Many common audio test and measurement procedures require characterization of the output signal of the device under test in terms of harmonic (sinusoidal) components and residual noise when the device processes sinusoidal imput signals. This work uses the Bayesian approach to statistical inference to address such problems as parameter estimation problems when discrete samples of the output signal are given. In the resulting Bayesian harmonic analysis the power spectrum computed from the discrete-time Furier transform appears as the logarithm of the posterior probability for the frequency of a single sinusoid rather than as an estimate of the signal spectrum; more complicated functions of the transform arise when analyzing signals with multiple sinusoids. Problems such as spectral leakage are addressed by nonlinear processing of the Fourier transform, offering several advantages over methods that use (linear) windowing of data.
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