Envelope demodulation has become a key technique in rolling bearing fault diagnosis. However, selecting the optimal frequency modulation band that captures rich fault information remains a challenge, especially in the presence of low signal-to-noise ratios, accidental pulses, and irrelevant harmonics. This paper presents a novel approach, LSESgram, for optimal frequency modulation band selection. Unlike existing methods such as Spectral Kurtosis and Kurtogram, which struggle under noisy conditions, LSESgram is robust to noise and interference. It first extracts spectral trends using a scale-space-like theory, then performs multi-level segmentation based on these trends. The LSES indicator is then used to identify the optimal demodulation frequency band. The method is validated with simulation and experimental signals, showing superior performance compared to Fast Kurtogram, Infogram, and Autogram.