Algebra & Function Basics: Equations, variables, operations that describe signals
Linear Systems: Superposition principle, homogeneity, additivity
Trigonometry: Sine, cosine functions as fundamental wave descriptions
Geometry: Vector representations, spatial relationships of signals
Calculus: Differentiation for rates of change, integration for accumulation
Complex Numbers: Representing amplitude and phase simultaneously
Exponential Functions: Growth and decay, natural logarithms
Frequency Domain Analysis: Spectrum representation of signals
Fourier Series: Representation of periodic signals as sums of sinusoids
Fourier Transform: Analysis of non-periodic signals
Discrete Fourier Transform: Digital implementation of Fourier analysis
Fast Fourier Transform: Efficient computation algorithms
Convolution: Mathematical operation describing linear system responses
Correlation: Measuring similarity between signals
Laplace Transform: Analysis of continuous-time systems
Z-Transform: Analysis of discrete-time systems
Transfer Functions: System description in transform domains
Differential Equations: Describing continuous-time systems
Difference Equations: Describing discrete-time systems
Filter Theory: Mathematical basis of frequency-selective systems
Window Functions: Time-domain weighting for spectral analysis
Statistical Analysis: Probability distributions, random signals, noise analysis
Time-Frequency Analysis: Wavelet transforms, short-time Fourier transform
Numerical Methods: Computational approaches to signal processing
Applied Mathematics for Restoration: Mathematical foundations of audio recovery
Matrix Operations: Mathematical basis for immersive audio processing
Information Theory: Compression and coding foundations