Digital Signal Processing: A User's Guide by Douglas L. Jones. - HTML preview

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Index

characteristic polynomial, Homogeneous Solution

coefficient vector, Simplifying our Equation

complement, Direct Sums

complex exponential sequence, Complex Exponentials

continuous random process, Random Process

continuous time fourier transform, Introduction

continuous-time fourier transform, Introduction

control theory, Examples of Pole/Zero Plots

correlation, Correlation, Glossary

correlation coefficient, Correlation Coefficient

correlation functions, Correlation

covariance, Covariance, Glossary

crosscorrelation, Crosscorrelation Function, Glossary

crosscorrelation function, Crosscorrelation Function

D

decimation in frequency, Decimation in frequency

decimation in time, Decimation in time, Radix-4 FFT Algorithms

decompose, Alternate Representation

delayed, Systems in the Time-Domain

deterministic linear prediction, Prony's Method

deterministic signals, Deterministic Signals

dft even symmetric, Symmetry

dft odd symmetric, Symmetry

dft-symmetric, Effects of Windowing

difference equation, Systems in the Time-Domain, Introduction, Glossary

digital aliasing, Decimation: sampling rate reduction (by an integer factor M)

direct method, Solving a LCCDE

direct sum, Direct Sums

direct-form fir filter structure, FIR Filter Structures

discrete fourier transform (dft), Sampling DTFT

discrete random process, Random Process

discrete-time sinc function, Discrete-Time Fourier Transform (DTFT)

dithering, Assumption #1

E

ergodic, Time Averages

extended prony method, Prony's Method

F

finite, Aside

finite dimensional, Dimension

first-order stationary, First-Order Stationary Process

flights, Example FFT Code

flow-graph-reversal theorem, Transpose-form FIR filter structures

fourier series, Equations

fourier transform, Basic Definition of the Z-Transform

G

generalized linear phase, Restrictions on h(n) to get linear phase

geometric series, Discrete-Time Fourier Transform (DTFT)

gibbs phenomena, Fourier's Daring Leap

gradient descent, Quadratic minimization problems

H

hamming window, Effects of Windowing

hann window, Effects of Windowing

hanning, Effects of Windowing

hilbert space, Orthogonal Compliments

homogeneous solution, Direct Method

I

identity matrix, Examples

in-place algorithm, Radix-2 decimation-in-time FFT, Radix-2 decimation-in-frequency algorithm, Radix-4 FFT Algorithms

independent, Properties of Variance

index map, Rader's Conversion

indirect method, Solving a LCCDE

initial conditions, Difference Equation

interpolation, Interpolation: by an integer factor L

invertible, Inverses

J

joint density function, Distribution and Density Functions

joint distribution function, Distribution and Density Functions

L

lag, Auto-correlation-based approach

large-scale limit cycle, Large-scale limit cycles

linear discrete-time systems, Systems in the Time-Domain

linear predictor, Prony's Method

linear transformation, Linear Transformations

linearly dependent, Linear Independence

linearly independent, Linear Independence, Mean Value

live, Illustrations

M

matrix representation, Matrices

mean, Mean Value

mean-square value, Mean-Square Value

minimum phase, Analog Filter Design

misadjustment factor, Second-order Convergence Analysis of the LMS Algorithm and Misadjustment Error

moment, Mean-Square Value

N

narrow-band spectrogram, Short Time Fourier Transform

non-recursive structure, FIR Filter Structures

nonstationary, Introduction

O

optimal, L-∞ Optimal Lowpass Filter Design Lemma

order, Difference Equation

orthogonal, Orthogonality, Review of Linear Algebra

orthogonal compliment, Orthogonal Compliments

orthonormal, Orthogonality

orthonormal basis, Main Idea

overflow, Overflow Error

P

particular solution, Direct Method

pearson's correlation coefficient, Correlation Coefficient

perfect reconstruction filters, DFT-Based Filterbanks

picket-fence effect, Zero-Padding

pole-zero cancellation, Examples of Pole/Zero Plots

poles, Introduction to Poles and Zeros of the Z-Transform, Glossary

polyphase filters, Interpolation

polyphase structures, Interpolation

power series, Region of Convergence

power spectral density (psd), Classical Statistical Spectral Estimation

pre-classical, Impulse-Invariant Design

prediction, Adaptive IIR filters

primitive root, Fact from number theory

probability density function (pdf), Distribution and Density Functions

probability distribution function, Distribution and Density Functions

prony's method, Prony's Method

Q

quantization error, Truncation Error

quantized, Transpose-Form IIR Filter Structure

R

rader's conversion, Rader's Conversion

radix-2, Decimation in time, Decimation in frequency

radix-4, Radix-4 FFT Algorithms

radix-4 butterfly, Radix-4 FFT Algorithms

radix-4 decimation-in-time fft, Radix-4 FFT Algorithms

raised-cosine windows, Effects of Windowing

random process, Random Process, Glossary

random sequence, Random Process

random signals, Stochastic Signals

realization, Random Process, Glossary

rectangle, Effects of Windowing

recursive least squares, Computational Considerations

roc, Region of Convergence

rounding, Fixed-Point Quantization

roundoff error, Truncation Error

running fft, Running FFT

S

sample function, Random Process, Glossary

saturation, Fixed-Point Quantization

scale, Scaling

scalloping loss, Zero-Padding

second-order stationary, Second-Order and Strict-Sense Stationary Process

sensitivity, Sensitivity analysis

shift-invariant , Systems in the Time-Domain

side lobe, Zero-Padding

sign bit, Two's-Complement Integer Representation

small-scale limit cycles, Small-scale limit cycles

span, Spanning Sets

spectrogram, Short Time Fourier Transform

stable, Pole/Zero Plots and the Region of Convergence

stage, Additional Simplification, Decimation in frequency

standard basis, Matrices

state, State and the State-Variable Representation, Glossary

stationary process, Introduction, Glossary

stationary processes, Introduction

stochastic gradient, The LMS Adaptive Filter Algorithm

stochastic signals, Stochastic Signals

strict sense stationary (sss), Second-Order and Strict-Sense Stationary Process

subspace, Subspaces

T

table lookup, Precompute twiddle factors

the stagecoach effect, Sampling too slowly

time-varying behavior, Note

toeplitz, Linear Prediction

training signal, Important Application

transfer function, Conversion to Z-Transform

transforms, Examples

transmultiplexors, Uniform DFT Filter Banks

truncation, Effects of Windowing, Fixed-Point Quantization

truncation error, Truncation Error

twiddle factor, Summary of FFT algorithms, Decimation in time, Decimation in frequency

twiddle factors, Radix-4 FFT Algorithms

twiddle-factor, Power-of-two FFTs, Additional Simplification, Decimation in frequency

U

uncorrelated, Mean Value

unilateral z-transform, Basic Definition of the Z-Transform

unique, Alternate Representation

unit sample, Unit Sample, Unit Step

unitary, Review of Linear Algebra

V

variance, Variance

vector-radix ffts, Multi-dimensional FFTs

vectors, Examples

W

well-defined, Dimension

wide-band spectrogram, Short Time Fourier Transform

wide-sense stationary (wss), Wide-Sense Stationary Process

window, Effects of Windowing

wraparound, Fixed-Point Quantization

Y

yule-walker, Statistical Linear Prediction

Z

z-plane, The Complex Plane

z-transform, Basic Definition of the Z-Transform

z-transforms, Table of Common z-Transforms

zero-input limit cycles, Large-scale limit cycles

zero-padding, Zero-Padding

zeros, Introduction to Poles and Zeros of the Z-Transform, Glossary