New Results on Perceptual Distortion Minimization and Nonlinear Least-Squares Frequency Estimation

• Published in: IEEE transactions on audio, speech, and language processing Vol. 19; no. 7; pp. 2239 - 2244
• Main Authors: Christensen, M. G., Jensen, S. H.
• Format: Journal Article
• Language: English
• Published: Piscataway, NJ IEEE 01.09.2011; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; Audio coding; Audio signals; Coding, codes; Detection, estimation, filtering, equalization, prediction; Distortion; Distortion measurement; Exact sciences and technology; Frequency estimation; Gaussian; Information, signal and communications theory; Least squares method; Lower bounds; matching pursuit; Matching pursuit algorithms; Miscellaneous; Natural language processing; Nonlinear distortion; Optimization; Psychoacoustic models; Signal and communications theory; Signal processing; Signal representation. Spectral analysis; Signal, noise; Smoothness; spectral analysis; Speech; Telecommunications and information theory; Performance evaluation; Parameter estimation; High resolution; Audio signal processing; Acoustic signal; Signal estimation; Iterative method; spectral analysis; Frequency estimation; Acoustic signal processing; Audio coding; Audio signal; Gaussian noise; Least squares method; Spectrum analysis; Matching pursuit; Frequency response; Sinusoidal signal; Signal analysis; Cramer Rao inequality
• ISSN: 1558-7916; 1558-7924
• DOI: 10.1109/TASL.2011.2129507

In a paper in this journal, a framework was presented wherein a number of practical methods for finding the perceptually most important sinusoids in audio signals could be related using a particular perceptually motivated distortion measure, and it was argued that for Gaussian noise and a large number of samples, these methods should attain the Cramér-Rao lower bound. In this correspondence, we report some new results on this subject. Specifically, we analyze the finite-sample performance of these methods in experiments, and we conclude that for a high number of samples, they perform close to the Cramér-Rao lower bound. However, for a low number of observations, we demonstrate that special care must be taken in designing the perceptually motivated distortion measure if high-resolution estimates are desired. In particular, the smoothness of the frequency response of the perceptual filter that implements the distortion measure is shown to be important.