Tuesday, November 17^{th}, 2015
Room 202 in Packard Bldg., Stanford University
Parking Generally Free In Nearby Lots After 4:00 pm
Map
Refreshments and Conversation at 6:00 P.M.
Presentation at 6:30 P.M.
Ratedistortion of subNyquist sampled processes
Alon Kipnis
PhD Candidate, Stanford EE Department
Abstract
Consider the task of analog to digital conversion in which a continuous
time random process is mapped into a stream of bits. The optimal tradeoff
between the bitrate and the minimal average distortion in recovering the
waveform from its bit representation is described by the Shannon ratedistortion
function of the continuoustime source. Traditionally, in
solving for the optimal mapping and the ratedistortion function we assume
that the analog waveform has a discrete time version, as in the case of a
bandlimited signal sampled above its Nyquist frequency. Such assumption,
however, may not hold in many scenarios due to wideband signaling and A/D
technology limitations. A more relevant assumption in such scenarios is
that only a subNyquist sampled version of the source can be observed, and
that the error in analog to digital conversion is due to both subsampling
and finite bit representation. This assumption gives rise to a combined
sampling and source coding problem, in which the quantities of merit are
the sampling frequency, the bitrate and the average distortion.
In this talk we will characterize the optimal tradeoff among these
three parameters. The resulting ratedistortionsampling frequency function can
be seen as a generalization of the classical ShannonKotelnikovWhittaker
sampling theorem to the case where finite bit rate representation is required.
This characterization also provides us with a new critical sampling rate: the
minimal sampling rate required to achieve the ratedistortion function of a
Gaussian stationary process for a given ratedistortion pair. That is, although
the Nyquist rate is the minimal sampling frequency that allows perfect
reconstruction of a bandlimited signal from its samples, relaxing perfect
reconstruction to a prescribed distortion allows sampling below the Nyquist rate
while achieving the same ratedistortion tradeoff.
