Efficient time-varying loudness estimation via the hopping Goertzel DFT

The efficient and accurate time-varying measurement of loudness is an important problem in audio and acoustics. In this work, we present an optimization to the multi-resolution spectrogram used in the loudness model of Glasberg and Moore (Jour. Aud. Eng. Soc, 2002). This optimization is based on a modification to the sliding Goertzel DFT algorithm, referred to as the hopping Goertzel DFT. As in Glasberg and Moore´s model, multi-resolution spectra are computed at 1 ms intervals, using 6 different bands with spectral resolution inversely proportional to frequency. Initial PC-based tests show a significant efficiency improvement with the hopping Goertzel technique versus the use of parallel FFTs for multi-resolution spectrogram computation.