An analysis of the high resolution property of group delay function with applications to audio signal processing

• Theoretical proof for the high resolution property of group delay function.
• n dB bandwidth of group delay function is lesser than that of magnitude spectrum.
• Extend the property for multi-resonator systems using empirical measures.
• Group delay is better compared to magnitude spectrum on three applications.

This paper provides a new insight into the high resolution property of the negative derivative of the phase response of a system. Group delay functions have been proposed and applied successfully as an alternative to conventional magnitude spectrum based applications in speech and music processing. One of the reasons claimed for its superior performance is the high spectral resolution. Most of the existing work use empirical analysis to show this property. In this paper, we show mathematically that for a single resonator, the ratio of the value of the peak in the magnitude spectrum to the value at a frequency that is n dB below the peak, is always much lower than the ratio of that of the minimum phase group delay spectrum. The results are extended for multiple resonators using numerical analyses. The theoretical results are reinforced using three applications, namely, pitch estimation, formant estimation and onset detection. The average deviation from the location of the pitch value/formant value/musical onset is about 53% lower than that of similar techniques that use the magnitude spectrum of the signal.