lecture7-f08

lecture7-f08 - Administrative EE264 Digital Signal...

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EE264 Digital Signal Processing Lecture 7 Oversampling in A-to-D Conversion October 13, 2008 Ronald W. Schafer Department of Electrical Engineering Stanford University STANFORD UNIVERSITY, EE264 Administrative • HW 3 due on Tuesday, Oct. 14 by 5pm in EE264 drawer on 2 nd floor Packard. HW 4 posted by Oct. 14. • READ: Sections 4.8 and 4.9 of DTSP and supplemental notes posted on website . • Review Sessions: Thursdays 4:15 - 5pm Gates B03 (available online) • Office Hours: – RWS: Mon./Weds 10-11, and 12:15-12:45 – Raunaq: Mon. 5-7pm, Tues. 9:00-11:00 am – Rahim: Friday 4-6pm • Grader: Pegah Afshar STANFORD UNIVERSITY, EE264 Overview of Lecture • READ: Sections 4.8 and 4.9 of DTSP • Oversampling eases anti-aliasing filtering • Oversampling can be used to improve signal-to- quantization noise ratio • Noise shaping in oversampled A-to-D and D-to-A conversion • Introduction and review of properties of LTI systems. STANFORD UNIVERSITY, EE264 Digital Processing of Analog Signals • Practical considerations in implementations: – The input signal cannot be perfectly bandlimited – A-to-D and D-to-A converters have finite- precision output and input respectively – Only finite-precision arithmetic is available for computations A-to-D Converter D-to-A Converter Finite- Precision Algorithm x c ( t ) x [ n ] y [ n ] y c ( t )
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STANFORD UNIVERSITY, EE264 Representation of A-to-D Converter Quantization step-size for ( B +1)-bit quantizer Δ= 2 X m 2 B + 1 = X m 2 B x [ n ] ˆ x [ n ] ˆ x [ n ] 011 010 001 000 111 110 101 100 111 110 101 100 011 010 001 000 2 X m A-to-D Converter STANFORD UNIVERSITY, EE264 Quantization Error • Each sample is quantized and each sample has a quantization error defined as • Since each sample falls in an interval of length Δ, and the quantized sample falls in the middle of that interval, • We call this “quantization noise” because it seems to vary randomly. Clearly, the strength (power) of this noise is proportional to Δ 2 ; i.e., e [ n ] = ˆ x [ n ] x [ n ] ( Δ /2) < e [ n ] ( Δ /2). σ e 2 = K Δ 2 STANFORD UNIVERSITY, EE264 Linear Noise Model • Error is uncorrelated with the input. • Error is uniformly distributed over the interval • Error is stationary white noise, (i.e. flat spectrum) P e ( ω ) = e 2 = 1 Δ e 2 de = −Δ /2 Δ Δ 2 12 ,| | π ( Δ < e [ n ] ( Δ x [ n ] ˆ x [ n ] = Q x [ n ] () ˆ x [ n ] = x [ n ] + e [ n ] x [ n ] e [ n ] STANFORD UNIVERSITY, EE264 Quantizer Signal-to-Noise Ratio • Assume levels and amplitude range .
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lecture7-f08 - Administrative EE264 Digital Signal...

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