Signals &systems Prove that Example 2 10EE52 Prove that  T 2 sin (kw t)   2 0 0  w0 2f 1  f for T and is an integer. k Solution Let T 2 (kw  B t)dt 0 0 Recall 1  2 sin () cos(2) (11)  2 Thus,  B 1 1 (12) cos(2kw t)dt T    0  2 2   o    (13)  1   1 1  t    sin(2kw t)  2  2kw  2 0             0 1 T  0     B sin(2kw0T ) 2   (14) 1   T    sin(2k * 2 )   2   T  2 Example 3
Signals &systems Example 2 Prove that  T  sin 2 (kw t)  0 2 0 w0  2f f  1 T for and k is an integer. Solution Let T B  2 (kw t)dt 0 0 Recall sin 2 ()  1  cos(2) 2 Thus, B  T  1  1 cos(2kw t)dt  2 2 0  o       1   1 1   t   sin(2kw t)     0   2  2  2kw        0 T 1  0 B    sin(2kw0T )  2   T  1     sin(2k * 2 ) 2      T 2 Example 3 Prove that 10EE52 (11) (12) (13) (14)
U4-L18-_-Fourier-Series-and-examples.docx