2 research outputs found
Systematic DFT Frames: Principle, Eigenvalues Structure, and Applications
Motivated by a host of recent applications requiring some amount of
redundancy, frames are becoming a standard tool in the signal processing
toolbox. In this paper, we study a specific class of frames, known as discrete
Fourier transform (DFT) codes, and introduce the notion of systematic frames
for this class. This is encouraged by a new application of frames, namely,
distributed source coding that uses DFT codes for compression. Studying their
extreme eigenvalues, we show that, unlike DFT frames, systematic DFT frames are
not necessarily tight. Then, we come up with conditions for which these frames
can be tight. In either case, the best and worst systematic frames are
established in the minimum mean-squared reconstruction error sense. Eigenvalues
of DFT frames and their subframes play a pivotal role in this work.
Particularly, we derive some bounds on the extreme eigenvalues DFT subframes
which are used to prove most of the results; these bounds are valuable
independently