Fractional biorthogonal partners in fractionally spaced equalizers

Conference Record of the Thirty-Sixth Asilomar Conference on Signals, Systems and Computers, 2002.

It is well known that a broad class of non bandlimited signals can be reconstmcted from u n i f o n l y spaced samples by relating the problem to the inversion of a digital filter. This simple idea has given rise to many applications, some of them quite sophisticated. This includes spline interpolation, fractionally spaced equalization (FSE) of noisy channels and more recently, rational FSEs. On the theoretical front, it has given rise to the idea of biorthogonal partners which unify many aspects of wavelet theory into the same framework. In this paper we give an overview of the main results in this area.'

The role of biorthogonal partners in sampling theory for non bandlimited signals: a review

Conference Record of the Thirty-Sixth Asilomar Conference on Signals, Systems and Computers, 2002.

Fractional biorthogonal partners and application in signal interpolation

2002 IEEE International Symposium on Circuits and Systems. Proceedings (Cat. No.02CH37353)

The concept of biorthogonal partners has been introduced recently by the authors. The work presented in this paper is an extension of some of these results to the case where the upsampling and downsampling ratios are not integers but rational numbers. Hence the name fractional biorthogonal partners. The conditions for the existence of stable and of FIR fractional biorthogonal partners are derived. This result gives rise to an all-FIR spline interpolation technique with the minimum amount of required oversampling. This technique is illustrated by an interpolation example.

Fractional biorthogonal partners in channel equalization and signal interpolation

IEEE Trans. Signal Process.

2003

Abstract-The concept of biorthogonal partners has been introduced recently by the authors. The work presented here is an extension of some of these results to the case where the upsampling and downsampling ratios are not integers but rational numbers, hence, the name fractional biorthogonal partners. The conditions for the existence of stable and of finite impulse response (FIR) fractional biorthogonal partners are derived. It is also shown that the FIR solutions (when they exist) are not unique. This property is further explored in one of the applications of fractional biorthogonal partners, namely, the fractionally spaced equalization in digital communications. The goal is to construct zero-forcing equalizers (ZFEs) that also combat the channel noise. The performance of these equalizers is assessed through computer simulations. Another application considered is the all-FIR interpolation technique with the minimum amount of oversampling required in the input signal. We also consider the extension of the least squares approximation problem to the setting of fractional biorthogonal partners.