Chapter 4 Problem solution (b) Construct a signal that has properties (1),(4), and (5)and does not have the others 1.Re{X(io)}=0→x(-)=-x 4.」X(o)o=0→x()-=0 5.axiom=0s dxr(t) 0 dt t=0 3. There does not exist a real a such that ejdoxlja) is real x(t+a) is not even 6. XGo) is not periodic For example, x(t =e39 Chapter 4 Problem Solution (b) Construct a signal that has properties (1),(4),and (5) and does not have the others. 1. ReX(j)= 0  x(−t) = −x(t) ( ) = 0  + − 4. X j d ( ) 0 0  = t= x t ( ) = 0  + − 5. X j d ( ) 0 0  = t= dt dx t 3. There does not exist a real such that is real. ( )   e X j j  x(t +) is not even. 6. is not periodic X(j) For example, x(t) = t 3 , t 5 , t 7 