= Linear filter
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A linear filter obeys the <superposition principle>: filtering $\alpha x+\beta z$ gives $\alpha T[x]+\beta T[z]$. Many familiar examples are also <linear time-invariant systems>, represented by an <impulse response> and <convolution>. Linearity alone does not imply time invariance: multiplying $x[n]$ by the index $n$ is linear but changes its behavior when the same input is shifted.
The <moving average> is a <finite impulse response> example implemented by arithmetic; a <band-pass filter> can instead be built from a <series RLC circuit>. Their <frequency responses> explain which oscillations pass through. Choosing a filter means choosing how much amplitude, timing and detail may change, not simply removing every visible fluctuation.
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