1,287 research outputs found
Nonparametric estimation of the dynamic range of music signals
The dynamic range is an important parameter which measures the spread of
sound power, and for music signals it is a measure of recording quality. There
are various descriptive measures of sound power, none of which has strong
statistical foundations. We start from a nonparametric model for sound waves
where an additive stochastic term has the role to catch transient energy. This
component is recovered by a simple rate-optimal kernel estimator that requires
a single data-driven tuning. The distribution of its variance is approximated
by a consistent random subsampling method that is able to cope with the massive
size of the typical dataset. Based on the latter, we propose a statistic, and
an estimation method that is able to represent the dynamic range concept
consistently. The behavior of the statistic is assessed based on a large
numerical experiment where we simulate dynamic compression on a selection of
real music signals. Application of the method to real data also shows how the
proposed method can predict subjective experts' opinions about the hifi quality
of a recording
An Analysis of Mutually Dispersive Brown Symbols for Non-Linear Ambiguity Suppression
This thesis significantly advances research towards the implementation of optimal Non-linear Ambiguity Suppression (NLS) waveforms by analyzing the Brown theorem. The Brown theorem is reintroduced with the use of simplified linear algebraic notation. A methodology for Brown symbol design and digitization is provided, and the concept of dispersive gain is introduced. Numerical methods are utilized to design, synthesize, and analyze Brown symbol performance. The theoretical performance in compression and dispersion of Brown symbols is demonstrated and is shown to exhibit significant improvement compared to discrete codes. As a result of this research a process is derived for the design of optimal mutually dispersive symbols for any sized family. In other words, the limitations imposed by conjugate LFM are overcome using NLS waveforms that provide an effective-fold increase in radar unambiguous range. This research effort has taken a theorem from its infancy, validated it analytically, simplified it algebraically, tested it for realizability, and now provides a means for the synthesis and digitization of pulse coded waveforms that generate an N-fold increase in radar effective unambiguous range. Peripherally, this effort has motivated many avenues of future research
Estimation of Overspread Scattering Functions
In many radar scenarios, the radar target or the medium is assumed to possess
randomly varying parts. The properties of a target are described by a random
process known as the spreading function. Its second order statistics under the
WSSUS assumption are given by the scattering function. Recent developments in
operator sampling theory suggest novel channel sounding procedures that allow
for the determination of the spreading function given complete statistical
knowledge of the operator echo from a single sounding by a weighted pulse
train.
We construct and analyze a novel estimator for the scattering function based
on these findings. Our results apply whenever the scattering function is
supported on a compact subset of the time-frequency plane. We do not make any
restrictions either on the geometry of this support set, or on its area. Our
estimator can be seen as a generalization of an averaged periodogram estimator
for the case of a non-rectangular geometry of the support set of the scattering
function
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