Following information is given about a signal $x[n]$
- $x[n]$ is real and even signal
- $x[n]$ has a period $N=10$ and Fourier coefficients $a_k$
- $a_{11}=5$
- $\frac1 {10}\sum_{n=0}^9 |x[n]|^2=50$
How can we obtain $x[n]$ from these information?
I know the first info makes the Fourier coefficients real and even, third info makes the Fourier coefficient $a_1=a_{11}=5$(since Fourier coeffs are also periodic with N=10) and fourth info is Parsevals theorem.