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Noise is unwanted variation in a signal. Whether a component is unwanted depends on the measurement task: suppressing fast variation helps only when that variation is expendable. White noise provides one mathematical model; it does not describe every source of disturbance. A linear filter may reduce some noise while also altering the desired signal.

Signal processing transforms or analyzes signals to extract information, change a representation, or improve a measurement. Examples include smoothing a sensor record, selecting a band of frequencies, and decomposing a recording through Fourier analysis. A signal is a mathematical representation of a physical record; deciding which variation is meaningful and which is noise is part of the problem.

A linear filter offers a simple entry point. Its output is assembled from weighted copies of its input. A moving average can reduce rapid variation, but it also changes timing and can erase useful detail. The worked example below makes that tradeoff explicit rather than treating a smoother plot as automatic improvement.

Two complementary views make the subject appealing. An impulse response describes the effect of a localized input; a frequency response describes the effect of a sustained oscillation. For a linear time-invariant system, both describe the same operation, connected by convolution and Fourier analysis. ^[ref].