The time-delay graph and the delayogram - new visualizations for time delay

For about 60 years, the spectrogram has been an excellent visualization tool for observing the acoustic and prosodic features of a speech signal. However, a visual tool has been lacking for information that is typically represented by the speech signal´s phase. When a talker is remote from one or more microphones, the times of arrival of the direct wave and those of reflections become important. In this letter, we introduce two visualizations that have proven to be quite useful for us in understanding phasic behaviors of microphone arrays. A time delay versus frequency plot for a window of time is called the time-delay graph, and an ensemble of projected time-delay graphs is called the delayogram. These visualizations are introduced, and simulated and real-speech data examples of both displays are presented. The time-delay graph is compared to the phase transform generalized cross-correlation (GCC-PHAT) for two real-data examples.