Abstract Fast kurtogram (FK) is an effective method for resonance demodulation analysis, which segments the frequency spectrum of raw signal by constructing a tree-shaped band-pass filter bank based on alternate dichotomy or trisection method, then the modulation information is extracted via selecting the maximum kurtosis of components. Though FK has a high computation efficiency, it can not adaptively segment the frequency band due to its 1/3 binary tree structure. Besides, the different characteristics of frequency band filtered signal cannot be comprehensively reflected due to the use of a single kurtosis index in FK. To overcome the above shortcomings of FK, a novel frequency band selection method named Powergram is proposed based on auto-regressive (AR) power spectrum. First of all, the AR power spectrum is computed to overcome the influence of noise and irrelevant components on spectrum segmentation. Second, the minima point nearest to the midpoint of two adjacent maxima is selected as the segmentation boundary, where the maximum segmentation level is preset in advance. Third, a new fusion indicator is constructed by weighting the indexes of kurtosis, correlation coefficient, and spectral negentropy. After that, the frequency band with largest fusion indicator is selected as the optimal demodulation frequency band (ODFB). Then, the envelope spectrum of ODFB filtered signal is analyzed to identify the fault characteristic frequency and complete the fault diagnosis. Finally, Powergram is applied to the simulated and tested data of faulty gear via comparing it with existing FB-based FK and Autogram approaches. The analysis results show that the introduced approach is better than the comparison methods in ODFB selection and fault characteristic extraction.