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Lesson 05-Finite Wordlength Effects

Lesson 05-Finite Wordlength Effects - Finite Wordlength...

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Lesson 05 Finite Wordlength Effects Challenge 04 Lesson 05 Data Acquisition Survey Quantization Errors Challenge 05 What’s the deal? • How are continuous time signals quantized? • What is a quantization error? • How can quantization errors be computed? • How can quantization errors be interpreted?

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Lesson 05 Challenge 04 You are working at your multimedia PC doing some hedonistic voice recordings with a pirated copy of MATLAB’s audio suite, sampling at 8kSa/ s. Your dog “Killer” is asleep at your feet. You decide that it’s time to feed Killer and head to the kitchen. You are amazed that even though you heard nothing, as soon as you remove the pull-top tab on the dog food can cover, Killer is standing right next to you. Upon returning to you PC you find out you left the record button on. You listen to the recorded sounds and find out that there is a detectible 3kHz tone which, when played, sounds like the slow weird tearing of a pull-top. What frequency (most probably) did Killer hear? (Assume you can hear out to 15kHz)
Lesson 05 Challenge 04 Analyze the question using the unit circle approach to aliasing. Given f s =8000 Sa/s Did Killer hear the basaeband 3000Hz signal? ± 4000, … 3000 Yes, but you would have head this too. 0, ± 8000, …

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Lesson 05 Challenge 04 Given f s =8000 Sa/s Did Killer hear the non-baseband sources mapped to 3000Hz? ± 4000, … 3000 Yes, but you would have head them too. 0, ± 8000, … -5000, 11000, -13000?
Lesson 05 Challenge 04 Given f s =8000 Sa/s What about 19000Hz? ± 4000, … 3000 You wouldn’t have heard it but Killer did. 0, ± 8000, … 19000 = 16000 + 3000

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Lesson 05 Typical Data Acquisition System Remember, Shannon’s sampling theorem applies to the discrete-time  portion of this system. The digital portion introduces errors, called quantization errors.  The DSP  engineer needs to be able to quantify these errors.
Lesson 05 Data Conversion But first, an Analog to Digital survey ADC overview ADC types ADC enhancements Today’s DSP solutions are ADC – bound and not compute – bound!

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Lesson 05 Data Conversion Practical ADC system  with programmable  conversion rates. Anti-aliasing filter
Lesson 05 ADC Types Delta-sigma ( ∆Σ ) converter. Loop Filter e(t)

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Lesson 05 ADC Types Delta-sigma ( ∆Σ ) converter.
Lesson 05 ADC Types Flash converters

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Lesson 05 ADC Types Successive approximation (SA) converter.
Lesson 05 ADC Types Subrange converter.

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Lesson 05 ADC Types Pipelined converter.
Lesson 05 ADC Types Folding or interpolating converter.

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Lesson 05 ADC Comparison (Pentek) Note: Input BW ~ 2x f s
Lesson 05 ADC Comparison 10 2       10 9 Sa/S 24 20 16 12 8 4 Precision  (bits) Sigma-Delta Successive  Approximation Subrange Pipeline Folded Flash 20b~120db 10b~60db

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Lesson 05 ADC Comparison Source: Analog Devices ADC Comparison Attribute Flash Pipelined SAR Σ∆ Throughput 1 2 3 4 Resolution (Effectve # of bits - ENOB) 4 3 2 1 Latency 1 3 2 4 Suitability for converting multiple signal per ADC 1 2 1 3 Undersampling * * * Dithering (increase resolution) * * * * permitted Ranked 1-4 (1 highest)
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