Chapter Thirteen. Digital Signal Processing Tricks

Thirteen Digital Signal Processing Tricks

As we study the literature of digital signal processing, we'll encounter some creative techniques that professionals use to make their algorithms more efficient. These practical techniques are straightforward examples of the philosophy "don't work hard, work smart," and studying them will give us a deeper understanding of the underlying mathematical subtleties of DSP. In this chapter, we present a collection of these tricks of the trade, in no particular order, and explore several of them in detail because doing so reinforces the lessons we've learned in previous chapters.

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Chapter One. Discrete Sequences and Systems

• Chapter One. Discrete Sequences and Systems
• DISCRETE SEQUENCES AND THEIR NOTATION
• SIGNAL AMPLITUDE, MAGNITUDE, POWER
• SIGNAL PROCESSING OPERATIONAL SYMBOLS
• INTRODUCTION TO DISCRETE LINEAR TIME-INVARIANT SYSTEMS
• DISCRETE LINEAR SYSTEMS
• TIME-INVARIANT SYSTEMS
• THE COMMUTATIVE PROPERTY OF LINEAR TIME-INVARIANT SYSTEMS
• ANALYZING LINEAR TIME-INVARIANT SYSTEMS
• REFERENCES

Chapter Two. Periodic Sampling

• Chapter Two. Periodic Sampling
• ALIASING: SIGNAL AMBIGUITY IN THE FREQUENCY DOMAIN
• SAMPLING LOW-PASS SIGNALS
• SAMPLING BANDPASS SIGNALS
• SPECTRAL INVERSION IN BANDPASS SAMPLING
• REFERENCES

Chapter Three. The Discrete Fourier Transform

• Chapter Three. The Discrete Fourier Transform
• UNDERSTANDING THE DFT EQUATION
• DFT SYMMETRY
• DFT LINEARITY
• DFT MAGNITUDES
• DFT FREQUENCY AXIS
• DFT SHIFTING THEOREM
• INVERSE DFT
• DFT LEAKAGE
• WINDOWS
• DFT SCALLOPING LOSS
• DFT RESOLUTION, ZERO PADDING, AND FREQUENCY-DOMAIN SAMPLING
• DFT PROCESSING GAIN
• THE DFT OF RECTANGULAR FUNCTIONS
• THE DFT FREQUENCY RESPONSE TO A COMPLEX INPUT
• THE DFT FREQUENCY RESPONSE TO A REAL COSINE INPUT
• THE DFT SINGLE-BIN FREQUENCY RESPONSE TO A REAL COSINE INPUT
• INTERPRETING THE DFT
• REFERENCES

Chapter Four. The Fast Fourier Transform

• Chapter Four. The Fast Fourier Transform
• RELATIONSHIP OF THE FFT TO THE DFT
• HINTS ON USING FFTS IN PRACTICE
• FFT SOFTWARE PROGRAMS
• DERIVATION OF THE RADIX-2 FFT ALGORITHM
• FFT INPUT/OUTPUT DATA INDEX BIT REVERSAL
• RADIX-2 FFT BUTTERFLY STRUCTURES
• REFERENCES

Chapter Five. Finite Impulse Response Filters

• Chapter Five. Finite Impulse Response Filters
• AN INTRODUCTION TO FINITE IMPULSE RESPONSE (FIR) FILTERS
• CONVOLUTION IN FIR FILTERS
• LOW-PASS FIR FILTER DESIGN
• BANDPASS FIR FILTER DESIGN
• HIGHPASS FIR FILTER DESIGN
• REMEZ EXCHANGE FIR FILTER DESIGN METHOD
• HALF-BAND FIR FILTERS
• PHASE RESPONSE OF FIR FILTERS
• A GENERIC DESCRIPTION OF DISCRETE CONVOLUTION
• REFERENCES

Chapter Six. Infinite Impulse Response Filters

• Chapter Six. Infinite Impulse Response Filters
• AN INTRODUCTION TO INFINITE IMPULSE RESPONSE FILTERS
• THE LAPLACE TRANSFORM
• THE Z-TRANSFORM
• IMPULSE INVARIANCE IIR FILTER DESIGN METHOD
• BILINEAR TRANSFORM IIR FILTER DESIGN METHOD
• OPTIMIZED IIR FILTER DESIGN METHOD
• PITFALLS IN BUILDING IIR FILTERS
• IMPROVING IIR FILTERS WITH CASCADED STRUCTURES
• A BRIEF COMPARISON OF IIR AND FIR FILTERS
• REFERENCES

Chapter Seven. Specialized Lowpass FIR Filters

• Chapter Seven. Specialized Lowpass FIR Filters
• FREQUENCY SAMPLING FILTERS: THE LOST ART
• INTERPOLATED LOWPASS FIR FILTERS
• REFERENCES

Chapter Eight. Quadrature Signals

• Chapter Eight. Quadrature Signals
• WHY CARE ABOUT QUADRATURE SIGNALS?
• THE NOTATION OF COMPLEX NUMBERS
• REPRESENTING REAL SIGNALS USING COMPLEX PHASORS
• A FEW THOUGHTS ON NEGATIVE FREQUENCY
• QUADRATURE SIGNALS IN THE FREQUENCY DOMAIN
• BANDPASS QUADRATURE SIGNALS IN THE FREQUENCY DOMAIN
• COMPLEX DOWN-CONVERSION
• A COMPLEX DOWN-CONVERSION EXAMPLE
• AN ALTERNATE DOWN-CONVERSION METHOD
• REFERENCES

Chapter Nine. The Discrete Hilbert Transform

• Chapter Nine. The Discrete Hilbert Transform
• HILBERT TRANSFORM DEFINITION
• WHY CARE ABOUT THE HILBERT TRANSFORM?
• IMPULSE RESPONSE OF A HILBERT TRANSFORMER
• DESIGNING A DISCRETE HILBERT TRANSFORMER
• TIME-DOMAIN ANALYTIC SIGNAL GENERATION
• COMPARING ANALYTIC SIGNAL GENERATION METHODS
• REFERENCES

Chapter Ten. Sample Rate Conversion

• Chapter Ten. Sample Rate Conversion
• DECIMATION
• INTERPOLATION
• COMBINING DECIMATION AND INTERPOLATION
• POLYPHASE FILTERS
• CASCADED INTEGRATOR-COMB FILTERS
• REFERENCES

Chapter Eleven. Signal Averaging

• Chapter Eleven. Signal Averaging
• COHERENT AVERAGING
• INCOHERENT AVERAGING
• AVERAGING MULTIPLE FAST FOURIER TRANSFORMS
• FILTERING ASPECTS OF TIME-DOMAIN AVERAGING
• EXPONENTIAL AVERAGING
• REFERENCES

Chapter Twelve. Digital Data Formats and Their Effects

• Chapter Twelve. Digital Data Formats and Their Effects
• FIXED-POINT BINARY FORMATS
• BINARY NUMBER PRECISION AND DYNAMIC RANGE
• EFFECTS OF FINITE FIXED-POINT BINARY WORD LENGTH
• FLOATING-POINT BINARY FORMATS
• BLOCK FLOATING-POINT BINARY FORMAT
• REFERENCES

Chapter Thirteen. Digital Signal Processing Tricks

• Chapter Thirteen. Digital Signal Processing Tricks
• FREQUENCY TRANSLATION WITHOUT MULTIPLICATION
• HIGH-SPEED VECTOR MAGNITUDE APPROXIMATION
• FREQUENCY-DOMAIN WINDOWING
• FAST MULTIPLICATION OF COMPLEX NUMBERS
• EFFICIENTLY PERFORMING THE FFT OF REAL SEQUENCES
• COMPUTING THE INVERSE FFT USING THE FORWARD FFT
• SIMPLIFIED FIR FILTER STRUCTURE
• REDUCING A/D CONVERTER QUANTIZATION NOISE
• A/D CONVERTER TESTING TECHNIQUES
• FAST FIR FILTERING USING THE FFT
• GENERATING NORMALLY DISTRIBUTED RANDOM DATA
• ZERO-PHASE FILTERING
• SHARPENED FIR FILTERS
• INTERPOLATING A BANDPASS SIGNAL
• SPECTRAL PEAK LOCATION ALGORITHM
• COMPUTING FFT TWIDDLE FACTORS
• SINGLE TONE DETECTION
• THE SLIDING DFT
• THE ZOOM FFT
• A PRACTICAL SPECTRUM ANALYZER
• AN EFFICIENT ARCTANGENT APPROXIMATION
• FREQUENCY DEMODULATION ALGORITHMS
• DC REMOVAL
• IMPROVING TRADITIONAL CIC FILTERS
• SMOOTHING IMPULSIVE NOISE
• EFFICIENT POLYNOMIAL EVALUATION
• DESIGNING VERY HIGH-ORDER FIR FILTERS
• TIME-DOMAIN INTERPOLATION USING THE FFT
• FREQUENCY TRANSLATION USING DECIMATION
• AUTOMATIC GAIN CONTROL (AGC)
• APPROXIMATE ENVELOPE DETECTION
• A QUADRATURE OSCILLATOR
• DUAL-MODE AVERAGING
• REFERENCES

Appendix A. The Arithmetic of Complex Numbers

• Appendix A. The Arithmetic of Complex Numbers
• Section A.1. GRAPHICAL REPRESENTATION OF REAL AND COMPLEX NUMBERS
• Section A.2. ARITHMETIC REPRESENTATION OF COMPLEX NUMBERS
• Section A.3. ARITHMETIC OPERATIONS OF COMPLEX NUMBERS
• Section A.4. SOME PRACTICAL IMPLICATIONS OF USING COMPLEX NUMBERS
• REFERENCES

Appendix B. Closed Form of a Geometric Series

• Appendix B. Closed Form of a Geometric Series

Appendix C. Time Reversal and the DFT

• Appendix C. Time Reversal and the DFT

Appendix D. Mean, Variance, and Standard Deviation

• Appendix D. Mean, Variance, and Standard Deviation
• Section D.1. STATISTICAL MEASURES
• Section D.2. STANDARD DEVIATION, OR RMS, OF A CONTINUOUS SINEWAVE
• Section D.3. THE MEAN AND VARIANCE OF RANDOM FUNCTIONS
• Section D.4. THE NORMAL PROBABILITY DENSITY FUNCTION
• REFERENCES

Appendix E. Decibels (dB and dBm)

• Appendix E. Decibels (dB and dBm)
• Section E.1. USING LOGARITHMS TO DETERMINE RELATIVE SIGNAL POWER
• Section E.2. SOME USEFUL DECIBEL NUMBERS
• Section E.3. ABSOLUTE POWER USING DECIBELS

Appendix F. Digital Filter Terminology

• Appendix F. Digital Filter Terminology
• REFERENCES

Appendix G. Frequency Sampling Filter Derivations

• Appendix G. Frequency Sampling Filter Derivations
• Section G.1. FREQUENCY RESPONSE OF A COMB FILTER
• Section G.2. SINGLE COMPLEX FSF FREQUENCY RESPONSE
• Section G.3. MULTISECTION COMPLEX FSF PHASE
• Section G.4. MULTISECTION COMPLEX FSF FREQUENCY RESPONSE
• Section G.5. REAL FSF TRANSFER FUNCTION
• Section G.6. TYPE-IV FSF FREQUENCY RESPONSE

Appendix H. Frequency Sampling Filter Design Tables

• Appendix H. Frequency Sampling Filter Design Tables

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Understanding Digital Signal Processing (2nd Edition)

ISBN: 0131089897
EAN: 2147483647

Year: 2004
Pages: 183

Authors: Richard G. Lyons

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