: ▁▁▁ ▁Each ▁signal ▁or ▁system ▁that ▁can ▁be ▁transformed ▁has ▁a ▁unique ▁Fourier ▁transform . ▁There ▁is ▁only ▁one ▁time ▁signal ▁for ▁any ▁frequency ▁signal , ▁and ▁vice ▁vers a . ▁ ▁Lap lace ▁transform ▁ ▁The ▁Lap lace ▁transform ▁is ▁a ▁generalized ▁Fourier ▁transform . ▁ ▁It ▁allows ▁a ▁transform ▁of ▁any ▁system ▁or ▁signal ▁because ▁it ▁is ▁a ▁transform ▁into ▁the ▁complex ▁plane ▁instead ▁of ▁just ▁the ▁j ω ▁line ▁like ▁the ▁Fourier ▁transform . ▁ ▁The ▁major ▁difference ▁is ▁that ▁the ▁Lap lace ▁transform ▁has ▁a ▁region ▁of ▁convergence ▁for ▁which ▁the ▁transform ▁is ▁valid . ▁ ▁This ▁implies ▁that ▁a ▁signal ▁in ▁frequency ▁may ▁have ▁more ▁than ▁one ▁signal ▁in ▁time ; ▁the ▁correct ▁time ▁signal ▁for ▁the ▁transform ▁is ▁determined ▁by ▁the ▁region ▁of ▁convergence . ▁ ▁If ▁the ▁region ▁of ▁convergence ▁includes ▁the ▁j ω ▁axis , ▁j ω ▁can ▁be ▁subst it uted ▁into ▁the ▁Lap lace ▁transform ▁for ▁s ▁and ▁it ' s ▁the ▁same ▁as ▁the ▁Fourier ▁transform . ▁ ▁The ▁Lap lace ▁transform ▁is : ▁ ▁and ▁the ▁inverse ▁Lap lace ▁transform , ▁if ▁all ▁the ▁singular ities ▁of ▁X ( s ) ▁are ▁in ▁the ▁left ▁half ▁of ▁the ▁complex ▁plane , ▁is : ▁ ▁B ode ▁plots ▁B ode ▁plots ▁are ▁plots ▁of ▁magnitude ▁vs . ▁frequency ▁and ▁phase ▁vs . ▁frequency ▁for ▁a ▁system . ▁ ▁The ▁magnitude ▁axis ▁is ▁in ▁[ De ci bel ] ▁( d B ). ▁ ▁The ▁phase ▁axis ▁is ▁in ▁either ▁degrees ▁or