physical layer (modulation, equalization, multiplexing, etc.); OSI layer 2, the data link layer (forward error correction); OSI layer 6, the presentation layer (source coding, including analog-to-digital conversion and data compression). Typical devices Filters for example analog (passive or active) or digital (FIR, IIR, frequency domain or stochastic filters, etc.) Samplers and analog-to-digital converters for signal acquisition and reconstruction, which involves measuring a physical signal, storing or transferring it as digital signal, and possibly later rebuilding the original signal or an approximation thereof. Signal compressors Digital signal processors (DSPs) Mathematical methods applied Differential equations Recurrence relations Transform theory Time-frequency analysis for processing non-stationary signals Spectral estimation for determining the spectral content (i.e., the distribution of power over frequency) of a time series Statistical signal processing analyzing and extracting information from signals and noise based on their stochastic properties Linear time-invariant system theory, and transform theory Polynomial signal processing analysis of systems which relate input and output using polynomials System identification and classification Calculus Complex analysis Vector spaces and Linear algebra Functional analysis Probability and stochastic processes Detection theory Estimation theory Optimization Numerical methods Time series Data mining for statistical analysis of relations between large quantities of variables (in this context representing many physical signals), to extract previously unknown interesting patterns See also Algebraic signal processing Audio filter Bounded variation Digital image processing Dynamic range compression, companding, limiting, and noise gating Fourier transform Information theory Least-squares spectral analysis Non-local means Reverberation Sensitivity (electronics) Time series References Further reading Kainam Thomas Wong : Statistical Signal Processing lecture notes at the University of Waterloo, Canada. Ali H. Sayed, Adaptive Filters, Wiley, NJ, 2008, . Thomas Kailath, Ali H. Sayed, and Babak Hassibi, Linear Estimation, Prentice-Hall, NJ, 2000, . External links Signal Processing for Communications – free online textbook by Paolo Prandoni and Martin Vetterli (2008) Scientists and Engineers Guide to Digital Signal Processing – free online textbook by Stephen Smith Mass media technology Telecommunication theory