GNU Scientific Library – Reference Manual: DWT References

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### 32.5 References and Further Reading

The mathematical background to wavelet transforms is covered in the original lectures by Daubechies,

- Ingrid Daubechies. Ten Lectures on Wavelets. CBMS-NSF Regional Conference Series in Applied Mathematics (1992), SIAM, ISBN 0898712742.

An easy to read introduction to the subject with an emphasis on the application of the wavelet transform in various branches of science is,

- Paul S. Addison. The Illustrated Wavelet Transform Handbook. Institute of Physics Publishing (2002), ISBN 0750306920.

For extensive coverage of signal analysis by wavelets, wavelet packets and local cosine bases see,

- S. G. Mallat. A wavelet tour of signal processing (Second edition). Academic Press (1999), ISBN 012466606X.

The concept of multiresolution analysis underlying the wavelet transform is described in,

- S. G. Mallat. Multiresolution Approximations and Wavelet Orthonormal Bases of L^2(R). Transactions of the American Mathematical Society, 315(1), 1989, 69–87.

- S. G. Mallat. A Theory for Multiresolution Signal Decomposition—The Wavelet Representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11, 1989, 674–693.

The coefficients for the individual wavelet families implemented by the library can be found in the following papers,

- I. Daubechies. Orthonormal Bases of Compactly Supported Wavelets. Communications on Pure and Applied Mathematics, 41 (1988) 909–996.

- A. Cohen, I. Daubechies, and J.-C. Feauveau. Biorthogonal Bases of Compactly Supported Wavelets. Communications on Pure and Applied Mathematics, 45 (1992) 485–560.

The PhysioNet archive of physiological datasets can be found online at http://www.physionet.org/ and is described in the following paper,

- Goldberger et al. PhysioBank, PhysioToolkit, and PhysioNet: Components of a New Research Resource for Complex Physiologic Signals. Circulation 101(23):e215-e220 2000.

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