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מכללת BITLEE. קורס DSP יישומי לתעשיה. DSP- D igital S ignal P rocessing. FROM ANALOG TO DIGITAL DOMAIN. 25 March 2004. TOPICS. Analog vs. digital: why, what & how What is DSP? What is DSP used for? Speech & Audio processing Image & Video processing Adaptive filtering

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Bitlee

מכללת BITLEE

קורס DSP יישומי לתעשיה


Bitlee

DSP-

Digital

Signal

Processing


From analog to digital domain

FROM ANALOG TO DIGITAL DOMAIN

25 March 2004


Topics

TOPICS

  • 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


Analog digital signals

Analog

Digital

Discrete function Vk of discrete sampling variable tk, with k = integer: Vk = V(tk).

Continuous function V of continuous variable t (time, space etc) : V(t).

Uniform (periodic) sampling. Sampling frequency fS = 1/ tS

Analog & digital signals


Digital vs analog proc ing

Limitations

Advantages

  • 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!).

  • More flexible.

  • Often easier system upgrade.

  • Data easily stored.

  • Better control over accuracy requirements.

  • Noise reduction.

Digital vs analog proc’ing

Digital Signal Processing (DSPing)


Dsping aim tools

  • Predicting a system’s output.

  • Implementing a certain processing task.

  • Studying a certain signal.

Applications

  • General purpose processors (GPP), -controllers.

  • Digital Signal Processors (DSP).

  • Programmable logic ( PLD, FPGA ).

Hardware

Fast

Faster

real-time DSPing

  • Programming languages: Pascal, C / C++ ...

  • “High level” languages: Matlab, Mathcad, Mathematica…

  • Dedicated tools (ex: filter design s/w packages).

Software

DSPing: aim & tools


What is dsp

What is DSP?

Digital Signal Processing – the processing or manipulation of signals using digital techniques

Digital Signal Processor

Input Signal

Output Signal

ADC

DAC

Analogue to Digital Converter

Digital to Analogue Converter


What is dsp1

What is DSP?

  • 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 used for

What is DSP Used For?

…And much more!


Bitlee

DATA

VIDEO

AUDIO

DSP Technology & Markets

VOICE


Digital system example

General scheme

ANALOG DOMAIN

FilterAntialiasing

FilterAntialiasing

Sometimes steps missing

- Filter + A/D

- D/A + filter

A/D

A/D

DIGITAL DOMAIN

Digital Processing

Digital Processing

D/A

ANALOG DOMAIN

Topics of this lecture.

FilterReconstruction

Digital system example


Digital system implementation

ANALOG INPUT

Antialiasing Filter

1

2

3

A/D

Digital Processing

• Digital format.

What to use for processing?

See slide “DSPing aim & tools”

DIGITAL OUTPUT

Digital system implementation

KEY DECISION POINTS:

Analysis bandwidth, Dynamic range

•Sampling rate.

• Pass / stop bands.

• No. of bits. Parameters.


Sampling

1

*

Ex: train wheels in a movie.

25 frames (=samples) per second.

Train starts wheels ‘go’ clockwise.

Train accelerates wheels ‘go’ counter-clockwise.

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

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

Here we’ll talk about uniform sampling.

Sampling

How fast must we sample a continuous signal to preserve its info content?

Why?

Frequency misidentification due to low sampling frequency.


Generalized sampling theorem

Lowpass Spectrum

f

-fmax

fmax

Bandpass Spectrum

f

–f1

f2

–f2

f1

Generalized Sampling Theorem

  • Sampling rate must be greater than twice the analog signal’s bandwidth

    • Bandwidth is defined asnon-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


Sampling 2

1

__ s(t) = sin(2f0t)

s(t) @ fS

f0 = 1 Hz, fS = 3 Hz

__ s1(t) = sin(8f0t)

__ s2(t) = sin(14f0t)

s(t) @ fS represents exactly all sine-waves sk(t) defined by:

sk (t) = sin( 2 (f0 + k fS) t ) , k 

Sampling - 2


The sampling theorem

1

Example

Condition on fS?

F1

F2

F3

fS > 300 Hz

F1=25 Hz, F2 = 150 Hz, F3 = 50 Hz

fMAX

The sampling theorem

A signal s(t) with maximum frequency fMAX can be recovered if sampled at frequency fS > 2 fMAX .

Theo*

*Multiple proposers: Whittaker(s), Nyquist, Shannon, Kotel’nikov.

Naming gets

confusing !

Nyquist frequency (rate) fN = 2 fMAXor fMAXor fS,MINor fS,MIN/2


Sampling low pass signals

1

(a)Band-limited signal:

frequencies in [-B, B] (fMAX = B).

(a)

(b)

(b)Time sampling frequency repetition.

fS > 2 B no aliasing.

(c)

(c)fS 2 B aliasing !

Aliasing: signal ambiguity in frequency domain

Sampling low-pass signals


Antialiasing filter

1

(a)

(a),(b)Out-of-band noise can aliase into band of interest. Filter it before!

(c)Antialiasing filter

(b)

  • 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 filter


Some adc parameters

2

Different applications have different needs.

  • Number of bits N (~resolution)

  • Data throughput (~speed)

  • Signal-to-noise ratio (SNR)

  • Signal-to-noise-&-distortion rate (SINAD)

  • Effective Number of Bits (ENOB)

  • Spurious-free dynamic range (SFDR)

  • Integral non-linearity (INL)

  • Differential non-linearity (DNL)

Radar systems

Static distortion

Communication

Dynamic distortion

Imaging / video

NB: Definitions may be slightly manufacturer-dependent!

(Some) ADC parameters


Adc number of bits n

2

Continuous input signal digitized into 2N levels.

Uniform, bipolar transfer function (N=3)

Quantisation step q =

V FSR

2N

Ex: VFSR = 1V , N = 12 q = 244.1 V

Voltage ( = q)

Scale factor (= 1 / 2N )

Percentage (= 100 / 2N )

LSB

Quantisation error

ADC - Number of bits N


Digital telephony pcm pulse code modulation

Digital Telephony PCM (Pulse Code Modulation)

  • Standard telephone signal:

    _ Telephone speech bandwidth 300hz-3.4khz

    • Sampling Rate: 8 kHz

    • 8-bit samples

    • Data transfer rate = 88= 64kbits/s (64kbps)

    • ATU-TI G711


Digital audio

Digital 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 = 21644,100 = 1.4 Mbits/s

    • 1 hour of music = 1.43,600 = 635 MB


Frequency domain hints

1

Example

Ear + brain act as frequency analyser: audio spectrum split into many narrow bands low-power sounds detected out of loud background.

  • Bandwidth: indicates rate of change of a signal. High bandwidth signal changes fast.

Frequency domain (hints)

  • Time & frequency: two complementary signal descriptions. Signals seen as “projected’ onto time or frequency domains.


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