מכללת bitlee קורס dsp יישומי לתעשיה. dsp- digital signal processing
TRANSCRIPT
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BITLEEBITLEEמכללת מכללת
יישומי לתעשיה יישומי לתעשיהDSPDSPקורס קורס
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DSP-
Digital
Signal
Processing
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FROM ANALOG FROM ANALOG TO DIGITAL DOMAINTO DIGITAL DOMAIN
25 March 200425 March 2004
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TOPICSTOPICS
Analog vs. digital: why, what & how
What is DSP?
What is DSP used for?
Speech & Audio processing Image & Video processing Adaptive filtering
Digital system example
Sampling & aliasing
Frequency analysis: why? & applications
DSP Devices and Architectures
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-0.2
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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
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Digital Digital vsvs analog proc’ing analog proc’ingDigital Signal Processing (DSPing)
• More flexible.
• Often easier system upgrade.
• Data easily stored.
• Better control over accuracy requirements.
• Noise reduction.
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
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DSPing: aim & toolsDSPing: 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
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What is DSP?What is DSP?
• Digital Signal Processing – the processing or manipulation of signals using digital techniques
ADC DACDigital Signal
ProcessorAnalogue to Digital Converter
Digital to Analogue Converter
Input Signal
Output Signal
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•Feed in analog signal
•Convert from analog to Digital
•Process mathematical representation of signal
•Convert from digital back to analog
•Output analog signal
•Real Time Processing of the mathematical
representations of signals
What is DSP?What is DSP?
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What is DSP Used For?What is DSP Used For?
……And much more!And much more!
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VIDEO
AUDIO
DATA
VOICE
DSP Technology & Markets
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Digital system exampleDigital system example
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Filter Antialiasing
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Digital Processing
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V Filter Reconstructio
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Sometimes steps missing
- Filter + A/D
- D/A + filter
General scheme
Topics of Topics of this lecture.this lecture.
Digital Processing
Filter
Antialiasing
A/D
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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
2
3Digital
Processing
A/D
Antialiasing Filter
ANALOG INPUTANALOG INPUT
DIGITAL DIGITAL OUTPUTOUTPUT
• Digital format.
What to use for processing? See slide “DSPing aim & tools”
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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.
**
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Generalized Sampling TheoremGeneralized Sampling Theorem
• Sampling rate must be greater than twice the analog signal’s bandwidth– Bandwidth is defined as
non-zero extent of spectrumof the continuous-time signalin positive frequencies
– Lowpass spectrum on right:bandwidth is fmax
– Bandpass spectrum on right:bandwidth is f2 – f1
Bandpass Spectrum
f1 f2f
–f2 –f1
Lowpass Spectrum
fmax-fmax
f
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Sampling Sampling - 2- 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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The sampling theoremThe sampling theoremA 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
1
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 !
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Sampling low-pass signalsSampling 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
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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.
(c) Antialiasing Antialiasing filterfilter
1
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(Some) ADC parameters(Some) ADC parameters1. Number of bits N (~resolution)
2. Data throughput (~speed)
3. Signal-to-noise ratio (SNR)
4. Signal-to-noise-&-distortion rate (SINAD)
5. Effective Number of Bits (ENOB)
6. Spurious-free dynamic range (SFDR)
7. Integral non-linearity (INL)
8. Differential non-linearity (DNL)
9. …
NB: Definitions may be slightly manufacturer-dependent!NB: Definitions may be slightly manufacturer-dependent!
Different Different applications have applications have different needs.different needs.
2
Static distortionStatic distortion
Dynamic distortionDynamic distortion
Imaging / video
Communication
Radar systems
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ADC - Number of bits NADC - Number of bits NContinuous input signal digitized into 2N levels.
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001
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VFSR
Uniform, bipolar transfer function Uniform, bipolar transfer function (N=3)(N=3)
Quantisation stepQuantisation step q =V FSR
2N
Ex: VFSR = 1V , N = 12 q = 244.1 V
LSBLSB
Voltage ( = q)
Scale factor (= 1 / 2N )
Percentage (= 100 / 2N )
-1
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0
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- q / 2
q / 2
Quantisation errorQuantisation error
2
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Digital Telephony Digital Telephony PCM (Pulse Code Modulation)PCM (Pulse Code Modulation)
• Standard telephone signal:
_ Telephone speech bandwidth 300hz-3.4khz
– Sampling Rate: 8 kHz– 8-bit samples– Data transfer rate = 88= 64kbits/s (64kbps)– ATU-TI G711
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Digital AudioDigital Audio
• Standard music CD:
_ Sound is audible in 20 Hz to 20 kHz range:
– Sampling Rate: 44.1 kHz– 16-bit samples– 2-channel stereo– Data transfer rate = 21644,100 = 1.4 Mbits/s– 1 hour of music = 1.43,600 = 635 MB
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Frequency domain Frequency domain (hints)(hints) Time & frequencyTime & frequency: two complementary signal descriptions.
Signals seen as “projected’ onto time or frequency domains.
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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