Group delay spectrogram of speech signals without phase wrapping

This paper proposes a method for displaying the phase information in speech signals through group delay spectrogram, without the need for phase unwrapping. The method involves scaling down the phase values without affecting the shape of the phase or group delay function, thus preserving the information of the phase spectrum. This is accomplished using single-frequency filtering (SFF) of speech signals to obtain the instantaneous complex SFF spectrum. The SFF involves filtering a frequency-shifting signal using a resonator at half the sampling frequency. The SFF spectrum displays characteristics similar to the standard short-time Fourier transform (STFT) spectrum, but without the effects of truncation due to windowing operation. The objective of the present study is to show that features of speech production can also be observed in the phase information, displayed through the group delay spectrogram. The time-frequency resolution in the group delay spectrogram depends on the choice of the bandwidth of the resonator used in the SFF analysis. The speech production features displayed in the group delay spectrogram are examined for different types of speech signals at different time-frequency resolutions.