Signal processing
= Signal processing
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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>. https://ocw.mit.edu/courses/res-6-007-signals-and-systems-spring-2011/0400ba59406d52d94c079d99928156ee_MITRES_6_007S11_lec04.pdf[Alan Oppenheim, MIT Signals and Systems, lecture 4: impulses, complex exponentials and convolution]{ref}.