Fundamentals of Signal Processing by Minh N. Do - HTML preview

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Index

characteristic polynomial, Homogeneous Solution

circular convolution, Compute IDFT of Y[k]

coefficient vector, Simplifying our Equation

complement, Direct Sums

complex exponential sequence, Complex Exponentials

complex exponentials, Introduction

computational algorithm, The FFT Algorithm, Glossary

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

countably infinite, Filtering in the Frequency Domain

covariance, Covariance, Glossary

crosscorrelation, Crosscorrelation Function, Glossary

crosscorrelation function, Crosscorrelation Function

D

de-noising, DWT Application - De-noising

deblurring, Image Restoration

decompose, Alternate Representation

delayed, Linear Time-Invariant Systems

deterministic signals, Deterministic Signals

difference equation, Linear Time-Invariant Systems, Introduction, Glossary

direct method, Solving a LCCDE

direct sum, Direct Sums

discrete fourier transform (dft), Sampling DTFT

discrete random process, Random Process

discrete time fourier transform, Introduction

discrete wavelet transform, Main Concepts

discrete-time fourier transform, Introduction

downsampling, Downsampling

E

envelop delay, WHY LINEAR-PHASE: MORE

ergodic, Time Averages

F

fft, The FFT Algorithm, Glossary

finite, Aside

finite dimensional, Dimension

first-order stationary, First-Order Stationary Process

fourier series, Equations, Equations

fourier transform, Basic Definition of the Z-Transform

frames, Spectrograms

functional, Introduction to Systems

G

gibbs phenomena, Fourier's Daring Leap

gradient descent, Quadratic minimization problems

group delay, WHY LINEAR-PHASE: MORE

H

hanning window, Spectrograms

hilbert space, Orthogonal Compliments, Hilbert Spaces

homogeneous solution, Direct Method

I

identity matrix, Examples

independent, Properties of Variance

indirect method, Solving a LCCDE

initial conditions, Difference Equation

inner product space, Hilbert Spaces

invertible, Inverses

J

joint density function, Distribution and Density Functions

joint distribution function, Distribution and Density Functions

L

linear discrete-time systems, Linear Time-Invariant Systems

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

moment, Mean-Square Value

mother wavelet, Main Concepts

multi-resolution, Main Concepts

N

narrow-band spectrogram, Short Time Fourier Transform

nonstationary, Introduction

normed linear space, Hilbert Spaces

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

P

particular solution, Direct Method

pearson's correlation coefficient, Correlation Coefficient

periodic, Main Concepts

phase delay, WHY LINEAR-PHASE?

pole-zero cancellation, Examples of Pole/Zero Plots

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

power series, Region of Convergence

probability density function (pdf), Distribution and Density Functions

probability distribution function, Distribution and Density Functions

R

random process, Random Process, Glossary

random sequence, Random Process

random signals, Stochastic Signals

realization, Random Process, Glossary

recursive least squares, Computational Considerations

resampling, Resampling with Rational Factor

roc, Region of Convergence

S

sample function, Random Process, Glossary

sample-rate conversion, Resampling with Rational Factor

scaling function, Main Concepts, The Haar System as an Example of DWT

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

shift-invariant , Linear Time-Invariant Systems

signal, Signals Represent Information

span, Spanning Sets

spectral masking, Sub-band Processing

spectrogram, Short Time Fourier Transform

stable, Pole/Zero Plots and the Region of Convergence

standard basis, Matrices

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

sub-bands, Sub-band Processing

subspace, Subspaces

symmetries, How does the FFT work?

T

the stagecoach effect, Sampling too slowly

time-varying behavior, Note

training signal, Important Application

transfer function, Conversion to Z-Transform

transforms, Examples

twiddle factors, How does the FFT work?

U

uncorrelated, Mean Value

uncountably infinite, Filtering in the Frequency Domain

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

unique, Alternate Representation

unit sample, Unit Sample, Unit Step

unit-sample response, Filtering in the Frequency Domain

unitary, Review of Linear Algebra

upsampling, Upsampling

V

variance, Variance

vectors, Examples

W

wavelets, Main Concepts

well-defined, Dimension

well-matched, DWT Application - De-noising

wide-band spectrogram, Short Time Fourier Transform

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

window, Spectrograms

Z

z-plane, The Complex Plane

z-transform, Basic Definition of the Z-Transform

z-transforms, Table of Common z-Transforms

zero-pad, Filtering in the Frequency Domain

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