MIT6_003S10_lec22

# MIT6_003S10_lec22 - 6.003 Signals and Systems Sampling and...

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6.003: Signals and Systems Sampling and Quantization April 29, 2010

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Last Time: Sampling Sampling allows the use of modern digital electronics to process, record, transmit, store, and retrieve CT signals. audio: MP3, CD, cell phone pictures: digital camera, printer video: DVD everything on the web
Last Time: Sampling ω T x [ n ] x r ( t ) Impulse x p ( t )= Theory Sampling: x ( t ) x [ n ]= x ( nT ) Bandlimited Reconstruction: LPF Reconstruction x [ n ] δ ( t nT ) ω 2 s ω 2 s Sampling Theorem: If X ( )=0 ∀| ω | > ω 2 s then x r ( t x ( t ) . Practice Aliasing anti-aliasing ﬁlter

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Today Digital recording, transmission, storage, and retrieval requires dis- crete representations of both time (e.g., sampling) and amplitude. audio: MP3, CD, cell phone pictures: digital camera, printer video: DVD everything on the web Quantization: discrete representations for amplitudes
Quantization We measure discrete amplitudes in bits. 1 Output voltage -1 -1 0 0 1 2 bits 00 01 10 -1 0 1 Input voltage Input voltage 3 bits -1 0 1 Input voltage 4 bits 0 0.5 1 -1 0 1 0 0.5 1 0 0.5 1 Time (second) Time (second) Time (second) Bit rate = (# bits/sample) × (# samples/sec)

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Check Yourself We hear sounds that range in amplitude from 1,000,000 to 1. How many bits are needed to represent this range? 1. 5 bits 2. 10 bits 3. 20 bits 4. 30 bits 5. 40 bits
Check Yourself How many bits are needed to represent 1,000,000:1? bits range 1 2 2 4 3 8 4 1 6 5 3 2 6 6 4 7 128 8 256 9 512 10 1 , 024 11 2 , 048 12 4 , 096 13 8 , 192 14 16 , 384 15 32 , 768 16 65 , 536 17 131 , 072 18 262 , 144 19 524 , 288 20 1 , 048 , 576

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Check Yourself We hear sounds that range in amplitude from 1,000,000 to 1. How many bits are needed to represent this range? 3 1. 5 bits 2. 10 bits 3. 20 bits 4. 30 bits 5. 40 bits
Quantization Demonstration Quantizing Music 16 bits/sample 8 bits/sample 6 bits/sample 4 bits/sample 3 bits/sample 2 bit/sample J.S. Bach, Sonata No. 1 in G minor Mvmt. IV. Presto Nathan Milstein, violin

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Quantization We measure discrete amplitudes in bits. -1 0 1 Output voltage 2 bits 3 bits 4 bits 00 01 10 -1 0 1 -1 0 1 -1 0 1 Input voltage Input voltage Input voltage -1 0 1 0 0.5 1 0 0.5 1 0 0.5 1 Time (second) Time (second) Time (second) Example: audio CD 2 channels × 16 bits × 44 , 100 samples × 60 sec × 74 min 6 . 3 G bits sample sec min 0 . 78 G bytes
Quantizing Images Converting an image from a continuous representation to a discrete representation involves the same sort of issues. This image has 280 × 280 pixels, with brightness quantized to 8 bits.

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Quantizing Images 8 bit image 7 bit image
Quantizing Images 8 bit image 6 bit image

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Quantizing Images 8 bit image 5 bit image
Quantizing Images 8 bit image 4 bit image

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Quantizing Images 8 bit image 3 bit image
Quantizing Images 8 bit image 2 bit image

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Quantizing Images 8 bit image 1 bit image
Check Yourself What is the most objectionable artifact of coarse quantization?

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MIT6_003S10_lec22 - 6.003 Signals and Systems Sampling and...

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