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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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מכללת BITLEE

קורס DSP יישומי לתעשיה


DSP-

Digital

Signal

Processing


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

  • Digital system example

  • Sampling & aliasing

  • Frequency analysis: why? & applications

  • DSP Devices and Architectures


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


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)


  • 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?

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 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?

…And much more!


DATA

VIDEO

AUDIO

DSP Technology & Markets

VOICE


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


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.


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.


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


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


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


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


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


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


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)

  • 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

  • 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


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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