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The recently proposed consistent resampling theory for non-bandlimited signals is applied to image resizing and rotation. Images with high frequency components can be resampled using this scheme to achieve high quality performance. Image resizing is treated as resampling using non-ideal interpolation functions. Both zoom in and zoom out by non-integer factors are considered. Image rotation is also formulated as a resampling process. We show that our approach outperforms other linear image processing techniques without increasing the computational cost.

Currently, digital signal processing systems typically assume that the signals are bandlimited. This is due to our knowledge based on the uniform sampling theorem for bandlimited signals which was established over 50 years ago by the works of Whittaker, Kotel'nikov and Shannon. However, in practice the digital signals are mostly of finite length. This kind of signals are not strictly bandlimited. Furthermore, advances in electronics have led to the use of very wide bandwidth signals and systems, such as Ultra-Wide Band (UWB) communication systems with signal bandwidths of several giga-hertz. This kind of signals can effectively be viewed as having infinite bandwidth. Thus there is a need to extend existing theory and techniques for signals of finite bandwidths to that for non-bandlimited signals. Two recent approaches to a more general sampling theory for non-bandlimited signals have been published. One is for signals with finite rate of innovation. The other introduced the concept of consistent sampling. It views sampling and reconstruction as projections of signals onto subspaces spanned by the sampling (acquisition) and reconstruction (synthesis) functions. Consistent sampling is achieved if the same discrete signal is obtained when the reconstructed continuous signal is sampled. However, it has been shown that when this generalized theory is applied to the de-interlacing of video signals, incorrect results are obtained. This is because de-interlacing is essentially a resampling problem rather than a sampling problem because both the input and output are discrete. While the theory for the resampling for bandlimited signals is well established, the problem of resampling without bandlimited constraints is largely unexplored. The aim of this thesis is to develop a resampling theory for non-bandlimited discrete signals and explore some of its potential applications. The first major contribution is the the theory and techniques for designing an optimal resampling syst

The recently proposed consistent resampling scheme is applied to three practical applications. Signals that are not necessarily bandlimited can be resampled using this scheme to achieve high quality performance. The most important part is the design of a suitable prefilter which minimizes a novel distance metric proposed by the authors. This metric is also used as a measure of the system performance as a whole. In all three cases, whether the signal is noiseless or noisy, the consistent resampling approach outperforms the classic interpolation and resampling techniques without increasing the computational cost. Details of each application are provided. © 2007 IEEE.

We propose a novel approach to demodulate timehopping pulse position modulated (PPM) impulse radio signals using a fully digital receiver. The pulses are viewed as non-uniform samples of an underlying continuous signal. They are then interpolated and consistently uniformly resampled using an appropriate kernel. A non-uniformly sampled signal is consistently resampled if the original samples can be deduced from the resampled uniform sequence using a suitable methodology. Such resampled sequence can be used to determine the position of the original pulses. In this paper, we showed how the B-splines can be used as an interpolating kernel and an algorithm to detect the position of the PPM pulses is developed. © 2006 IEEE.