港科大 信号系统英文课件 Key+Points+in+Signals+and+Systems-Chapters+1,2.doc

Key Concepts in Signals and Systems – Chapters 1,2 1. Understand basic signals: Unit step and impulse: ][ ],[ ),( ),(nnuttu?? Unit step is integral/sum of impulse Sampling property of impulse ][][][][ );()()()( 000000nnngnnngtttgtttg?????????? Time scaling of continuous-time impulse: )(|| 1)(ta at??? frequency notation ??js??? is decay constant and? is oscillation (angular) frequency exponential allows us to describe things that oscillate and decay or grow at the same time:?? teee t st st?? cos Re ?? sinusoid (setting 0??):?? tee tjtj??? cos Re ?? D iscrete-plex exponential: ?? nzzezezz nn snnj?? cos || Re :||???? es sinusoid when we set?? neez njnj??? cos Re :1||??? For DT signals, changing the angular frequency by2?or the ordinary frequency by1 does not change anything: nkjnjnjeee )2()2(????????? Be able to visualize and plot signals: Examples: )1(??tu ,)2()1(???tutu )(tje ??,)1( )(???tue tj?]1[ ez nnuz ?? Periodic Signal and Poisson Sum Poisson sum of any signal )(tx is always periodic :?????? k kT tx)( Rectangular Wave: )]()([ 11 kT Ttu kT Ttu k?????????? 2 Impulse Response and Convolution Impulse response ][ ),(nhth For all LTI systems, output is convolution of input with impulse response ???????? nmkmkkmhkxknhkxnhnxny ;,][][][][][*][][??????????dthxthtxty)()()(*)()( Convolution simply means the output at time nor