This paper introduces a DOA estimation method for sources beyond the aliasing frequency. The method utilizes multiple frequencies of sources to exploit the frequency difference between them, enabling processing at a frequency below the aliasing frequency. Gridless sparse processing with atomic norm minimization is derived for DOA using difference frequency (DF). This approach achieves higher DOA resolution than previous DF-DOA estimators by enforcing sparsity in the beamforming spectrum and estimating DOAs in the continuous angular domain. We consider one or more measurements in both time (snapshot) and frequency (DF). We also analyze approaches for considering multiple DFs: multi-DF and multi-DF spectral-averaging. Numerical simulations demonstrate the effective performance of the method compared to existing DF techniques.