Orthogonal Basis of Shifts in Space of Trigonometric Polynomials

The orthonormal basis of a system of shifts of one trigonometric polynomial exist in the space of complex trigonometric polynomials with components from $m$ to $n$ and in the space of real trigonometric polynomials with components from $0$ to $n$. Under condition $0<m<n$ there is no orthogonal basis of shifts of one trigonometric polynomial in this space real trigonometric polynomials with components from $m$ to $n$. The system of shifts of two trigonometric polynomials are orthogonal basis in this space.