Power spectrum estimation with logarithmically uniform resolution in frequency

Conventional harmonic analysis involves the representation of the average power of a random process in frequency bands which are equally spaced and equal in frequency resolution or bandwidth. In practical applications such as auditory acoustics and data reduction, a canonical representation of the power spectrum sometimes consists of estimates of the average power in frequency bands which are equally spaced and of equal bandwidth on a logarithmic frequency scale.

This dissertation develops two general techniques for logarithmic spectrum estimation. The first approach uses a bank of lowpass filters whose output average powers are differenced to obtain the required estimates. The second applies a family of frequency dependent windows to the periodogram of the data to obtain the spectrum estimates.

The computational requirements and statistical properties of the proposed approaches are derived and compared to conventional methods. Other logarithmically uniform frequency resolution approaches which have appeared in the literature are also presented and compared with the two new techniques introduced. To illustrate the general principles involved the new estimators are implemented and applied to a set of sinusoidal test data and a set of stochastic test data.