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יישומי לתעשיה יישומי לתעשיהDSPDSPקורס קורס

DSP-

Digital

Signal

Processing

FROM ANALOG FROM ANALOG TO DIGITAL DOMAINTO DIGITAL DOMAIN

25 March 200425 March 2004

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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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

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

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

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

•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?

What is DSP Used For?What is DSP Used For?

……And much more!And much more!

VIDEO

AUDIO

DATA

VOICE

DSP Technology & Markets

Digital system exampleDigital system example

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Digital Processing

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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

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”

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.

**

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

Sampling Sampling - 2- 2

__ s(t) = sin(2f0t)

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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

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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 !

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)

1

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

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

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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.

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Static distortionStatic distortion

Dynamic distortionDynamic distortion

Imaging / video

Communication

Radar systems

ADC - Number of bits NADC - Number of bits NContinuous input signal digitized into 2N levels.

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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 )

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q / 2

Quantisation errorQuantisation error

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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

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

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