Is there a standard approach for solving the following system: $$ m_k = \sum_{j=1}^N a_j e^{-2\pi i \mu_j k \delta}, \quad k = 0, 1, 2, \ldots, $$ where $N \in \mathbb{N}$, $m_k \in \mathbb{C}$, $\delta \in \mathbb{R}_+$ are given; $a_j \in \mathbb{C}$, $\mu_j \in \mathbb{R}$ are unkown?
I tried to find articles on the topic, but I failed: all of them consider other moment problems which differ from mine. I would be grateful for any references.