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—Two digital filters () and () are said to be biorthogonal partners of each other if their cascade () () satisfies the Nyquist or zero-crossing property. Biorthogonal partners arise in many different contexts such as filterbank theory, exact and least squares digital interpolation, and multiresolution theory. They also play a central role in the theory of… (More)

1 The cyclic prefix system is widely used for frequency domain equalization in discrete multitone channels. In this paper we show how the idea of fractionally spaced equalization (FSE) can be adapted to cyclic prefix systems. We derive the condition for a perfect FSE, and show that there is a certain freedom in the choice of the equalizer coefficients. This… (More)

1 In this paper we review the recent impact of transmultiplexers in digital communications. Filter bank precoders, conditions for equalization, and multiuser interference cancellation are reviewed. The idea behind blind channel identification is reviewed as well. The emphasis is mostly on the theoretical infrastructure, and the list of references provide a… (More)

B-splines are commonly used for continuous representation of discrete time signals. This kind of representation proves to be very useful in applications such as image interpolation, rotation and edge detection. In all these applications, the first step is to compute the B-spline coefficients of the signal, and this involves the use of an IIR noncausal… (More)

1 It is well-known that certain non bandlimited signals such as splines can be reconstructed from uniformly spaced samples similar to bandlimited signals. This usually requires noncausal IIR filters. We revisit this result and consider extensions such as derivative sampling theorems and pulse sampling theorems. It turns out that spline-like signals can… (More)

Multiple Input Multiple Output (MIMO) biorthogonal partners arise in many different contexts, one of them being multiwavelet theory. They also play a central role in the theory of MIMO channel equalization, especially with fractionally spaced equalizers. In this paper we first derive some theoretical properties of MIMO biorthogonal partners. We develop… (More)

The concept of fractional biorthogonal partners has been introduced recently by the authors. They arise in many different contexts , one of them being channel equalization with fractionally spaced equalizers. If the amount of oversampling at the receiver is not an integer, but a rational number, the problem of fractionally spaced equalization can be treated… (More)

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 down-sampling ratios are not integers but rational numbers. Hence the name fractional biorthogonal partners. The conditions for the existence of stable and of FIR… (More)

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 FIR fractional… (More)