4,299 research outputs found
Approximation of L\"owdin Orthogonalization to a Spectrally Efficient Orthogonal Overlapping PPM Design for UWB Impulse Radio
In this paper we consider the design of spectrally efficient time-limited
pulses for ultrawideband (UWB) systems using an overlapping pulse position
modulation scheme. For this we investigate an orthogonalization method, which
was developed in 1950 by Per-Olov L\"owdin. Our objective is to obtain a set of
N orthogonal (L\"owdin) pulses, which remain time-limited and spectrally
efficient for UWB systems, from a set of N equidistant translates of a
time-limited optimal spectral designed UWB pulse. We derive an approximate
L\"owdin orthogonalization (ALO) by using circulant approximations for the Gram
matrix to obtain a practical filter implementation. We show that the centered
ALO and L\"owdin pulses converge pointwise to the same Nyquist pulse as N tends
to infinity. The set of translates of the Nyquist pulse forms an orthonormal
basis or the shift-invariant space generated by the initial spectral optimal
pulse. The ALO transform provides a closed-form approximation of the L\"owdin
transform, which can be implemented in an analog fashion without the need of
analog to digital conversions. Furthermore, we investigate the interplay
between the optimization and the orthogonalization procedure by using methods
from the theory of shift-invariant spaces. Finally we develop a connection
between our results and wavelet and frame theory.Comment: 33 pages, 11 figures. Accepted for publication 9 Sep 201
Generic Feasibility of Perfect Reconstruction with Short FIR Filters in Multi-channel Systems
We study the feasibility of short finite impulse response (FIR) synthesis for
perfect reconstruction (PR) in generic FIR filter banks. Among all PR synthesis
banks, we focus on the one with the minimum filter length. For filter banks
with oversampling factors of at least two, we provide prescriptions for the
shortest filter length of the synthesis bank that would guarantee PR almost
surely. The prescribed length is as short or shorter than the analysis filters
and has an approximate inverse relationship with the oversampling factor. Our
results are in form of necessary and sufficient statements that hold
generically, hence only fail for elaborately-designed nongeneric examples. We
provide extensive numerical verification of the theoretical results and
demonstrate that the gap between the derived filter length prescriptions and
the true minimum is small. The results have potential applications in synthesis
FB design problems, where the analysis bank is given, and for analysis of
fundamental limitations in blind signals reconstruction from data collected by
unknown subsampled multi-channel systems.Comment: Manuscript submitted to IEEE Transactions on Signal Processin
Output Filter Aware Optimization of the Noise Shaping Properties of {\Delta}{\Sigma} Modulators via Semi-Definite Programming
The Noise Transfer Function (NTF) of {\Delta}{\Sigma} modulators is typically
designed after the features of the input signal. We suggest that in many
applications, and notably those involving D/D and D/A conversion or actuation,
the NTF should instead be shaped after the properties of the
output/reconstruction filter. To this aim, we propose a framework for optimal
design based on the Kalman-Yakubovich-Popov (KYP) lemma and semi-definite
programming. Some examples illustrate how in practical cases the proposed
strategy can outperform more standard approaches.Comment: 14 pages, 18 figures, journal. Code accompanying the paper is
available at http://pydsm.googlecode.co
Signal recovery from wavelet transform maxima
Cataloged from PDF version of article.This paper presents an iterative algorithm for signal recovery
from discrete-time wavelet transform maxima. The signal recovery
algorithm is developed by using the method of projections onto convex
sets. Convergence of the algorithm is assured
Digital Signal Processing
Contains reports on three research projects.U. S. Navy Office of Naval Research (Contract N00014-67-A-0204-0064)National Science Foundation (Grant GK-31353
Discrete multitone modulation with principal component filter banks
Discrete multitone (DMT) modulation is an attractive method for communication over a nonflat channel with possibly colored noise. The uniform discrete Fourier transform (DFT) filter bank and cosine modulated filter bank have in the past been used in this system because of low complexity. We show in this paper that principal component filter banks (PCFB) which are known to be optimal for data compression and denoising applications, are also optimal for a number of criteria in DMT modulation communication. For example, the PCFB of the effective channel noise power spectrum (noise psd weighted by the inverse of the channel gain) is optimal for DMT modulation in the sense of maximizing bit rate for fixed power and error probabilities. We also establish an optimality property of the PCFB when scalar prefilters and postfilters are used around the channel. The difference between the PCFB and a traditional filter bank such as the brickwall filter bank or DFT filter bank is significant for effective power spectra which depart considerably from monotonicity. The twisted pair channel with its bridged taps, next and fext noises, and AM interference, therefore appears to be a good candidate for the application of a PCFB. This is demonstrated with the help of numerical results for the case of the ADSL channel
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