Digital signal processing

Digital signal processing analyzes and transforms signals represented as sequences of numerical samples. It uses algorithms to extract information, modify signals, or generate new ones.

Sampling (signal processing): Sampling converts a continuous-time signal into a sequence of values measured at discrete time intervals. It turns continuous signals into the numerical sequences that digital processing operates on.
Linear time-invariant system: A linear time-invariant system obeys superposition and responds consistently to time shifts. Many core DSP methods model filters as linear time-invariant systems.
Digital audio: Digital audio represents sound as numerical samples that can be stored, processed, and reproduced. Audio is a prominent use of sampling, filtering, and compression.
Analog signal processing: Analog signal processing transforms continuous-valued signals using physical circuits or other continuous systems. It performs related tasks without representing signals as numerical samples.
Harry Nyquist: Harry Nyquist was an electrical engineer whose work established limits on signaling and sampling rates. His analysis helped establish the sampling principles behind digital signal representation.
Nyquist–Shannon sampling theorem: The theorem states conditions under which a band-limited continuous signal can be reconstructed from uniform samples. It explains the sampling-rate limit for avoiding aliasing during digitization.
Convolution: Convolution combines two functions or sequences to describe how one signal is shaped by another. It computes the output of a linear time-invariant system from its input and impulse response.
Image processing: Image processing uses computational methods to analyze or modify images. A digital image is a sampled spatial signal, processed with many DSP techniques.
Analog-to-digital converter: An analog-to-digital converter produces digital samples from an analog input signal. It marks the hardware boundary between analog signals and digital processing.
Claude Shannon: Claude Shannon was a mathematician and engineer who founded information theory and formalized signal communication limits. His sampling theorem gave a rigorous basis for reconstructing band-limited signals.

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