5a sampling and quantization - hawa.work sampling and quantization.pdf · title: microsoft...

2/8/2018

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Lecture 5a: Sampling and Quantization

Dr. Mohammed HawaElectrical Engineering Department

University of Jordan

EE421: Communications I

Copyright © Dr. Mohammed Hawa Electrical Engineering Department, University of Jordan

Digitization

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Digital Systems Advantages

• Immunity to noise (threshold detection; regenerative repeaters).

• Multiplexing at the baseband level (e.g., TDM) and carrier level (e.g., FDM, CDMA and OFDMA).

• Spread spectrum techniques and orthogonality.• Channel coding (i.e., error correcting codes).• Source coding techniques (i.e., compression). Also

Encryption.• Exchanging SNR for bandwidth.• Using microprocessors and DSP.• Digital signal storage is relatively easy and

inexpensive.

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Digitization

• Sampling (discrete analog signal).• Quantization (quantized discrete signal)• Mapping (stream of 1’s and 0’s). • Encoding and Pulse Shaping (digital baseband signal).

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Analog Signal

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Ideal Sampling

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Practical Sampling

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Samlping

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Ideal Sampling

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Aliasing

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Anti-Aliasing Filter

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Natural Sampling

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Practical Sampling: PAM

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t0 V

m(t)

t0 V

ω0

γ|M(ω)|

2πB−2πB

x(t)

ω

|X(ω)|

LPFγ /Ts γ /Tsγ /Ts γ /Tsγ /Ts γ /Tsγ /Ts

0 ωs−ωs 2ωs−2ωs 3ωs−3ωs

t0 V

x(t)

Ts

t0 V

p(t)

ω0

|P(ω)|

2π/τ−2π/τ

|τ sinc(ωτ/2π)|1.0

τ

ω

|X(ω)|

LPFτ γ / Ts

0 2π/τ−2π/τ

Ts

∗


PAM: Wider Pulses (S/H)

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t0 V

m(t)

t0 V

ω0

γ|M(ω)|

2πB−2πB

x(t)

ω

|X(ω)|

LPFγ /Ts γ /Tsγ /Ts γ /Tsγ /Ts γ /Tsγ /Ts

0 ωs−ωs 2ωs−2ωs 3ωs−3ωs

t0 V

x(t)

Ts

t0 V

p(t)

ω0

|P(ω)|

2π/τ−2π/τ

|τ sinc(ωτ/2π)|1.0

τ

ω

|X(ω)|

LPFτ γ / Ts

0 2π/τ−2π/τ

Ts

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Distortion solved by Equalizer

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Summary

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After Sampling!

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Quantization (L = 5)

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Quantization (L = 10)

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Quantization (Approx.)

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Quantization Error

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Quantization Error

�� = �2��2�� =

�2�� 23�2 �

= 3�2�2��2

= 3�2��2

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Uniform Quantization

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Compander

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Effect is Expansion/Compression

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Compading Improvement (dB)

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Mapping

T0 = Ts / log2 (L)

f0 [bps] = fs [samples/s] × log2 (L) [bits/sample]

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Source Coding

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Audio Compression

• Landline telephony (PCM, no compression)– 64 kbps

• Linear Prediction Coding (LPC) vocoder– e.g., RPE-LTP (regular pulse excitation, long-term

prediction) LPC codec (GSM cellular phones, Full Rate): 13 kbps.

• Code-Excited linear Prediction (CELP) vocoder– Algebraic CELP(ACELP) (GSM cellular phones,

Enhanced Full Rate): 12.2 kbps

– FS-1016 (United States Department of Defense): 4.8 kbps

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Video Compression

• ITU-T: International Telecommunication Union - Telecommunication • MPEG: Moving Picture Experts Group

• MPEG-2: DVD, Digital TV Broadcasting.

• H.261: Videophone.

• H.263: Low bit rate Video Conferencing.

• H.264: Almost everything.

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MPEG

MPEG-1

MPEG-2

ITU-T

H.261

H.263

H.264/MPEG-4 Part 10 or

AVC (Advanced Video Coding)

H.265/MPEG-H Part 2 or

HEVC (High Efficiency Video Coding)

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Channel Coding

� = ��ℎ × log2�1 + ��

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