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MIT6_003S10_lec23

MIT6_003S10_lec23 - 6.003 Signals and Systems Quantization...

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6.003: Signals and Systems Quantization and Modulation May 4, 2010
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Last Time Quantization: discrete representation of amplitudes. 1 0 2 bits 4 bits 00 01 10 3 bits Output voltage -1 -1 0 1 -1 0 1 -1 0 1 Input voltage Input voltage Input voltage 0 0.5 1 -1 0 1 Time (second) 0 0.5 1 Time (second) 0 0.5 1 Time (second) Digital representations of signals require discrete representations of both the independent variable (time, space, ...) and dependent variable (amplitude).
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Quantizing Images Quantizing creates distortion. 8 bits 6 bits 4 bits 3 bits 2 bits 1 bit
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Quantization Adding noise (dither) can reduce the perceptual effect of quantiza- tion. Quantization: y = Q ( x ) Quantization with dither: y = Q ( x + n )
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Quantizing Images Adding noise (dither) reduces “banding” in images. 3 bits 2 bits 1 bit 3 bits dither 2 bits dither 1 bit dither
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Quantizing Sound Adding noise (dither) can reduces “distortions” in sound. 16 bits/sample 4 bits/sample 4 bits with dither/sample 3 bits/sample 3 bits with dither/sample 2 bit/sample 2 bit with dither/sample J.S. Bach, Sonata No. 1 in G minor Mvmt. IV. Presto Nathan Milstein, violin
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Robert’s Technique Robert’s technique decorrelates quantization errors from the signal. Quantization: y = Q ( x ) Quantization with dither: y = Q ( x + n ) Quantization with Robert’s technique: y = Q ( x + n ) n
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Quantizing Images Robert’s technique decorrelates quantization errors from the signal. 3 bits dither 2 bits dither 1 bit dither 3 bits Robert’s 2 bits Robert’s 1 bit Roberts
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Quantizing Sound Robert’s technique decorrelates quantization errors from the signal. 16 bits/sample 2 bits/sample 2 bits with dither/sample 2 bits with Robert’s technique/sample J.S. Bach, Sonata No. 1 in G minor Mvmt. IV. Presto Nathan Milstein, violin
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Fourier Analysis Quantization x ( t ) | X ( ) | t ω Dither x ( t ) | X ( ) | t ω Robert’s Technique x ( t ) | X ( ) | t ω
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Modulation Applications of signals and systems in communication systems. Example: Transmit voice via telephone wires (copper) mic amp telephone wire amp speaker Works well: basis of local land-based telephones.
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Wireless Communication In cellular communication systems, signals are transmitted via elec- tromagnetic (E/M) waves.
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