Filter (signal processing)

A system or operation that selectively changes or removes components of a signal, often according to frequency. Filters shape signals by altering properties such as amplitude, phase, or timing.

Transfer function: A mathematical description of a system’s output relative to its input, commonly expressed in the frequency or complex domain. It describes how a linear filter changes each frequency component.
Signal: A varying quantity that carries information about a phenomenon or message. A filter operates on signals, altering selected properties while producing another signal.
Anti-aliasing filter: A low-pass filter applied before sampling to suppress frequencies that would alias. It protects digitized signals from high-frequency content folding into false lower frequencies.
Analog filter: A filter implemented with continuous-time physical components such as resistors, capacitors, and amplifiers. It processes continuous signals directly, unlike a filter computed from digital samples.
Group delay: The rate at which a system’s phase shift changes with angular frequency. Unequal group delay across frequencies can distort the timing and shape of filtered signals.
Impulse response: A system’s output when its input is an idealized impulse. Convolving a signal with this response implements a linear time-invariant filter.
Fourier transform: A mathematical transform that represents a function as a distribution of frequencies. It makes frequency-selective filtering explicit by expressing a signal’s spectral components.
Matched filter: A filter designed to maximize signal-to-noise ratio for a known signal in additive white noise. It detects known waveforms in noisy radar and communications signals.
Digital filter: A filter implemented by numerical operations on discrete-time samples. It offers programmable behavior and repeatable coefficients instead of analog component values.
Phase distortion: A change in the relative phase relationships among a signal’s frequency components. A filter can alter waveform shape even when its amplitude response is nearly flat.

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