Analog sparse signals resulting from biomedical and sensing network applications are typically non–stationary with frequency–varying spectra. By ignoring that the maximum frequency of their spectra is changing, uniform sampling of sparse signals collects unnecessary samples in quiescent segments of the signal. A more appropriate sampling approach would be signal–dependent. Moreover, in many of these applications power consumption and analog processing are issues of great importance that need to be considered. In this paper we present a signal dependent non–uniform sampler that uses a Modified Asynchronous Sigma Delta Modulator which consumes low–power and can be processed using analog procedures. Using Prolate Spheroidal Wave Functions (PSWF) interpolation of the original signal is performed, thus giving an asynchronous analog to digital and digital to analog conversion. Stable solutions are obtained by using modulated PSWFs functions. The advantage of the adapted asynchronous sampler is that range of frequencies of the sparse signal is taken into account avoiding aliasing. Moreover, it requires saving only the zero–crossing times of the non–uniform samples, or their differences, and the reconstruction can be done using their quantized values and a PSWF–based interpolation. The range of frequencies analyzed can be changed and the sampler can be implemented as a bank of filters for unknown range of frequencies. The performance of the proposed algorithm is illustrated with an electroencephalogram (EEG) signal.
This paper provides a time-frequency approach to modeling and estimating the communication channel, and to
symbol transmission in multi-carrier wireless systems. The method is based on the evolutionary spectral theory
of signals and systems. Multi-carrier systems, such as orthogonal frequency division multiplexing (OFMD) and
multi-carrier spread spectrum (MCSS), are very efficient in fast fading channels. However, the basic pulse used
in the modulation causes dispersion in time-frequency, complicating inter-symbol and inter-channel interferences.
Our time-frequency approach deals separately with the channel modeling and estimation, and with the symbol
transmission. Using the properties of the response of the channel to a linear chirp signal it is shown that the
typical linear time-variant channel model, needed to characterize multi-path and Doppler, is simplified into a
linear time-invariant model of minimal order. Time and Doppler shifts are represented by equivalent time-shifts,
and are estimated in a blind fashion from the evolutionary kernel of the received signal. Thus, the linear chirp
signal is used as a pilot sequence to characterize the channel. A coherent receiver uses such information to detect
the sent symbols. A multi-user OFDM system is obtained using a linear chirp as the modulating signal for basic
pulses shifted in time, and by choosing the instantaneous frequency of the linear chirp to be of unity slope for an
optimal time-frequency lattice. This optimal lattice increases the transmission rate, diminishes the inter-symbol
and inter-channel interference, and provides a new way of looking at OFDM. This approach is extended to
MCSS. To illustrate the concepts, simulations, with different signal to noise ratios, are performed. The results
are encouraging and worth of further investigation.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.