EARTH460 Study Guide - Midterm Guide: Low-Pass Filter, Fourier Series, Dirac Delta Function

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Finite number of extrema points/discontinuities over a single period. Rest of it is harmonic component magnitude of which contains info about g(t) Converges to g(t) where g(t) continuous avg of left and right hand limits at discontinuities (ie in the middle of the discontinuity in the heaviside looking function) For g(t), c0 is real valued, cn are complex valued. These coefficients represent frequency spectrum of the periodic time signal g(t) Amplitude spectrum = even, non-negative function goes to zero as n goes to infinity. Phase = odd = 0 when frequency is zero. If g(t) is an even function then phase spectrum = 0 sinc(t) and boxcar(t) Shifting a time signal only affects phase spectrum amp spectrum remains unchanged phase spectrum of shifted time signal has an additional linear term. Scaling in time/freq domain inverse scaling in the freq/time domain. Taking derivative of a time signal enhances higher frequency components and suppresses lower frequency components of it"s fourier transform.