Tang, D.F. (2012) A fast algorithm for spectral interpolation of sampled data. [MIMS Preprint]
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Abstract
This paper describes a fast algorithm to interpolate between samples of a bandwidth-limited signal that has been sampled at regular intervals. The algorithm is most suited to situations when a small amount of error in the interpolated values is acceptable, the larger the acceptable error, the more efficient is the algorithm. This can be useful in singnal processing, image processing and as an alternative to finite difference calculations. The same algorithm can be used to calculate the value of an $n^{th}$ degree polynomial at the $2n^{th}$ degree Chebyshev points, given its values at the $n^{th}$ degree Chebyshev points, thus providing a fast algorithm for the approximate multiplicaltion of polynomials. This could be used in, for example, computer algebra systems. We consider signals of finite duration, but the same technique can be used to deal with infinite signals so could be used to achieve fast and power-efficient interpolation of streamed data. On a prarallel architecture, the algorithm also requires less inter-process communication than interpolation using a Fast Fourier Transform method.
| Item Type: | MIMS Preprint |
|---|---|
| Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis MSC 2010, the AMS's Mathematics Subject Classification > 68 Computer science |
| Depositing User: | Mr D.F. Tang |
| Date Deposited: | 30 Apr 2012 |
| Last Modified: | 08 Nov 2017 18:18 |
| URI: | https://eprints.maths.manchester.ac.uk/id/eprint/1814 |
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