Chapter 1 Signals and systems Sinusoids and complex exponential Decomposition: The complex exponential signal can thus be written in terms of its real and imaginary parts AcoS(O,t+o)=AReelobtg Asin(@t+)=AIme( i+9) This decomposition of the sinusoid can be traced to Euler's relation Oo: Fundamental Frequency ①: Phase A: Amplitude 2006 Fall2006 Fall Sinusoids and Complex Exponential ⚫ Decomposition: The complex exponential signal can thus be written in terms of its real and imaginary parts cos( ) Re{ } ( ) 0 0    + + = j t A t A e sin( ) Im{ } ( ) 0 0    + + = j t A t A e Chapter 1 Signals and Systems (This decomposition of the sinusoid can be traced to Euler's relation) ω0 :Fundamental Frequency Φ :Phase A :Amplitude