Introduction to Digital Signal Processing
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Transcript of Introduction to Digital Signal Processing
Introduction to Digital Signal Processing
Introduction to Digital Signal ProcessingPrepared by:Engr. Tirso Llantada
Learning ObjectivesWhy process signals digitally?What is DSP?Converting Analog into DigitalElectronicallyComputationallyHow Does It Work?Faithful DuplicationResolution Trade-offs
Consumer Audio Stereo A/D, D/A PLL MixersMultimedia Stereo audio Imaging Graphics palette Voltage regulation
Wireless / Cellular Voice-band audio RF codecs Voltage regulationHDD PRML read channel MR pre-amp Servo control SCSI tranceiversAutomotive Digital radio A/D/A Active suspension Voltage regulationDTAD Speech synthesizer Mixed-signalprocessorDSP:TechnologyEnabler
Applications
Why Process Signals DigitallyDigital signal processing techniques are now so powerful that sometimes it is extremely difficult, if not impossible, for analogue signal processing to achieve similar performance.Analogue signal processing is achieved by using analogue components. (Resistors , Capacitors , Inductors)With DSP it is easy to Change applications, Correct applications, and Update applications.Additionally DSP reduces Noise susceptibility, Chip count, Development time, Cost, Power consumption.
LimitationHigh frequency signals cannot be processed digitally because of two reasons:Analog to Digital Converters, ADC cannot work fast enough.The application can be too complex to be performed in real-time.
What is DSP?Converting a continuously changing waveform (analog) into a series of discrete levels (digital)
What is DSP?The analog waveform is sliced into equal segments and the waveform amplitude is measured in the middle of each segmentThe collection of measurements make up the digital representation of the waveform
What is DSP?
Converting Analog into DigitalElectronicallyThe device that does the conversion is called an Analog to Digital Converter (ADC)There is a device that converts digital to analog that is called a Digital to Analog Converter (DAC)
Converting Analog into DigitalElectronicallyThe simplest form of ADC uses a resistance ladder to switch in the appropriate number of resistors in series to create the desired voltage that is compared to the input (unknown) voltage
Converting Analog into DigitalElectronicallyThe output of the resistance ladder is compared to the analog voltage in a comparatorWhen there is a match, the digital equivalent (switch configuration) is captured
Converting Analog into DigitalComputationally
The analog voltage can now be compared with the digitally generated voltage in the comparatorThrough a technique called binary search, the digitally generated voltage is adjusted in steps until it is equal (within tolerances) to the analog voltageWhen the two are equal, the digital value of the voltage is the outcome
Converting Analog into DigitalComputationallyThe binary search is a mathematical technique that uses an initial guess, the expected high, and the expected low in a simple computation to refine a new guessThe computation continues until the refined guess matches the actual value (or until the maximum number of calculations is reached)The following sequence takes you through a binary search computation
Binary SearchInitial conditionsExpected high 5-voltsExpected low 0-volts5-volts 256-binary0-volts 0-binaryVoltage to be converted3.42-voltsEquates to 175 binary
AnalogDigital5-volts2560-volts0
2.5-volts128
3.42-voltsUnknown (175)
Binary SearchBinary search algorithm:
First Guess:
AnalogDigital5-volts2560-volts0
128
3.42-voltsunknown
Guess is Low
Binary SearchNew Guess (2):
AnalogDigital5-volts2560-volts0
192
3.42-voltsunknown
Guess is High
Binary SearchNew Guess (3):
AnalogDigital5-volts2560-volts0
160
3.42-voltsunknown
Guess is Low
Binary SearchNew Guess (4):
AnalogDigital5-volts2560-volts0
176
3.42-voltsunknown
Guess is High
Binary SearchNew Guess (5):
AnalogDigital5-volts2560-volts0
168
3.42-voltsunknown
Guess is Low
Binary SearchNew Guess (6):
AnalogDigital5-volts2560-volts0
172
3.42-voltsunknown
Guess is Low (but getting close)
Binary SearchNew Guess (7):
AnalogDigital5-volts2560-volts0
174
3.42-voltsunknown
Guess is Low (but getting really, really, close)
Binary SearchNew Guess (8):
AnalogDigital5-volts2560-volts0
3.42-volts175!
Guess is Right On
Binary SearchThe speed the binary search is accomplished depends on:The clock speed of the ADCThe number of bits resolutionCan be shortened by a good guess (but usually is not worth the effort)
How Does It Work?Faithful DuplicationNow that we can slice up a waveform and convert it into digital form, lets take a look at how it is used in DSPDraw a simple waveform on graph paperScale appropriatelyGather digital data points to represent the waveform
Starting Waveform Used to Create Digital Data
Waveform Created from Digital Data
How Does It Work?Faithful DuplicationCompare the original with the recreating, note similarities and differences
Noise Filtering Using Averaging
Half Sample Rate
1/3 Sample Rate
1/6 Sample Rate
1/12 Sample Rate
How Does It Work?Resolution Trade-offsWhat conclusions can you draw from the changes in sampling rate?At what point does the waveform get too corrupted by the reduced number of samples?Is there a point where more samples does not appear to improve the quality of the duplication?
How Does It Work?Resolution Trade-offsBit Resolution
High Bit Count
Good Duplication
Slow
Low Bit Count
Poor Duplication
Fast
Sample Rate
High Sample Rate
Good Duplication
Slow
Low Sample Rate
Poor Duplication
Fast
Example 1A signal, 100 Hz, is sampled at 4000Hz. DetermineSampling intervalNumber of samples taken in one cycle of the input signalNumber of samples taken in 4 seconds durationNumber of cycles taken in 4 seconds durationFrequency of the Reproduced Signal
Example 2A signal, 100 Hz, is sampled at 150Hz. DetermineSampling intervalNumber of samples taken in one cycle of the input signalNumber of samples taken in 4 seconds durationNumber of cycles taken in 4 seconds durationFrequency of the Reproduced Signal
Example 3Sketch the spectrum of the sampled version of the given signal
0Hz 20 Hz 40Hz2
1
Example 4Define the equation of the signal representing the samples of the inputX(t) = 3 cos(100t) 2sin(500t + 180)Fs = 400 Hz
V-7V-6V-lowV-1V-2V-3V-4V-5V-highSW-8SW-7SW-6SW-5SW-4SW-3SW-2SW-1OutputAnalog VoltageResistance Ladder VoltageComparator OutputHigherEqualLowerChart10105055757812512210-20-48-100-110-130-75-90-30045809010010010890-8-40-55-80-45-38-15-225434558708055500
RawTimeAmplitude
Sheet1TimeRawAve before/aftereliminate extremes (100/-100)000011020102503850355605547569755789378612510810071228610081037109-20-19-2010-48-56-4811-100-86-10012-110-113-10013-130-105-10014-75-98-7515-90-65-9016-30-40-301705018454245198072802090909021100971002210010310023108991002490639025-814-826-40-34-4027-55-58-5528-80-60-8029-45-54-4530-38-33-3831-15-18-1532-23-2332522253443384335454945365858583770697038806880395562554050355041000Timeevery 2ndTimeevery 3rdTimeevery 6thTimeevery 1200000000110250612512-11035557812-110249057881018453658712211-10024904109-2014-7530-3811-100170365813-130209041015-902310817026-40198029-452110032-223108354525-8388027-5541029-4531-153325354537703955410
Sheet1
RawTimeAmplitude
Sheet2
Ave before/afterTimeAmplitude
Sheet3
eliminate extremes (100/-100)TimeAmplitude
every 2ndTimeAmplitude
every 6thTimeAmplitude
every 3rdTimeAmplitude
every 12TimeAmplitudeevery 12th
Chart202038.33333333336069.333333333392.6666666667108.333333333385.666666666737.3333333333-19.3333333333-56-86-113.3333333333-105-98.3333333333-65-40541.666666666771.66666666679096.6666666667102.666666666799.333333333363.333333333314-34.3333333333-58.3333333333-60-54.3333333333-32.6666666667-18.33333333332.66666666672237.666666666748.666666666757.666666666769.333333333368.333333333361.6666666667350
Ave before/afterTimeAmplitude
Sheet1TimeRawAve before/aftereliminate extremes (100/-100)000011020102503850355605547569755789378612510810071228610081037109-20-19-2010-48-56-4811-100-86-10012-110-113-10013-130-105-10014-75-98-7515-90-65-9016-30-40-301705018454245198072802090909021100971002210010310023108991002490639025-814-826-40-34-4027-55-58-5528-80-60-8029-45-54-4530-38-33-3831-15-18-1532-23-2332522253443384335454945365858583770697038806880395562554050355041000Timeevery 2ndTimeevery 3rdTimeevery 6thTimeevery 1200000000110250612512-11035557812-110249057881018453658712211-10024904109-2014-7530-3811-100170365813-130209041015-902310817026-40198029-452110032-223108354525-8388027-5541029-4531-153325354537703955410
Sheet1
RawTimeAmplitude
Sheet2
Ave before/afterTimeAmplitude
Sheet3
eliminate extremes (100/-100)TimeAmplitude
every 2ndTimeAmplitude
every 6thTimeAmplitude
every 3rdTimeAmplitude
every 12TimeAmplitudeevery 12th
Chart50105055757812512210-20-48-100-110-130-75-90-30045809010010010890-8-40-55-80-45-38-15-225434558708055500
RawTimeAmplitude
Sheet1TimeRawAve before/aftereliminate extremes (100/-100)000011020102503850355605547569755789378612510810071228610081037109-20-19-2010-48-56-4811-100-86-10012-110-113-10013-130-105-10014-75-98-7515-90-65-9016-30-40-301705018454245198072802090909021100971002210010310023108991002490639025-814-826-40-34-4027-55-58-5528-80-60-8029-45-54-4530-38-33-3831-15-18-1532-23-2332522253443384335454945365858583770697038806880395562554050355041000Timeevery 2ndTimeevery 3rdTimeevery 6thTimeevery 1200000000110250612512-11035557812-110249057881018453658712211-10024904109-2014-7530-3811-100170365813-130209041015-902310817026-40198029-452110032-223108354525-8388027-5541029-4531-153325354537703955410
Sheet1
RawTimeAmplitude
Sheet2
Ave before/afterTimeAmplitude
Sheet3
eliminate extremes (100/-100)TimeAmplitude
every 2ndTimeAmplitude
every 6thTimeAmplitude
every 3rdTimeAmplitude
every 12TimeAmplitudeevery 12th
Chart90105578122-20-100-130-90080100108-8-55-45-15254570550
every 2ndTimeAmplitude
Sheet1TimeRawAve before/aftereliminate extremes (100/-100)000011020102503850355605547569755789378612510810071228610081037109-20-19-2010-48-56-4811-100-86-10012-110-113-10013-130-105-10014-75-98-7515-90-65-9016-30-40-301705018454245198072802090909021100971002210010310023108991002490639025-814-826-40-34-4027-55-58-5528-80-60-8029-45-54-4530-38-33-3831-15-18-1532-23-2332522253443384335454945365858583770697038806880395562554050355041000Timeevery 2ndTimeevery 3rdTimeevery 6thTimeevery 1200000000110250612512-11035557812-110249057881018453658712211-10024904109-2014-7530-3811-100170365813-130209041015-902310817026-40198029-452110032-223108354525-8388027-5541029-4531-153325354537703955410
Sheet1
RawTimeAmplitude
Sheet2
Ave before/afterTimeAmplitude
Sheet3
eliminate extremes (100/-100)TimeAmplitude
every 2ndTimeAmplitude
every 6thTimeAmplitude
every 3rdTimeAmplitude
every 12TimeAmplitudeevery 12th
Chart50105055757812512210-20-48-100-110-130-75-90-30045809010010010890-8-40-55-80-45-38-15-225434558708055500
RawTimeAmplitude
Sheet1TimeRawAve before/aftereliminate extremes (100/-100)000011020102503850355605547569755789378612510810071228610081037109-20-19-2010-48-56-4811-100-86-10012-110-113-10013-130-105-10014-75-98-7515-90-65-9016-30-40-301705018454245198072802090909021100971002210010310023108991002490639025-814-826-40-34-4027-55-58-5528-80-60-8029-45-54-4530-38-33-3831-15-18-1532-23-2332522253443384335454945365858583770697038806880395562554050355041000Timeevery 2ndTimeevery 3rdTimeevery 6thTimeevery 1200000000110250612512-11035557812-110249057881018453658712211-10024904109-2014-7530-3811-100170365813-130209041015-902310817026-40198029-452110032-223108354525-8388027-5541029-4531-153325354537703955410
Sheet1
RawTimeAmplitude
Sheet2
Ave before/afterTimeAmplitude
Sheet3
eliminate extremes (100/-100)TimeAmplitude
every 2ndTimeAmplitude
every 6thTimeAmplitude
every 3rdTimeAmplitude
every 12TimeAmplitudeevery 12th
Chart100507810-100-75090108-40-45-245800
every 3rdTimeAmplitude
Sheet1TimeRawAve before/aftereliminate extremes (100/-100)000011020102503850355605547569755789378612510810071228610081037109-20-19-2010-48-56-4811-100-86-10012-110-113-10013-130-105-10014-75-98-7515-90-65-9016-30-40-301705018454245198072802090909021100971002210010310023108991002490639025-814-826-40-34-4027-55-58-5528-80-60-8029-45-54-4530-38-33-3831-15-18-1532-23-2332522253443384335454945365858583770697038806880395562554050355041000Timeevery 2ndTimeevery 3rdTimeevery 6thTimeevery 1200000000110250612512-11035557812-110249057881018453658712211-10024904109-2014-7530-3811-100170365813-130209041015-902310817026-40198029-452110032-223108354525-8388027-5541029-4531-153325354537703955410
Sheet1
RawTimeAmplitude
Sheet2
Ave before/afterTimeAmplitude
Sheet3
eliminate extremes (100/-100)TimeAmplitude
every 2ndTimeAmplitude
every 6thTimeAmplitude
every 3rdTimeAmplitude
every 12TimeAmplitudeevery 12th
Chart50105055757812512210-20-48-100-110-130-75-90-30045809010010010890-8-40-55-80-45-38-15-225434558708055500
RawTimeAmplitude
Sheet1TimeRawAve before/aftereliminate extremes (100/-100)000011020102503850355605547569755789378612510810071228610081037109-20-19-2010-48-56-4811-100-86-10012-110-113-10013-130-105-10014-75-98-7515-90-65-9016-30-40-301705018454245198072802090909021100971002210010310023108991002490639025-814-826-40-34-4027-55-58-5528-80-60-8029-45-54-4530-38-33-3831-15-18-1532-23-2332522253443384335454945365858583770697038806880395562554050355041000Timeevery 2ndTimeevery 3rdTimeevery 6thTimeevery 1200000000110250612512-11035557812-110249057881018453658712211-10024904109-2014-7530-3811-100170365813-130209041015-902310817026-40198029-452110032-223108354525-8388027-5541029-4531-153325354537703955410
Sheet1
RawTimeAmplitude
Sheet2
Ave before/afterTimeAmplitude
Sheet3
eliminate extremes (100/-100)TimeAmplitude
every 2ndTimeAmplitude
every 6thTimeAmplitude
every 3rdTimeAmplitude
every 12TimeAmplitudeevery 12th
Chart110125-1104590-38580
every 6thTimeAmplitude
Sheet1TimeRawAve before/aftereliminate extremes (100/-100)000011020102503850355605547569755789378612510810071228610081037109-20-19-2010-48-56-4811-100-86-10012-110-113-10013-130-105-10014-75-98-7515-90-65-9016-30-40-301705018454245198072802090909021100971002210010310023108991002490639025-814-826-40-34-4027-55-58-5528-80-60-8029-45-54-4530-38-33-3831-15-18-1532-23-2332522253443384335454945365858583770697038806880395562554050355041000Timeevery 2ndTimeevery 3rdTimeevery 6thTimeevery 1200000000110250612512-11035557812-110249057881018453658712211-10024904109-2014-7530-3811-100170365813-130209041015-902310817026-40198029-452110032-223108354525-8388027-5541029-4531-153325354537703955410
Sheet1
RawTimeAmplitude
Sheet2
Ave before/afterTimeAmplitude
Sheet3
eliminate extremes (100/-100)TimeAmplitude
every 2ndTimeAmplitude
every 6thTimeAmplitude
every 3rdTimeAmplitude
every 12TimeAmplitudeevery 12th
Chart50105055757812512210-20-48-100-110-130-75-90-30045809010010010890-8-40-55-80-45-38-15-225434558708055500
RawTimeAmplitude
Sheet1TimeRawAve before/aftereliminate extremes (100/-100)000011020102503850355605547569755789378612510810071228610081037109-20-19-2010-48-56-4811-100-86-10012-110-113-10013-130-105-10014-75-98-7515-90-65-9016-30-40-301705018454245198072802090909021100971002210010310023108991002490639025-814-826-40-34-4027-55-58-5528-80-60-8029-45-54-4530-38-33-3831-15-18-1532-23-2332522253443384335454945365858583770697038806880395562554050355041000Timeevery 2ndTimeevery 3rdTimeevery 6thTimeevery 1200000000110250612512-11035557812-110249057881018453658712211-10024904109-2014-7530-3811-100170365813-130209041015-902310817026-40198029-452110032-223108354525-8388027-5541029-4531-153325354537703955410
Sheet1
RawTimeAmplitude
Sheet2
Ave before/afterTimeAmplitude
Sheet3
eliminate extremes (100/-100)TimeAmplitude
every 2ndTimeAmplitude
every 6thTimeAmplitude
every 3rdTimeAmplitude
every 12TimeAmplitudeevery 12th
Chart120-11090580
every 12TimeAmplitudeevery 12th
Sheet1TimeRawAve before/aftereliminate extremes (100/-100)000011020102503850355605547569755789378612510810071228610081037109-20-19-2010-48-56-4811-100-86-10012-110-113-10013-130-105-10014-75-98-7515-90-65-9016-30-40-301705018454245198072802090909021100971002210010310023108991002490639025-814-826-40-34-4027-55-58-5528-80-60-8029-45-54-4530-38-33-3831-15-18-1532-23-2332522253443384335454945365858583770697038806880395562554050355041000Timeevery 2ndTimeevery 3rdTimeevery 6thTimeevery 1200000000110250612512-11035557812-110249057881018453658712211-10024904109-2014-7530-3811-100170365813-130209041015-902310817026-40198029-452110032-223108354525-8388027-5541029-4531-153325354537703955410
Sheet1
RawTimeAmplitude
Sheet2
Ave before/afterTimeAmplitude
Sheet3
eliminate extremes (100/-100)TimeAmplitude
every 2ndTimeAmplitude
every 6thTimeAmplitude
every 3rdTimeAmplitude
every 12TimeAmplitudeevery 12th