Abstract: Low sampling rate power spectrum estimation could be applied in many domains. In the paper, firstly the compressed multi-coset sampling structure is adopted to obtain the compressed measuring values, and the relationship between correlation of measuring values and autocorrelation is built. Secondly, the estimation for signal autocorrelation is realized using least squares. At last, the power spectrum estimation is realized through frequency domain transformation. To reduce the compression rate, the realization structure based on minimal sparse rule is studied. The equivalent sampling rate for the method is M/N·f_s, which enables low sampling rate spectrum estimation without any sparse assumptions about the frequency or time domain signals. Through simulations, it proves that the system noise and additive noise performance is not as good as periodogram method. But if system design parameters are properly designed, the noise could be ignored. The corresponding theoretical analysis is given as well. The frequency resolution performance is improved compared to periodogram method, however, the method reduces the number of measured data, so for certain measured data, the frequency resolution performance is elevated greatly. Thus, the method is applicable to the low sampling power spectrum estimation of low SNR signals.