In contrast to a 1-D short-time analysis of speech, 2-D approaches aim at characterizing the speech signal attributes jointly in time and frequency. In this paper, we focus on the quasi-periodicity of a voiced spectro-temporal patch and quantify it by proposing an aperiodicity measure defined using the underlying frequency modulations in the patch. We further propose a time-frequency aperiodicity map obtained by overlapping and adding the aperiodicity measures across patches. The proposed aperiodicity map is utilized to obtain band-wise aperiodicity parameters, which are essential for high-quality speech synthesis. The aperiodicity in unvoiced patches is addressed by identifying them using the coherence of the patch. In addition, the proposed technique also provides voiced/unvoiced decisions boundaries of a speech signal. The effectiveness of the proposed band-wise aperiodicity parameters and voiced/unvoiced decisions is verified by incorporating them in an existing state-of-the-art vocoder for speech synthesis. Subjective listening tests show that the quality of the reconstructed speech is on par with that of the state-of-the-art WORLD vocoder in terms of mean opinion score, indicating that spectrotemporal approaches are highly promising for speech analysis and synthesis applications.