerUsingthedata,recreatethewaveformonasheetofgraphpaperWaveformCreatedfromDigitalDataHowDoesItWork?FaithfulDuplicationComparetheoriginalwiththerecreating,notesimilaritiesanddifferencesHowDoesItWork?FaithfulDuplicationOncethewaveformisindigitalform,therealpowerofDSPcanberealizedbymathematicalmanipulationofthedataUsingEXCELspreadsheetsoftwarecanassistinmanipulatingthedataandmakinggraphsquicklyLetsfirstdoalittlefilteringofnoiseHowDoesItWork?FaithfulDuplicationUsingyourrawdigitaldata,createanewtableofdatathataveragesthreedatapointsAveragethepointbeforeandthepointafterwiththepointinthemiddleEnteralldatainEXCELtohelpwithgraphingNoiseFilteringUsingAveragingHowDoesItWork?FaithfulDuplicationLetstakecareofsomestaticcrashesthatcausesomeinterferenceUsingyourrawdigitaldata,createanewtableofdatathatreplacesextremehighandlowvalues:Replacevaluesgreaterthan100with100Replacevalueslessthan-100with-100ClippingofStaticCrashesHowDoesItWork?ResolutionTrade-offsNowletstakealookathowsamplingratesaffectthefaithfulduplicationofthewaveformUsingyourrawdigitaldata,createanewtableofdataanddeleteeveryotherdatapointThisisthesameassamplingathalftherateHalfSampleRateHowDoesItWork?ResolutionTrade-offsUsingyourrawdigitaldata,createanewtableofdataanddeleteeverysecondandthirddatapointThisisthesameassamplingatone-thirdtherate1/2SampleRateHowDoesItWork?ResolutionTrade-offsUsingyourrawdigitaldata,createanewtableofdataanddeleteallbuteverysixthdatapointThisisthesameassamplingatone-sixththerate1/6SampleRateHowDoesItWork?ResolutionTrade-offsUsingyourrawdigitaldata,createanewtableofdataanddeleteallbuteverytwelfthdatapointThisisthesameassamplingatone-twelfththerate1/12SampleRateHowDoesItWork?ResolutionTrade-offsWhatconclusionscanyoudrawfromthechangesinsamplingrate?Atwhatpointdoesthewaveformgettoocorruptedbythereducednumberofsamples?Isthereapointwheremoresamplesdoesnotappeartoimprovethequalityoftheduplication?HowDoesItWork?ResolutionTrade-offsBitResolutionHighBitCountGoodDuplicationSlowLowBitCountPoorDuplicationFastSampleRateHighSampleRateGoodDuplicationSlowLowSampleRatePoorDuplicationFast