Principal component lter banks (PCFB's) sequentially compress most of the input signal energy into the rst few subbands, and are mathematically de ned using the notion of majorization. In a series of recent works, we have exploited connections between majorization and convexity theory to provide a uni ed explanation of PCFB optimality for numerous signal processing problems, involving compressi...

In this paper, we propose a continuous-domain version of principal-component analysis, with the constraint that the underlying family of templates appears at arbitrary orientations. We show that the corresponding principal components are steerable. Our method can be used for designing steerable filters so that they best approximate a given collection of reference templates. We apply this framew...

We consider optimal orthonormal filter banks for subband coding of wide sense cyclostationary signals, with -periodic second order statistics. An -channel over decimated uniform filter bank, with -periodic analysis and synthesis filters, is used as the subband coder. An average variance condition is used to measure the output distortion. We show that for at least three potential bit allocation ...

Remote monitoring of cardiopulmonary activities using quadrature direct conversion Doppler radar shows remarkable promise in medical and security applications. One major challenge for such monitoring is demodulation of the IQ signals and heart and respiration rate determination. This paper presents a rate finding algorithm based on extended kalman filter (EKF) and principal component analysis. ...

ÐMany software systems built in recent years have been developed using object-oriented technology and, in some cases, they already need adaptive maintenance in order to satisfy market and customer needs. In most cases, the estimation and prediction of maintenance effort is performed with difficulty due to the lack of metrics and suitable models. In this paper, a model and metrics for estimation...

For γ > − 1 2 , we provide the Karhunen-Lò eve expansion of the weighted mean-centered Wiener process , defined by Wγ (t) = 1 √ 1 + 2γ W t 1+2γ − 1 0 W u 1+2γ du , for t ∈ (0 , 1 ]. We show that the orthogonal functions in these expansions have simple expressions in term of Bessel functions. Moreover , we obtain that the L 2 [ 0 , 1 ] norm of Wγ is identical in distribution with the L 2 [ 0 , 1...

Discrete multitone modulation is an attractive method for communication over a non flat channel with possibly colored noise. The uniform 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, which are known to be optimal for data compression and denoising applications, ar...

When conjugate gradient (CG) methods are applied to a problem like velocity transform in 2-D, the principal artifact faced is the half-integration waveform (Claerbout, 1993, 1995). Logically, the best filter to suppress a half-integration waveform is the half-derivative filter. In practice, filters like the half-derivative filter have been reported as causing CG residuals to diverge (Lumley, 19...

The problem of optimizing digital filter banks based on input statistics was perhaps first addressed nearly four decades ago by Huang and Schultheiss. These authors actually considered a special case, namely transform coder optimization. Many of the subband coder optimization problems considered in recent years have close similarities to this work, though there are fundamental differences as we...

Theory of optimal orthonormal filter banks has recently been developed under the assumption that quantizers operate at high bit rates. We show that the theory can be simplified if a more general model for quantizers is used. With such a model, we show that principal component filter banks (PCFB) are optimal for orthonormal subband coding under all bit rates and bit allocation strategies. This e...