, ▁and ▁hence ▁in ▁the ▁study ▁of ▁radiation , ▁of ▁ac oust ics , ▁of ▁se ism ology , ▁of ▁mod ulation ▁of ▁radio ▁waves ▁in ▁electron ics , ▁and ▁of ▁electric ▁power ▁engineering . ▁ ▁A ▁Fourier ▁series ▁is ▁a ▁sum ▁of ▁this ▁form : ▁▁▁▁ ▁where ▁each ▁of ▁the ▁squares ▁() ▁is ▁a ▁different ▁number , ▁and ▁one ▁is ▁adding ▁infinitely ▁many ▁terms . ▁Fourier ▁used ▁these ▁for ▁studying ▁heat ▁flow ▁and ▁diffusion ▁( diff usion ▁is ▁the ▁process ▁where by , ▁when ▁you ▁drop ▁a ▁sugar ▁cube ▁into ▁a ▁gall on ▁of ▁water , ▁the ▁sugar ▁gradually ▁spread s ▁through ▁the ▁water , ▁or ▁a ▁poll ut ant ▁spread s ▁through ▁the ▁air , ▁or ▁any ▁dissol ved ▁subst ance ▁spread s ▁through ▁any ▁fluid ). ▁ ▁Fourier ▁series ▁are ▁also ▁applicable ▁to ▁subjects ▁whose ▁connection ▁with ▁wave ▁motion ▁is ▁far ▁from ▁obvious . ▁One ▁u bi quit ous ▁example ▁is ▁digital ▁compression ▁where by ▁images , ▁audio ▁and ▁video ▁data ▁are ▁com pressed ▁into ▁a ▁much ▁smaller ▁size ▁which ▁makes ▁their ▁transmission ▁feas ible ▁over ▁tele phone , ▁internet ▁and ▁broadcast ▁networks . ▁Another ▁example , ▁mentioned ▁above , ▁is ▁diffusion . ▁Among ▁others ▁are : ▁the ▁geometry ▁of ▁numbers , ▁is oper imet ric ▁problems , ▁rec urrence ▁of ▁random ▁wal ks , ▁quadratic ▁reci pro city , ▁the ▁central ▁limit ▁theorem , ▁He isen berg ' s ▁inequality . ▁ ▁Fourier ▁transform s ▁ ▁A ▁more ▁abstract ▁concept ▁than ▁Fourier ▁series ▁is ▁the ▁idea ▁of ▁Fourier ▁transform