Signals and Systems - M J Roberts 2003 Solutions Manual
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M. J. Roberts - 7/12/03 Solutions 2-1 Chapter 2 - Mathematical Description of Signals Solutions 1. If g t e t () = − − 7 2 3 write out and simplify (a) g3 7 9 () = − e (b) g2 7 7 22 3 7 2 − ( ) = = − − ( ) − −+ t e e t t (c) g t e t 10 4 7 5 11 + = − − (d) g jt e j t ( ) = − − 7 2 3 (e) g g cos jt jt e e e e t j t j t ( ) + − ( ) = + = ( ) − − − 2 7 2 7 2 3 2 2 3 (f) g g cos jt jt e e t jt jt − + − − = + = () − 3 2 3 2 2 7 2 7 2. If g x x x () = − + 2 4 4 write out and simplify (a) g z z z () = − + 2 4 4 (b) g u v u v u v u v uv u v + ( ) = + ( ) − + ( ) + = + + − − + 2 2 2 4 4 2 4 4 4 (c) g e e e e e e jt jt jt j t jt jt ( ) = ( ) − + = − + = − ( ) 2 2 2 4 4 4 4 2 (d) gg g t t t t t t t () ( ) = − + ( ) = − + ( ) − − + ( ) + 2 2 2 2 4 4 4 4 4 4 4 4 gg t t t t t () ( ) = − + − + 4 3 2 8 20 16 4 (e) g2 4 8 4 0 () = − + = 3. What would be the numerical value of “g” in each of the following MATLAB instructions? (a) t = 3 ; g = sin(t) ; 0.1411 (b) x = 1:5 ; g = cos(pi*x) ; [-1,1,-1,1,-1] (c) f = -1:0.5:1 ; w = 2*pi*f ; g = 1./(1+j*w) ;
