MIT6_003S10_lec22_handout

# MIT6_003S10_lec22_handout - 6.003: Signals and Systems...

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6.003: Signals and Systems Lecture 22 April 29, 2010 6.003: Signals and Systems Sampling and Quantization April 29, 2010 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 What to do with a billion transistors Gene Frantz , Texas Instruments Seminar, today, 4pm We are getting closer to a time when we will be able to co fectively integrate billions of transistors on an integrated circu fact, we are seeing the beginning of this era with the broad ado of multi-processing system-on-chips, which has both advantage disadvantages that should be considered. This talk will discu options we have, the issues we must face and the future we can forward to. Last Time: Sampling Theory Sampling: x ( t ) x [ n ]= x ( nT ) Bandlimited Reconstruction: LPF x [ n ] ω s 2 ω s 2 ω T Impulse Reconstruction x [ n ] δ ( t nT ) x p ( t )= x r ( t ) Sampling Theorem: If X ( )=0 ∀| ω | > ω 2 s then x r ( t x ( t ) . Practice Aliasing anti-aliasing ﬁlter 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 -1 0 0 1 1 Input voltage Output voltage 2 bits 3 bits 4 bits 00 01 10 0 0.5 1 -1 0 1 Time (second) 0 0.5 1 Time (second) 0 0.5 1 Time (second) -1 0 1 Input voltage -1 0 1 Input voltage Bit rate = (# bits/sample) × (# samples/sec) 1

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6.003: Signals and Systems Lecture 22 April 29, 2010 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 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 Quantization We measure discrete amplitudes in bits.
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## This note was uploaded on 11/07/2011 for the course ELECTRICA 6.003 taught by Professor Staff during the Summer '10 term at MIT.

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MIT6_003S10_lec22_handout - 6.003: Signals and Systems...

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