ELEC 3004: Signals, Systems & Control

Transcription

1 Noise & Data Acquisition ELEC 3004: Signals, Systems & Control Dr. Surya Singh, Prof. Brian Lovell & Dr. Paul Pounds Lecture # ## May 3, 2012 elec3004@itee.uq.edu.au School of Information Technology and Electrical Engineering at the University of Queensland Schedule of Events Week Date Lecture Title 1 1-Mar Overview Mar Signals & Systems 8-Mar Sampling 12-Mar Laplace 15-Mar LTI 19-Mar Convolution and Discrete Fourier Series 22-Mar Fourier Transform 26-Mar Fourier Transform Operations 29-Mar Applications: DFFT and DCT 2-Apr Exam 1 (10%) 5-Apr (Guest Lecture from Industry) 16-Apr Filters 19-Apr Filters 23-Apr Filters 26-Apr IIR Filters 30-Apr Multirate Filters 3-May Noise & Data Acquisition 7-May Holiday 10-May Quiz (10%) 14-May z-transform 17-May Introduction to Digital Control 21-May Stability of Digital Systems 24-May Estimation 28-May Kalman Filters & GPS 31-May Applications in Industry 2

2 Announcements We re working on the grading. Sorry for the delay! Homework 3 is coming! I have no additional news about Quiz 2! It will cover the material Brian covered. (Filters, etc.) 3 Outline Noise Dealing with it Interpolation Data Acquisition Connectors 4

3 I. Noise Note: this picture illustrates the concepts but it is not quantitatively precise Source: Prof. M. Siegel, CMU 5 Noise [2] Various Types: Thermal (white): Johnson noise, from thermal energy inherent in mass. Flicker or 1/f noise: Pink noise More noise at lower frequency Shot noise: Noise from quantum effects as current flows across a semiconductor barrier Avalanche noise: Noise from junction at breakdown (circuit at discharge) 6

4 Dealing with Noise Frequency Filters Band-Passing Modulation Give it a unique pattern Move it out of DC (sunlight) Phase Lock-in or synchronous detection Redundancy (measure twice) The System (don t get noise to begin with!) 7 How to beat the noise phase signal noise frequency Filtering (Narrow-banding): Only look at particular portion of frequency space Multiple measurements Other (modulation, etc.) 8

5 Noise Uncertainty Uncertainty: All measurement has some approximation A. Statistical uncertainty: quantified by mean & variance B. Systematic uncertainty: non-random error sources Law of Propagation of Uncertainty Combined uncertainty is root squared 9 Treating Uncertainty with Multiple Measurements 1. Over time: multiple readings of a quantity over time stationary or ergodic system Sometimes called integrating 2. Over space: single measurement (summed) from multiple sensors each distributed in space 3. Same Measurand: multiple measurements take of the same observable quantity by multiple, related instruments e.g., measure position & velocity simultaneously Basic sensor fusion. 10

6 I. Filters Band-pass Only allow a band (or range) of frequencies 0 db Signal magnitude Ideal filter pass-band -3 db ~ ½ power f 0 f c bandwidth real filter Initial frequency stop-band cutoff frequency Frequency 11 II. Interpolation & Re-sampling 12

7 Interpolation Increase sample rate Up-sampling by factor L L x u n x n / L, if n 0, L,2L,3L,... 0, otherwise e.g., x[n] = { } 2 x d [n] = { } Insert zeros between each sample 13 1 Up-sampled Sequence: x u [n] = x[n/2] Amplitude (x u [n]) Sample number (n/time) 14

8 Frequency Scaling /L Spectrum: X u [k] Image spectrums Angular Frequency -2 /L 2 /L 15 Interpolation Interpolation by factor L in time Produces frequency spectrum that is frequency scaled (by wl) X u ( w) x[ n]exp n jnwl X wl Replica spectrums (images) now appear in period {-, } to prevent aliasing images must be removed i.e., X u (w) must be bandlimited to /L with LPF 16

9 Interpolation Filter x[n] L x u [n] h[n] x u [n] Where x u [n] = x u [n] * h[n] Low-pass filter, h[n]: gain = L, cutoff /L X[k] L X u [k] H[k] X u [k] Where X u [k] = X u [k]h[k] X u [k] H[k] X u [k]

10 Interpolation Filters Both up and down-sampling require LPF Down-sampling: before decimation, prevents aliasing Up-sampling: after zero insertion, removes images Ideal brick-wall filter not realisable ideal sinc interpolation requires order (time extent) Therefore, practical LPF required Truncated (Windowed) Sinc Interpolation (DFT) Zero Order Hold (Nearest Neighbour) First Order Hold (Linear interpolation) Higher order: Quadratic or Cubic Interpolation Both FIR and IIR LPF implementations possible 19 Down-sampling: Example x[n] = { } down-sample factor M = 2 Moving average filter, gain = 1, w c /2 h ma [n] = {½ ½} (LPF) x [n] = x[n]*h ma [n] = { } x d [n] = { } Note: x[n] assumed zero beyond specified sequence Do not need to calculate values of x [n] that are decimated 20

11 Zero-order Hold Known as nearest neighbour (NN) Previous sample is held interpolated value is nearest original sample impulse response h nn [n] h nn 1, [ n] 0, L 2 n L 2, otherwise. Approximation is discontinuous Efficient as no computation required, just repeat values best suited to signals that are discontinuous, e.g., text 21 Zero Order Hold (NN) 8 Original samples interpolated samples

12 Zero Order Hold (NN) Impulse Response Frequency Response rect sinc Not a very good LPF, aliasing still occurs 23 First-order Hold (Linear) Sample interpolated from linear combination of two nearest samples Impulse response h lin [n] h lin 1 [ n] 0, n L, n L, otherwise. Interpolation is continuous in value, but discontinuous in gradient 2 multiplications required per sample best suited to smoothly varying signals (low gradients) 24

13 First Order Hold (Linear) 8 7 Original samples 6 5 interpolated samples First Order Hold (Linear) Impulse Response Frequency Response triang sinc 2 Improved LPF, but some loss in passband 26

14 Linear Interpolation: Example x[n] = { } up-sample factor L = 2 x u [n] = { } (insert zeros) Linear interpolation filter, gain = 2, w c /2 h lin [n] = {½ 1 ½} x u [n] = x u [n]*h lin [n] = { ½} Note: x u [n] assumed zero beyond specified sequence Interpolation passes through original samples 27 28

15 Re-sampling Combine up-sampling and down-sampling to re-sample to rational fractions L/M e.g., 2/3, 100/102 Usually, number original samples N re-sample to N samples need highest common factor between N and N As overall system is linear efficient (polyphase) implementations exist x[n] L h u [n] h [n] M d x r [n] 29 Applications of Re-sampling Multi-rate signal processing Minimising sample rate for processing bandwidth Over-sampling A/D and D/A conversion Reduction of quantisation noise Digital sample rate conversion CD (44.1KHz) DAT (48KHz) PAL (625 lines, 25 frames/s ) NTSC (525, 30 f/s) SDTV (576 lines, 50 f/s) HDTV (1125 lines, 50 f/s) Coding and compression Wavelets and QMFs Need to re-sample without going via analogue signal 30

16 Interpolation using the DFT DFT samples DTFT Normally N samples in both time & Frequency But we can increase the (DFT) sample density! By zero padding DFT zero padding sinc interpolation Windowed by length, N, of DFT (not ideal sinc) Applicable to other transforms e.g., DCT, Wavelets, etc Interpolation function is transform basis functions See lecture on applications of FFT for details 31 1 Original Sequence: x[n] Amplitude (x[n]) Sample number (n/time) 32

17 DFT 1 Orignal Spectrum: X[k] = 1 - k/pi X[k] Angular Frequency Replica Replica 33 34

18 Part II: DAQ There are many types of computing hardware available to the embedded system designer Selecting the right hardware is a critical part of the design cycle Requires an understanding of Computing requirements Available power Market size Interfaces 35 Data Acquisition Ex: PC104-DAS16Jr/16 1-Channel (16-bit) Analog to Digital Converter Multiplexer: Switches between 16 channels FPGA: talks to computer 36

19 DAQ Architecture & Terms Data Acquisition ADC No Multiplexer: Switches between MULTIPLE inputs to the ONE ADC!! Buffer/Register Samples and holds signal Adds delay Systems Issue: Processing (& drivers!) Interfacing 37 Analog to Digital Converter (A/D) HARWARE Take as input an analog signal Sample signal and output a digital number Key Parameters: Digital Resolution (8,10,12,16 bit) Sampling frequency (100KHz-10MHz) Input ranges normally +/-5 volts (may require amplification or scaling) 38

20 A/D Converters V ref Gnd Data to Computer Analog In Sample and Hold ADC D0-D7 Controller Data Register Interface Set Read Write Sync V+ V- Clock 39 Interfacing: Single-Ended 40

21 Interfacing: Differential 41 Practical anti aliasing filter Non-ideal filter, w c = w s =2 Filter usually 4th to 6th order (e.g., Butterworth) frequencies > wc may still be present not higher order as phase response gets worse (non-linear) Luckily, most real signals are lowpass in nature signal power reduces with increasing frequency e.g., speech naturally bandlimited (say < 8KHz) so, in practice aliasing is not (usually) a problem 42

22 Over-sampling A/D Converters Sample at rate Nyquist rate (say 8x) Relaxes stop-band criteria for analogue anti-aliasing filter use lower order analogue (IIR) filter i.e., less phase distortion fewer analogue components in filter Increased reliability, reduced aging and tolerance effects Apply digital decimation filter remove (unwanted) frequency components reduced aliasing effects Linear phase (FIR) filter Computationally efficient 43 Over-sampling A/D Converters 16 bit quantisation gives SNR 96dB White noise noise PSD: KHz (f s = 44.1KHz) If f s is doubled Noise bandwidth doubles: KHz Signal bandwidth remains: KHz Therefore, noise in KHz is halved! Apply decimation filter remove half the quantisation noise power 44.1KHz 176.4KHz 44

23 Signal Spectrum Quantisation Noise 0 f s /2 Doubled Sampling Frequency Digital lowpass filter 0 f s /2 Noise power halved (in band of interest) 45 Over-sampling D/A Converters Up-sample (interpolate) before D/A conversion Relaxes specifications for reconstruction filter use lower order IIR (reduced phase distortion) Apply digital interpolation (up-sampling) filter removes image spectrums reduces high frequency component from D/A converter (ZOH) use digital FIR filter, i.e., linear phase Computationally efficient As used on (some) CD Players! Up to 1bit A/D converters also known as delta de-modulation 46

24 9 D/A Output 9 Up-sampled D/A Output Sample number 2 1 smoother D/A o/p less high frequency energy for analogue reconstruction filter to remove Sample number 47 Part III: Cabling Is ½ science and ½ art Takes care Pays dividends Beats the noise! 48

25 Cabling Issues: Electrical 49 Grounding Low frequency symmetrical signal ~ Low frequency unsymmetrical signal ~ High frequency ~ 50

26 Ground Loop ~ ~ Later introduces ground loop. Why? 51 Wires Can & Do Move Bad! Good Source: J. Trevelyan, UWA 52

27 Connectors Purpose: transfer something Electrical, Optical, Hydraulic, Pneumatic, etc. Issues: Mechanics (Geometric Shape), Polarity (Orientation), Mating, Flow (has capability to transfer item), Environment, etc. 53 Electrical Connector Terms/Issues Conductive: Able to transfer the signal DC/AC Frequency Noise isolation/rejection Mechanical Assembly: Connector has to be join (easily) when needed and hold joint until disassembled Orientation: Can connector be inserted another (incorrect) way? Physical Layer (in Ethernet) 54

28 Some Popular Types Molex RJ-11 Packard RCA IDC MiniDIN 55 Numerous Vendors 56

29 Ex: Detailed Design & Usage Guides 1. Ø a b 8-17 mm 43 mm 54 mm 7-23 mm 52 mm 63 mm 4,5 10 b 15 a Ø Strip outer insulation and some shield, then strip inner wires (4 large, 3 thin) 2.1 Crimp special connector pins onto stripped wires ca.5mm Back shell Cable clamp (plastic) Middle shell (metal) Insert pins into keyed plastic connector guide pieces Assemble front shell, sealing O ring 51211AXX 57 Ex: USB Connector Strain relief Grounded Cover Finger Grip Power & Ground (on the outside) connect before signal lines (in the middle) 58

30 Common Connector Failures (1/3) Murphy s Law: If incorrect connection is possible it will happen Intermittent loss of contact Users will try to fit almost same connectors but not quite Screw connectors without rotation clamp Excessive flexure and vibration Excess disconnects and reconnects Corrosion or contamination 59 Common Connector Failures: Addressing Failures (2/3) Use high quality cables Use high quality connectors Ensure plugs only fit right socket Replace damaged cables don t attempt repairs Use sealed connectors if corrosion is possible 60

31 Common Connector Failures: System Approaches to Failures (3/3) Have spare cables, test them regularly Use serial digital communication, or optical communication, not parallel Use fault tolerant design Consider optical communication Eliminate unnecessary wires and cables Clean connectors 61 Group Practice: MineLab Metal Detector What are some of the good and troublesome issues here? 62

32 Switches More than just on & off Some Issues: Standards Bouncing Hysteresis 63 Switch Bounce Switches exhibit multiple transitions on ont digital system time scales Connection ~ms Why: age, inertia, dust, surface roughness Ex: Rising-edge switch bounce (for a 5A contact relay) Ideal switch Actual Voltage 6 ms Source: Maxim App Note

33 Switch Bounce Solutions Passive Filter Active Logic Circuits In R Out In R C C Schmitt trigger Many other alternatives Source: Maxim App Note Summary Digital re-sampling is ubiquitous! as more media becomes digital (music, voice, TV) Two broad techniques Time (spatial) domain Low pass filtering and decimation/interpolation Transform domain Extrapolating high frequency components Over-sampling can reduce both noise and analogue filter specifications during both Sampling (A/D) and reconstruction (D/A) 66