3.a d conversion
DESCRIPTION
Digital signal processingTRANSCRIPT
Dr. C.Ramesh Babu Durai- From analog to digital domain 2 / 30
TOPICSTOPICS
1. Impact of DSP
2. Analog vs. digital: why, what & how
3. Digital system example
4. Sampling & aliasing
5. ADCs: performance & choice
6. Digital data formats
Dr. C.Ramesh Babu Durai- From analog to digital domain 3 / 30
Digital vs AnalogDigital vs Analog
Digital Signal Processing
• More flexible.
• Often easier system upgrade.
• Data easily stored.
• Better control over accuracy requirements.
• Reproducibility.
AdvantagesAdvantages
• A/D & signal processors speed: wide-band signals still difficult to treat (real-time systems).
• Finite word-length effect.
• Obsolescence (analog electronics has it, too!).
LimitationsLimitations
Dr. C.Ramesh Babu Durai- From analog to digital domain 4 / 30
Impact of DSP on Modern LivingImpact of DSP on Modern Living
Cellular/mobile telephony Speech and channel coding Voice and data processing Power management Multipath equaliztion
Digital audio Stereo and surround sound Audio equalization and mixing Electronic music
Automotive Digital Audio Digital Radio Personal communication systems Active suspension
Medical electronics Critical/intensive care monitors Digital X-rays ECG analyzers Cardiac monitors Medical imaging
Personal computer Sound cards Data storage and retrieval Error correction/concealment Multimedia Modems
Dr. C.Ramesh Babu Durai- From analog to digital domain 5 / 30
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Analog & digital signalsAnalog & digital signals
Continuous functionContinuous function V of continuouscontinuous variable t (time, space etc) : V(t).
Analog
Discrete functionDiscrete function Vk of
discretediscrete sampling variable tk,
with k = integer: Vk = V(tk).
Digital
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Uniform (periodic) sampling. Sampling frequency fS = 1/ tS
Dr. C.Ramesh Babu Durai- From analog to digital domain 6 / 30
DSP: aim & toolsDSP: aim & tools
Software• Programming languages: Pascal, C / C++ ...
• “High level” languages: Matlab, Mathcad, Mathematica…
• Dedicated tools (ex: filter design s/w packages).
Applications• Predicting a system’s output.
• Implementing a certain processing task.
• Studying a certain signal.
• General purpose processors (GPP), -controllers.
• Digital Signal Processors (DSP).
• Programmable logic ( PLD, FPGA ).
Hardware real-time real-time DSPingDSPing
FastFast
FasterFaster
Dr. C.Ramesh Babu Durai- From analog to digital domain 7 / 30
Digital system exampleDigital system example
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Filter Antialiasing
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A/D
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Digital Processing
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V Filter Reconstructio
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Sometimes steps missing
- Filter + A/D
(ex: economics);
- D/A + filter
(ex: digital output wanted).
General scheme
Topics of Topics of this lecture.this lecture.
Digital Processing
Filter
Antialiasing
A/D
Dr. C.Ramesh Babu Durai- From analog to digital domain 8 / 30
Digital system implementationDigital system implementation
• Sampling rate.
• Pass / stop bands.
KEY DECISION POINTS:KEY DECISION POINTS:Analysis bandwidth, Dynamic
range
• No. of bits. Parameters.
1
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3Digital
Processing
A/D
Antialiasing Filter
ANALOG INPUTANALOG INPUT
DIGITAL DIGITAL OUTPUTOUTPUT
• Digital format.
What to use for processing? See slide “DSPing aim & tools”
Dr. C.Ramesh Babu Durai- From analog to digital domain 9 / 30
SamplingSamplingHow fast must we sample a continuous signal to preserve its info content?
Ex: train wheels in a movie.
25 frames (=samples) per second.
Frequency misidentification due to low sampling frequency.
Train starts wheels ‘go’ clockwise.
Train accelerates wheels ‘go’ counter-clockwise.
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Why?Why?
* Sampling: independent variable (ex: time) continuous discrete.
Quantisation: dependent variable (ex: voltage) continuous discrete.
Here we’ll talk about uniform sampling.
**
Dr. C.Ramesh Babu Durai- From analog to digital domain 10 / 30
Sampling - 2Sampling - 2
__ s(t) = sin(2f0t)
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s(t) @ fS
f0 = 1 Hz, fS = 3 Hz
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__ s1(t) = sin(8f0t)-1.2
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__ s2(t) = sin(14f0t)-1.2
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sk (t) = sin( 2 (f0 + k fS) t ) , k s(t) @ fS represents exactly all sine-waves sk(t) defined by:
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Dr. C.Ramesh Babu Durai- From analog to digital domain 11 / 30
The sampling theoremThe sampling theorem
A signal s(t) with maximum frequency fMAX can be recovered if sampled at frequency fS > 2 fMAX .
Condition on fS?
fS > 300 Hz
t)cos(100πt)πsin(30010t)πcos(503s(t)
F1=25 Hz, F2 = 150 Hz, F3 = 50 Hz
F1 F2 F3
fMAX
Example
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Theo*
* Multiple proposers: Whittaker(s), Nyquist, Shannon, Kotel’nikov.
Nyquist frequency (rate) fN = 2 fMAX or fMAX or fS,MIN or fS,MIN/2Naming getsconfusing !
Dr. C.Ramesh Babu Durai- From analog to digital domain 12 / 30
Frequency domain (hints) Frequency domain (hints)
Time & frequencyTime & frequency: two complementary signal descriptions. Signals seen as “projected’ onto time or frequency domains.
Warning: formal description makes use of “negative” frequencies !
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BandwidthBandwidth: indicates rate of change of a signal. High bandwidth signal changes fast.
EarEar + brain act as frequency analyser: audio spectrum split into many narrow bands low-power sounds detected out of loud background.
Example
Dr. C.Ramesh Babu Durai- From analog to digital domain 13 / 30
Sampling low-pass signals Sampling low-pass signals
-B 0 B f
Continuous spectrum (a) Band-limited signal:
frequencies in [-B, B] (fMAX = B).(a)
-B 0 B fS/2 f
Discrete spectrum No aliasing (b) Time sampling frequency
repetition.
fS > 2 B no aliasing.
(b)
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0 fS/2 f
Discrete spectrum Aliasing & corruption (c)
(c) fS 2 B aliasing !aliasing !
Aliasing: signal Aliasing: signal ambiguity in frequency ambiguity in frequency domaindomain
Dr. C.Ramesh Babu Durai- From analog to digital domain 14 / 30
Antialiasing filterAntialiasing filter
-B 0 B f
Signal of interest
Out of band noise Out of band
noise
-B 0 B fS/2 f
(a),(b) Out-of-band noise can
aliase into band of interest. Filter it Filter it
before!before!
(a)
(b)
-B 0 B f
Antialiasing fi lter Passband
f requency
(c)
Passband: depends on bandwidth of interest.
Attenuation AMIN : depends on
• ADC resolution ( number of bits N).
AMIN, dB ~ 6.02 N + 1.76
• Out-of-band noise magnitude.
Other parameters: ripple, stopband frequency...
(c) Antialiasing Antialiasing filterfilter
1
Dr. C.Ramesh Babu Durai- From analog to digital domain 15 / 30
Under-sampling (hints) Under-sampling (hints)1
Using spectral replications to reduce Using spectral replications to reduce sampling frequency fsampling frequency fSS req’ments. req’ments.
m
BCf2Sf1m
BCf2
m , selected so that fS > 2B
B
0 fC
f
Bandpass signal centered on f C
-fS 0 fS 2fS f fC
AdvantagesAdvantages
Slower ADCs / electronics Slower ADCs / electronics needed.needed.
Simpler antialiasing filters.Simpler antialiasing filters.
fC = 20 MHz, B = 5MHz
Without under-sampling fS > 40 MHz.
With under-sampling fS = 22.5 MHz (m=1);
= 17.5 MHz (m=2); = 11.66 MHz (m=3).
ExamplExamplee
Dr. C.Ramesh Babu Durai- From analog to digital domain 16 / 30
Over-sampling (hints)Over-sampling (hints)1
fOS = over-sampling frequency,
w = additional bits required. fOS = 4w · fS
Each additional bit implies over-sampling by a factor of four. Each additional bit implies over-sampling by a factor of four.
It works for:
- white noisewhite noise with amplitude sufficient to change the input signal randomly from sample to sample by at least LSB.
- Input that can take all values between two ADC bits.
Caveat
Oversampling : sampling at frequencies fS >> 2 fMAX .
Over-sampling & averaging may improve ADC resolution
( i.e. SNR, see )2