Matched sampling systems, relation to wavelets and implementation using PRCC filter banks

This paper deals with two types of sampling systems, namely, the interpolation and approximation sampling systems. Closed-form expressions are derived for the frequency responses of the filters used in these systems that are matched to the input process in the mean squared sense. Closed-form express...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2000-08, Vol.48 (8), p.2269-2278
Main Authors: Bopardikar, A.S., Rao, R.M., Adiga, B.S.
Format: Article
Language:English
Subjects:
Applied sciences
Approximation
Channel bank filters
Closed-form solution
Detection, estimation, filtering, equalization, prediction
Effectiveness
Exact sciences and technology
Exact solutions
Filter bank
Filter banks
Frequency
Image reconstruction
Impedance matching
Information, signal and communications theory
Interpolation
Matched filters
Mathematical analysis
Sampling
Sampling methods
Signal and communications theory
Signal sampling
Signal, noise
Telecommunications and information theory
Wavelet
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Summary:This paper deals with two types of sampling systems, namely, the interpolation and approximation sampling systems. Closed-form expressions are derived for the frequency responses of the filters used in these systems that are matched to the input process in the mean squared sense. Closed-form expressions are also derived for the mean squared error between the input and the reconstructed processes for these matched sampling systems. Using these expressions, it is shown that the Meyer scaling function and wavelet or functions derived from these arise naturally in the context of subsampled bandlimited processes. To implement these systems, the perfect reconstruction circular convolution (PRCC) filter bank is proposed as a framework for the frequency-sampled implementation of these systems. Examples of matched interpolation and approximation sampling systems are provided, and their performance is compared with some standard interpolators to demonstrate their efficacy.
ISSN:1053-587X
1941-0476
DOI:10.1109/78.852008