INTRODUCTION TO DIGITAL SIGNAL PROCESSING Dr. Hugh Blanton ENTC 4347.

INTRODUCTION TODIGITAL SIGNAL PROCESSING

Dr. Hugh Blanton

ENTC 4347

Dr. Blanton - ENTC 4347 - 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


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


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


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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


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


Digital system exampleDigital system example

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Filter Antialiasing

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Digital Processing

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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


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”


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.

1

Why?Why?

* Sampling: independent variable (ex: time) continuous discrete.

Quantisation: dependent variable (ex: voltage) continuous discrete.

Here we’ll talk about uniform sampling.

**


Sampling - 2Sampling - 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 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

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 !


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 !

1

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


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)

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.

Other parameters: ripple, stopband frequency...

(c) Antialiasing Antialiasing filterfilter

1


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


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

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INTRODUCTION TO DIGITAL SIGNAL PROCESSING Dr. Hugh Blanton ENTC 4347.

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