hamming

Recommendations

Info

DIGITAL FILTERS—III 121Figure 16.VInoise. No linear method can separate the signal from the noise at the same frequencies, but those beyond thesignal can be so removed by a low pass filter. Therefore, when we “over sample” we have a chance toremove more of the noise by a low pass filter.Remember, there is the implicit understanding we are processing a linear system. The old stock marketFourier analysis which revealed there was only white noise was interpreted to mean there was no way ofpredicting the future prices of the stocks—and this is correct only if you intend to use simple linearpredictors. It says nothing about the practical use of nonlinear predictors, however. Once again a widespread misinterpretation of a result because of a lack of understanding of the basics behind themathematical tool, and only knowing the tool itself. A little knowledge is a dangerous thing—especially ifyou lack the fundamentals!I carefully said in the opening talk on digital filters I thought at that time I knew nothing about them.What I did not know was, because I was then ignorant of recursive digital filter design, I had effectivelycreated it when I examined closely the theory of predictorcorrector methods of numerically solving ordinarydifferential equations. The corrector is practically a recursive digital filter!While doing the study on how to integrate a system of ordinary differential equation numerically I wasunhampered by any preconceived ideas about digital filters, and I soon realized a bounded input, in thewords of the filter experts, could produce, if you were integrating, an unbounded output—which they saidwas unstable, but clearly it is just what you must have if you are to integrate; even a constant will produce alinear growth in the output. Indeed, when later I faced integrating trajectories down to the surface of themoon where there is no air, hence no drag, hence no first derivatives explicitly in the equations, and wantedto take advantage of this by using a suitable formula for numerical integration, I found I had to have aquadratic error growth; a small roundoff error in the computation of the acceleration would not be correctedand would lead to a quadratic error in position: an error in the acceleration produces a quadratic growth inposition. That is the nature of the problem, unlike on earth where the air drag provides some feedbackcorrection to the wrong value of the acceleration and hence some correction to the error in the position.
122 CHAPTER 16Thus I have to this day the attitude stability in digital filters means “not exponential growth” from boundedinputs, but allows polynomial growth, and this is not the standard stability criterion derived from classicalanalog filters, where if it were not bounded you would melt things down —and anyway they had neverreally thought hard about integration as a filter process.We will take up this important topic of recursive filters, which are necessary for integration, in the nextchapter.
Page 2 and 3:
The Art of Doing Science and Engine
Page 4 and 5:
This edition published in the Taylo
Page 6 and 7:
23 Mathematics 16324 Quantum Mechan
Page 8 and 9:
The year 2020 seems a convenient da
Page 10 and 11:
1OrientationThe purpose of this cou
Page 12 and 13:
ORIENTATION 3Telephone Laboratories
Page 14 and 15:
they arise so you will not be left
Page 16 and 17:
ORIENTATION 7One of the main tasks
Page 18 and 19:
2Foundations of the Digital (Discre
Page 20 and 21:
FOUNDATIONS OF THE DIGITAL (DISCRET
Page 22 and 23:
Page 24 and 25:
Page 26 and 27:
3History of Computers— HarwareThe
Page 28 and 29:
HISTORY OF COMPUTERS—HARDWARE 19b
Page 30 and 31:
HISTORY OF COMPUTERS—HARDWARE 21T
Page 32 and 33:
HISTORY OF COMPUTERS—HARDWARE 23B
Page 34 and 35:
HISTORY OF COMPUTERS—SOFTWARE 25(
Page 36 and 37:
HISTORY OF COMPUTERS—SOFTWARE 27A
Page 38 and 39:
HISTORY OF COMPUTERS—SOFTWARE 29F
Page 40 and 41:
HISTORY OF COMPUTERS—SOFTWARE 31b
Page 42 and 43:
5History of Computer ApplicationAs
Page 44 and 45:
HISTORY OF COMPUTER APPLICATIONS 35
Page 46 and 47:
Page 48 and 49:
Page 50 and 51:
asic understanding of when the meth
Page 52 and 53:
ARTIFICIAL INTELLIGENCE—I 43chang
Page 54 and 55:
ARTIFICIAL INTELLIGENCE—I 45Early
Page 56 and 57:
7Artificial Intelligence—IIIn thi
Page 58 and 59:
ARTIFICIAL INTELLIGENCE—II 49mome
Page 60 and 61:
ARTIFICIAL INTELLIGENCE—II 51have
Page 62 and 63:
ARTIFICIAL INTELLIGENCE—II 53can
Page 64 and 65:
8Artificial Intelligenc—IIII sugg
Page 66 and 67:
9n-Dimensional spaceWhen I became a
Page 68 and 69:
N-DIMENSIONAL SPACE 59Figure 9. IIl
Page 70 and 71:
N-DIMENSIONAL SPACE 61and hence the
Page 72 and 73:
N-DIMENSIONAL SPACE 63where X and Y
Page 74 and 75:
N-DIMENSIONAL SPACE 653. D(x,y)=D(y
Page 76 and 77:
10Coding Theory—IHaving looked at
Page 78 and 79:
CODING THEORY—I 69is uniquely dec
Page 80 and 81: CODING THEORY—I 71Figure 10.IVFig
Page 82 and 83: CODING THEORY—I 73I feel it neces
Page 84 and 85: CODING THEORY—II 75Figure 11.IFig
Page 86 and 87: CODING THEORY—II 77Figure 11.VThi
Page 88 and 89: CODING THEORY—II 79in this scheme
Page 90 and 91: 12Error Correcting CodesThere are t
Page 92 and 93: ERROR CORRECTING CODES 83Figure 12.
Page 94 and 95: ERROR CORRECTING CODES 85old syndro
Page 96 and 97: ERROR CORRECTING CODES 87mention it
Page 98 and 99: 13Information TheoryInformation The
Page 100 and 101: INFORMATION THEORY 91Figure 13.IThi
Page 102 and 103: INFORMATION THEORY 93Figure 13.IIIc
Page 104 and 105: INFORMATION THEORY 95Let us critiqu
Page 106 and 107: 14Digital Filters—INow that we ha
Page 108 and 109: DIGITAL FILTERS—I 99for any other
Page 110 and 111: DIGITAL FILTERS—I 101Figure 14.IT
Page 112 and 113: DIGITAL FILTERS—I 103Figure 14.II
Page 114 and 115: DIGITAL FILTERS—I 105Figure 14.IV
Page 116 and 117: 15Digital Filters— IIWhen digital
Page 118 and 119: DIGITAL FILTERS—II 109Let us run
Page 120 and 121: DIGITAL FILTERS—II 111Figure 15.I
Page 122 and 123: DIGITAL FILTERS—II 113At x=0 this
Page 124 and 125: 16Digital Filters—IIIWe are now r
Page 126 and 127: DIGITAL FILTERS—III 117Figure 16.
Page 128 and 129: DIGITAL FILTERS—III 119We next tu
Page 132 and 133: 17Digital Filters—IVWe now turn t
Page 134 and 135: DIGITAL FILTERS—IV 125These recur
Page 136 and 137: DIGITAL FILTERS—IV 127Figure 17.I
Page 138 and 139: SIMULATION—I 129Figure 18.IThe fi
Page 140 and 141: SIMULATION—I 131(though they had
Page 142 and 143: SIMULATION—I 133Figure 18.IIIinte
Page 144 and 145: 19Simulation—IIWe now take up the
Page 146 and 147: SIMULATION—II 137The major part o
Page 148 and 149: SIMULATION—II 139energy or angula
Page 150 and 151: 20Simulation—IIII will continue t
Page 152 and 153: SIMULATION—III 143Figure 20.IVFig
Page 154 and 155: SIMULATION—III 145Figure 20.VIdow
Page 156 and 157: SIMULATION—III 147Figure 20.VIIIW
Page 158 and 159: SIMULATION—III 149Now to the next
Page 160 and 161: 21Fiber OpticsOne of the reasons fo
Page 162 and 163: FIBER OPTICS 153Figure 21.IIII did
Page 164 and 165: FIBER OPTICS 155Figure 21.IVFigure
Page 166 and 167: 22Computer Aided Instruction—CAIB
Page 168 and 169: COMPUTER AIDED INSTRUCTION—CAI 15
Page 170 and 171: and they all knew immediately it wa
Page 172 and 173: 23MathematicsAs you live your life
Page 174 and 175: MATHEMATICS 165Figure 23.IFigure 23
Page 176 and 177: MATHEMATICS 167illustrates my attit
Page 178 and 179: MATHEMATICS 169can use the same for
Page 180 and 181:
24Quantum MechanicsMost physicists
Page 182 and 183:
taught QM, no one has found a widel
Page 184 and 185:
QUANTUM MECHANICS 175I do not prete
Page 186 and 187:
CREATIVITY 177I hope the above has
Page 188 and 189:
CREATIVITY 179“memorizing the mat
Page 190 and 191:
26ExpertsAs remarked in an earlier
Page 192 and 193:
EXPERTS 183Figure 26.ILaboratories
Page 194 and 195:
EXPERTS 185Figure 26.IIthe final an
Page 196 and 197:
27Unreliable DataIt has been my exp
Page 198 and 199:
UNRELIABLE DATA 189But how about ba
Page 200 and 201:
UNRELIABLE DATA 191country might ge
Page 202 and 203:
UNRELIABLE DATA 193collection of qu
Page 204 and 205:
28Systems EngineeringParables are o
Page 206 and 207:
SYSTEMS ENGINEERING 197Cramming is
Page 208 and 209:
of traffic performance degrades imm
Page 210 and 211:
SYSTEMS ENGINEERING 201of the natur
Page 212 and 213:
YOU GET WHAT YOU MEASURE 203Figure
Page 214 and 215:
YOU GET WHAT YOU MEASURE 205still o
Page 216 and 217:
YOU GET WHAT YOU MEASURE 207whole o
Page 218 and 219:
30You and Your ResearchI have given
Page 220 and 221:
YOU AND YOUR RESEARCH 211Confidence
Page 222 and 223:
YOU AND YOUR RESEARCH 213know where
Page 224 and 225:
YOU AND YOUR RESEARCH 215believe, i
Page 226 and 227:
INDEX 217Godel’s theorem, 280grow
show all

hamming

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?