Stability Analysis of Resolving Pulses of Unknown Shape from Compressive Fourier Measurements

Meghna Kalra, Kiryung Lee

Abstract: We present the problem of resolving pulses of a common shape from noisy Fourier measurements. Specifically, the paper focuses on the challenge of estimating the locations when the pulse shape is unknown. We leverage compressed sensing techniques to implement a larger virtual aperture through random sampling, thereby avoiding the necessity to acquire measurements inversely proportional to minimum separation. Although a larger aperture is beneficial, it introduces a penalty when dealing with unknown non-trivial pulse shapes. We provide theoretical and numerical results to quantify the error and show the efficacy of this approach in accurately resolving pulse locations with acceptable error in the presence of noise and modeling error.

Submission Type: Full Paper