Question

The exponential Fourier series coefficient of a continuous time periodic signal is $C_k$, if$C_{-1}$ = $j2,C_{-3}=j0.1$, the time domain signal is real and odd and $C_k$ = 0 for |K |> 3. Then the signal has

• A. power equal to 10.02
• B. energy equal to 5.01
  
• C. power equal to 8.02
• D. energy equal to 10.2

Answer 1

The correct option is C power equal to 8.02

Since signal is periodic it will be power signal and signal is odd so $C_k$ value will be odd .
so $C_k=-C_{-k}$
Power of signal $=\sum _{k=-\infty }^{\infty }|C_k{|}^2=\sum _{k=-3}^3|C_k{|}^2$
$C_0$ = 0 as signal is odd and
$C_1=-C_{-1}$ , $C_3=-C_{-3}$
so Power $=2(2{)}^2$ +$2(0.1{)}^2$
$=8+0.02=8.02$