A new approach for determining the glottal activity from speech signals is presented in this paper. The approach is based on the use of single frequency filtering (SFF), proposed recently for voice activity detection. The variance (across frequency) of the spectral envelopes at each sampling instant is derived using the SFF of speech signal. The variance plot shows discontinuities corresponding to the impulse-like excitation within each glottal cycle. The proposed method uses filtering, thus avoiding the window effects of block processing, but the temporal resolution of the frequencies is still determined by the filtering process. The method also does not assume any knowledge of the average pitch period to derive the glottal activity features, such as the locations of the glottal closure instants (GCIs). The proposed GCI detection method is evaluated on five databases and compared with four existing methods on clean speech and telephone quality speech. From the experiments, it is observed that the performance of the proposed method is comparable to the existing methods on clean speech and significantly better on telephone quality speech.