$\text{H}$ is a circulant matrix (row $n$ is obtained by circularly shifting row $1$ to the right by $n$ positions) and $\text{F}$ is the $\text{DFT}$ matrix. Which of the following is true?
- $F H F^{H}$ is circulant, where $F^{H}$ is the inverse $\text{DFT}$ matrix.
- $F H F^{H}$ is tridiagonal
- $F H F^{H}$ is diagonal
- $F H F^{H}$ has real entries
- None of the above