This research paper provides a comprehensive exploration of signals and their mathematical models, discussing various signal types such as analog, discrete, quantized, and digital. It classifies signals based on spatial–temporal representation, predictability, existence domain, dimensionality, dynamics, validity, and repeatability, presenting detailed mathematical models for harmonic signals, complex-exponential signals, and rectangular video pulses. Additionally, it examines mathematical models for time-shifted signal functions and the principles of energy and power in electrical signals. The chapter underscores the significance of orthonormalized bases, generalized Fourier series, and spectral analysis, with applications in signal decomposition and performance measurement. It elucidates critical aspects of random processes, including correlation functions and power spectral density, while introducing practical methods for signal representation and reconstruction, particularly through Kotelnikov's theorem. Lastly, it explores the measurement of signal levels using decibels and real-world considerations for signal transmission and processing, providing a robust theoretical and practical framework for signal processing and telecommunications.