The main objective of this work is to enhance the performance of epoch detection in the case of emotional speech. Existing epoch estimation methods require either modeling of the vocal-tract system or a priori information of the average pitch period. The performance of existing epoch estimation methods degrades significantly due to rapid variation of the pitch period in the emotional speech. In the present work, we have utilized the advantage of zero time windowing method, which provides instantaneous spectral information at each sample point due to the contribution of that sample point itself. The amplitudes of spectral peaks are higher at the instants of epochs compared to neighbouring sample points. The proposed method uses the sum of three prominent spectral peaks at each sampling instant of the Hilbert envelope of Numerator Group Delay (HNGD) spectrum, for accurate detection of epochs in the emotional speech. The experimental result shows that the accuracy of the proposed method is better than existing methods in the case of emotional speech. It is also observed that the proposed method works well even for the aperiodic nature of the speech signal and it is robust against emotional speech.