lecture10-f08

lecture10-f08 - Administrative EE264 Digital Signal...

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EE264 Digital Signal Processing Lecture 10 Quantization in Digital Filter Implementations - I October 22, 2008 Ronald W. Schafer Department of Electrical Engineering Stanford University STANFORD UNIVERSITY, EE264 Administrative • HW 5 due on Tuesday, Nov. 4 by 5pm in EE264 drawer on 2 nd floor Packard. • Mid-term exam: Weds., Oct. 29 in class. – Building 200 (Lane History Corner) - Room 203 – Covers material through Lecture 9 and HW 4. – Open textbook and one 8.5x11 sheet of notes (both sides) • READ: Chapter 6 of DTSP . • Review Session: Thursdays 4:15 - 5pm Gates B03 (recording available online) • Office Hours: – RWS: Mon./Weds 10-11, and 12:15-12:45 – Raunaq: Mon. 5-7pm, Tues. 9-11am – Rahim: Friday 4-6pm • Grader: Pegah Afshar, Ramin Miri STANFORD UNIVERSITY, EE264 Overview of Lecture • READ: Finish Chapter Chapter 5, read Chapter 6. • Implementation of LTI Systems – FIR structures • Intro to quantization in implementations • Fixed-point numbers – 2’s complement system – Representing fractions by integers STANFORD UNIVERSITY, EE264 accumulation ± ² ³ ³ ³ ³ ³ ³ ´ ³ ³ ³ ³ ³ ³ FIR Systems • FIR system functions have only zeros • In this case, direct form I is just convolution. H ( z ) = b k z k k = 0 M = h [ k ] z k k = 0 M y [ n ] = (( h [0] x [ n ] + h [1] x [ n 1]) + h [2] x [ n 2]) + ... () To implement this filter, we must do multiply followed by accumulation (MAC).
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STANFORD UNIVERSITY, EE264 FIR Linear Phase Systems h [ M n ] = h [ n ] y [ n ] = h [0] x [ n ] + x [ M ] () + h [1] x [ n 1] + x [ M + y [ n ] = h [ k ] x [ n k ] k = 0 M M even STANFORD UNIVERSITY, EE264 FIR Transposed Direct Form • FIR direct form • FIR transposed direct form x [ n ] y [ n ] STANFORD UNIVERSITY, EE264 Quantization in LTI Implementation - I ( B i +1)-bit A-to-D ( B o +1)-bit D-to-A ( B +1)-bit Processor Idealized system B Q STANFORD UNIVERSITY, EE264 Linear White 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 ) = σ e 2 = Δ 2 12 = 2 2 B X m 2 12 ,| | π ( Δ /2) < e [ n ] ( Δ /2).
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STANFORD UNIVERSITY, EE264 Quantization in LTI Implementation - II ( B i +1)-bit A-to-D ( B o +1)-bit D-to-A ( B +1)-bit Processor σ e i 2 = 2 2 B i 12 e a 2 = 2 2 B 12 e o 2 = 2 2 B o 12 Assume X m = 1 STANFORD UNIVERSITY, EE264
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lecture10-f08 - Administrative EE264 Digital Signal...

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