Where does filter collide?

A system that passes some frequency components of a signal and attenuates others, described by its response across the frequency spectrum. In Oppenheim and Willsky's Signals and Systems a low-pass filter lets slow variation through and suppresses fast variation, a high-pass filter does the reverse, and each is characterised by a magnitude and phase response rather than by any estimate it produces. The referent is a fixed input-output map, usually linear and time-invariant, and its behaviour is set once the passband and stopband are chosen. It does not track a hidden state or model uncertainty; it simply shapes a signal by frequency.[1]

Unit

Gain (dimensionless or dB) as a function of frequency (Hz or rad/s)

Recovery means

Not applicable

Measured by

Frequency response, cutoff frequency, passband and stopband attenuation

A recursive algorithm that estimates the hidden state of a dynamic system from a stream of noisy measurements, updating its estimate each time new data arrive. Kalman's 1960 A New Approach to Linear Filtering and Prediction Problems gave the optimal linear-quadratic solution: predict the state forward with a model, then correct it by weighting the measurement against its uncertainty. Here filtering means inference over time, and the object is a probability distribution over an unobserved state, not a band of frequencies. The word it shares with the signal-processing meaning is the same, but this filter carries and revises a belief about what the system is doing, rather than shaping a waveform.[2]

Unit

Units of the estimated state, with an error covariance

Recovery means

Not applicable

Measured by

State estimate and its error covariance, updated recursively from measurements

The narrowing of the information a person sees when personalization algorithms select content to match inferred preferences, leaving out views and facts the person is not expected to want. Pariser's 2011 book The Filter Bubble argued that search and social platforms build an invisible, individual universe of information that reinforces what a user already believes. The referent is a social and epistemic outcome for a reader, produced by ranking systems, not a mathematical operator or a physical device. The word filter here names an effect on what reaches a person, and it makes no claim about frequencies or state estimates.[3]

Unit

No standard unit; studied as diversity or slant of exposed content

Recovery means

Not applicable

Measured by

Diversity, slant, or overlap of the content different users are shown