Sampling, Discrete Fourier Transforms and FFTs
There are many situations in which the functions we would like to analyze are mainly known through measurements. Consider, for example, the temperature at time t at some location. Whether this position is in a cup of coffee or a coupling in a rocket engine, it is overly idealistic to assume we can derive, from basic principles alone, a precise formula f (t) describing how this temperature varies with time. Instead, we might measure that temperature at various times —t0, t1, t2, … — and then base further analysis on that sequence of measured values — f (t0), f (t1), f (t2), … — along with, of course, our knowledge of thermodynamics.
Lack of knowledge is not the only reason to deal with a sequence ...
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