The eigenvalue decomposition (EVD) of a Hermitian matrix in terms of unitary matrices is well known. In this paper, we present an algorithm for the approximate EVD (AEVD) of a para-Hermitian (PH) system. Here, the approximate diagonalization is carried out successively by applying degree-1 finite impulse response (FIR) paraunitary (PU) transformations. The system parameters are chosen to make the zeroth order diagonal energy (ZODE) nondecreasing at each stage. Simulation results presented for the design of a signal-adapted PU filter bank (FB) show close agreement with the behavior of the infinite order principal component FB (PCFB).

The problem of variable sample rate conversion (SRC) has received much attention on account of its applications in software defined radios (SDRs) that must support a wide variety of data rates. In this paper, we investigate the spectral properties of variable SRC and focus on the interpolation error obtained using any two interpolation kernels. We show that SRC is a generalization of decimation for both rational and irrational conversion ratios. In addition, a frequency domain expression for the mean-squared interpolation error is derived and simplified. Simulations presented show the degradation effects of using practical piecewise polynomial based interpolants as opposed to the underlying bandlimited sine function for several input signals.

Starting with the maximum a posteriori (MAP) estimation approach, this paper derives the optimum (in the MAP estimation sense) means for performing symbol timing recovery in the absence of carrier phase information (i.e., prior to carrier phase recovery). Specifically, we examine the necessary modification of a well-known form of coherent symbol synchronizer, namely, the data transition tracking loop (DTTL) to allow its operation in the absence of carrier phase information, i.e., as a so-called noncoherent symbol sync loop. By employing such a noncoherent scheme, one can eliminate the need for iteration between the carrier and symbol sync functions, as typically takes place in receivers that more commonly perform carrier tracking and acquisition prior to symbol timing. The performance of both the linear and nonlinear versions of this noncoherent DTTL is obtained by a combination of analysis and simulation, and compared with that of the corresponding coherent DDTLs.

Starting with the maximum a posteriori (MAP)estimation approach, this paper derives the optimum (in the MAP estimation sense) means for performing symbol-timing recovery in the absence of carrier-phase information (i.e., prior to carrier-phase recovery). Specifically, we examine the necessary modification of a well-known form of coherent symbol synchronizer,namely, the data transition tracking loop (DTTL), to allow its operation in the absence of carrier-phase information, i.e., as a so-called noncoherent symbol sync loop. By employing such a noncoherent scheme, one can eliminate the need for iteration between the carrier and symbol sync functions,as typically takes place in receivers that more commonly perform carrier tracking and acquisition prior to symbol timing. The performance of both the linear and nonlinear versions of this noncoherent DTTL is obtained by a combination of analysis and simulation, and compared with that of the corresponding coherent DTTLs.

Recently, much attention has been given to the design of optimal finite impulse response (FIR) compaction filters. Such filters, which arise in the design of optimal signal-adapted orthonormal FIR filter banks, satisfy a magnitude squared Nyquist constraint in addition to the inherent FIR assumption. In this paper, we focus on the least squares optimal design of FIR filters whose magnitude squared response satisfies a Nyquist constraint. Using a complete characterization of such systems in terms of Householder-like building blocks, an iterative gradient based greedy algorithm is proposed to design such filters. Simulation results provided show the merit of the proposed technique for designing FIR compaction filters.

With the advent of wavelets for lossy data compression came the notion of representing signals in a certain vector space by their projections in well chosen subspaces of the original space. In this paper, we consider the subspace of signals generated by an overdecimated rational nonuniform filter bank and find the optimal conditions under which the mean-squared error between a given deterministic signal and its representation in this subspace is minimized for a fixed set of synthesis filters. Under these optimal conditions, it is shown that choosing the synthesis filters to further minimize this error is simply an energy compaction problem. With this, we introduce the notion of deterministic energy compaction filters for classes of signals. Simulation results are presented showing the merit of our proposed method for optimizing the synthesis filters.

With the advent of wavelets for lossy data compression came the notion of representing signals in a certain vector space by their projections in well chosen subspaces of the original space. In this paper, we consider the subspace of signals generated by an overdecimated rational nonuniform filter bank and find the optimal conditions under which the mean-squared error between a given deterministic signal and its representation in this subspace is minimized for a fixed set of synthesis filters. Under these optimal conditions, it is shown that choosing the synthesis filters to further minimize this error is simply an energy compaction problem. With this, we introduce the notion of deterministic energy compaction filters for classes of signals. Simulation results are presented showing the merit of our proposed method for optimizing the synthesis filters.

We present a new low-complexity method for the design of channel shortening equalizers for discrete multitone (DMT) modulation systems using the eigenfilter approach. In contrast to other such methods which require a Cholesky decomposition for each delay parameter value used, ours requires only one such decomposition. Simulation results show that our method performs nearly optimally in terms of observed bit rate.

The advent of discrete multitone modulation (DMT) systems in recent years has brought to light the importance of channel shortening equalizers. In this paper, we present a method for the design of one such equalizer for multiple-input multiple-output (MIMO) linear dispersive channels. This method is a generalization of one that was used for shortening of single-input single-output (SISO) channels. Experimental results presented show that our design method performs better than the minimum mean-squared error (MMSE) technique in terms of effective channel energy compaction.1

The design of time-domain equalizers or TEQs for discrete multitone modulation (DMT) systems has recently received much attention. In this paper, we present a generalization of one such design method which takes into account the noise observed in a DMT channel. Furthermore, we show how this generalization can be used for the design of fractionally spaced equalizers or FSEs. Experimental results are presented showing that our design method performs better than other known techniques.

One problem of great interest to the signal processing community is that of estimating the frequencies of sinusoids buried in noise. Traditional methods applied to a fullband signal fail to estimate accurately when the signal-to-noise ratio (SNR) or spacing between frequencies is small. They also fail when the noise is not white and its statistics are unknown. We consider these methods when applied to the subbands of a filter bank and show that, through proper choice of analysis filters, the local SNR and frequency spacing increase by the decimation ratio. We also show that the subband noise processes are, on average, more "white" than the fullband one in terms of the spectral flatness measure. This suggests that if the noise statistics are unknown, there will be less error by estimating in the subbands as opposed to the fullband. Experimental results support this theory, as we show.