Sampling a signal below the Shannon–Nyquist rate causes aliasing, meaning different frequencies to become indistinguishable. It is also well-known that recovering spectral information from a signal using a parametric method can be ill-posed or ill-conditioned and therefore should be done with caution.

We present an exponential analysis method to retrieve high-resolution information from coarse-scale measurements, using uniform downsampling. We exploit rather than avoid aliasing. While we loose the unicity of the solution by the downsampling, it allows to recondition the problem statement and increase the resolution.

Our technique can be combined with different existing implementations of multi-exponential analysis (matrix pencil, MUSIC, ESPRIT, APM, generalized overdetermined eigenvalue solver, simultaneous QR factorization, …) and so is very versatile. It seems to be especially useful in the presence of clusters of frequencies that are difficult to distinguish from one another.

对低于Shannon-Nyquist速率的信号进行采样会导致混叠，这意味着不同的频率变得难以区分。众所周知，使用参数方法从信号中恢复频谱信息可能是不适的或不适的，因此应谨慎进行。

我们提出一种指数分析方法，使用统一的下采样从粗略测量中检索高分辨率信息。我们利用而不是避免混淆。虽然我们通过下采样来放松解决方案的单一性，但它可以重新整理问题陈述并提高解决方案。

我们的技术可以与多指数分析的不同现有实现方式（矩阵铅笔，MUSIC，ESPRIT，APM，广义超额特征值求解器，同时QR分解...）相结合，因此非常通用。在存在难以彼此区分的频率簇的情况下，这似乎特别有用。