A general sampling theory for nonideal acquisition devices 论文

详细信息

发表期刊/会议

IEEE Transactions on Signal Processing

发表日期

1994-01-01

发表年份

1994

摘要

The authors first describe the general class of approximation spaces generated by translation of a function /spl psi/(x), and provide a full characterization of their basis functions. They then present a general sampling theorem for computing the approximation of signals in these subspaces based on a simple consistency principle. The theory puts no restrictions on the system input which can be an arbitrary finite energy signal; bandlimitedness is not required. In contrast to previous approaches, this formulation allows for an independent specification of the sampling (analysis) and approximation (synthesis) spaces. In particular, when both spaces are identical, the theorem provides a simple procedure for obtaining the least squares approximation of a signal. They discuss the properties of this new sampling procedure and present some examples of applications involving bandlimited, and polynomial spline signal representations. They also define a spectral coherence function that measures the "similarity" between the sampling and approximation spaces, and derive a relative performance bound for the comparison with the least squares solution.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>