Chapter 8 Problem solution 8.22 In Figure(a), a system is shown with inputx()and output y() The input signal has the Fourier transform (jo) shown in Figure(b) Determine and sketch y(o) H,GjO) 73 H Go) y 5W-3W 3W 5W 3W 0 3W 0 cos 5wt cos 3wt Figure(a) xGa) -2W0 2N0 Figure(b)6
6 8.22 In Figure (a) ,a system is shown with input and output The input signal has the Fourier transform shown in Figure (b) Determine and sketch . Chapter 8 Problem Solution X(j) Y(j) x(t) y(t) 0 1 −3W 3W H (j) 2 x(t) r(t) 1 r (t) 2 −3W 3W 1 H (j) 1 −5W 5W r (t) y(t) 3 cos5Wt cos3Wt X(j) − 2W 0 2W Figure (a) 1 Figure (b)
Problems for Fourier analysis Example 1 f() Determine the fourier A period of sin nt transform off(t) 2 t 2jo Fgo 丌- 7
7 Problems for Fourier Analysis ( ) 2 2 2 − − = − j e F j f (t) 0 1 2 1 t A period of sin t Example 1 Determine the Fourier transform of f (t)