Contents 1 What Is Digital Signal Processing? 1 The Phantom Technology 1 What Is a Signal? 2 Analog and Digital Signals 3 Digital Signal Processing 3 What You Should Remember 5 2 Analog Signals 7 What Is an Analog Signal? 7 A Temperature Analog Signal 7 An Audio Analog Signal 8 An Electrical Analog Signal 10 What Is an Electrical Voltage? 10 Sinusoidal Wave Voltages 13 Other Useful Periodic Analog Signals 19 A Human Speech Analog Signal 21 What You Should Remember 22 3 Frequency and the Spectra of Analog Signals 25 Frequency 25 Cycles per Second 26 Radians per Second 28 The Concept of Spectrum 29 Analog Signal Spectra 30 A Composite-Signal Spectral Example 32 Harmonics 34 Harmonic Distortion 37 Bandwidth 39 The Other Bandwidth 42 What You Should Remember 42 4 Digital Signals and How They Are Generated 43 What Is a Digital Signal? 43 The Notion of Digital 43 Digital Signals: Definition #1 44 Digital Signals: Definition #2 45 How Digital Signals Are Generated 48 Digital Signal Generation by Observation 48 Digital Signal Generation by Software 48 Digital Signal Generation by Sampling an Analog Signal 49 The Sample Rate of a Digital Signal 52 A Speech Digital Signal 53 An Example of Digital Signal Processing 55 Another Example of Digital Signal Processing 57 Two Important Aspects of Sampling Analog Signals 61 Sample Rate Restriction 62 Analog-to-Digital Converter Output Numbers 62 Sample Rate Conversion 63 Decimation 63 Interpolation 63 What You Should Remember 66 5 Sampling and the Spectra of Digital Signals 67 Analog Signal Spectra—A Quick Review 67 How Sampling Affects the Spectra of Digital Signals 71 The Mischief in Sampling Oscillating Quantities 73 Sampling Analog Sine Wave Voltages 76 Why We Care about Aliasing 80 The Spectrum of a Digital Sine Wave Signal 82 The Spectrum of a Digital Voice Signal 85 The Spectrum of a Digital Music Signal 86 Anti-Aliasing Filters 89 Analog-to-Digital Converter Output Numbers 93 What You Should Remember 94 6 How We Compute Digital Signal Spectra 95 Computing Digital Spectra 95 The Discrete Fourier Transform 96 The Fast Fourier Transform 96 A Spectral Computation Example 97 The Computations 97 What the Computations Mean 103 A Spectral Analysis Example 103 What You Should Remember 106 7 Wavelets 107 The Fast Fourier Transform (FFT)—A Quick Review 107 The Continuous Wavelet Transform (CWT) 109 Undecimated or Redundant Discrete Wavelet Transforms (UDWT/RDWT) 114 Conventional (Decimated) Discrete Wavelet Transforms (DWT) 114 What You Should Remember 117 8 Digital Filters 119 Analog Filtering 119 Generic Filter Types 121 Digital Filtering 122 What You Should Remember 126 9 Binary Numbers 127 Number Systems 128 Decimal Numbers, a Base-10 Number System 128 A Base-4 Number System 129 Binary Numbers, a Base-2 Number System 130 Using Binary Numbers at Home 132 Binary Data 133 Why Use Binary Numbers? 134 Digital Hardware Is Easy to Build 134 Binary Data Is Resistant to Degradation 135 Binary Numbers and Analog-to-Digital Converters 136 What You Should Remember 139 A Scientific Notation 141 B Decibels 145 Decibels Used to Describe Sound Power Values 146 Decibels Used to Measure Earthquakes 147 Decibels Used to Describe Signal Amplitudes 149 Decibels Used to Describe Filters 153 C AM and FM Radio Signals 155 AM Radio Signals 155 FM Radio Signals 157 Comparing AM and FM Radio 159 D Binary Number Formats 161 Unsigned Binary Number Format 161 Sign-Magnitude Binary Number Format 162 Two’s Complement Binary Number Format 163 Offset Binary Number Format 165 Alternate Binary Number Notation 166O ctal Binary Number Notation 166 Hexadecimal Binary Number Notation 166 Glossary 169
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