A.1  Euler’s equation
A.2  Trigonometry
A.3  Manipulating complex numbers and rational functions
A.4  Manipulating complex exponentials
A.5  Q function
A.6  Matched filter and Cauchy-Schwarz’s inequality
A.7  Geometric series
A.8  Sum of squares
A.9  Summations and integrals
A.10  Partial fraction decomposition
A.11  Calculus
A.12  Sinc Function
A.13  Rectangular Integration to Define Normalization Factors for Functions
A.13.1  Two normalizations for the histogram
A.13.2  Two normalizations for power distribution using FFT
A.14  Linear Algebra
A.14.1  Inner products and norms
A.14.2  Projection of a vector using inner product
A.14.3  Orthogonal basis allows inner products to transform signals
A.14.4  Moore-Penrose pseudoinverse
A.15  Gram-Schmidt orthonormalization procedure
A.16  Principal component analysis (PCA)
A.17  Fourier Analysis: Properties
A.18  Fourier Analysis: Pairs
A.19  Probability and Stochastic Processes
A.19.1  Joint and Conditional probability
A.19.2  Random variables
A.19.3  Expected value
A.19.4  Orthogonal versus uncorrelated
A.19.5  PDF of a sum of two independent random variables
A.20  Stochastic Processes
A.20.1  Cyclostationary random processes
A.20.2  Two cyclostationary signals: sampled and discrete-time upsampled
A.20.3  Converting a WSC into WSS by randomizing the phase
A.21  Estimation Theory
A.21.1  Probabilistic estimation theory
A.21.2  Minimum mean square error (MMSE) estimators
A.21.3  Orthogonality principle
A.22  One-dimensional linear prediction over time
A.22.1  The innovations process
A.23  Vector prediction exploring spatial correlation
A.24  Decibel (dB) and Related Definitions
A.25  Insertion loss and insertion frequency response
A.26  Discrete and Continuous-Time Impulses
A.26.1  Discrete-time impulse function
A.26.2  Why defining the continuous-time impulse? Some motivation
A.26.3  Definition of the continuous-time impulse as a limit
A.26.4  Continuous-time impulse is a distribution, not a function
A.26.5  Mathematical properties of the continuous-time impulse
A.26.6  Convolution with an impulse
A.26.7  Applications of the impulse
A.27  System Properties
A.27.1  Linearity (additivity and homogeneity)
A.27.2  Time-invariance (or shift-invariance)
A.27.3  Memory
A.27.4  Causality
A.27.5  Invertibility
A.27.6  Stability
A.27.7  Properties of Linear and time-invariant (LTI) systems
A.28  Fixed and Floating-Point Number Representations
A.28.1  Representing numbers in fixed-point
A.28.2  IEEE 754 floating-point standard