Resampling

Philippe Thevenaz 1 Introduction 393

Thierry Blu 1-1 Definition • 1.2 Scope • 1.3 Applications

Michael Unser 2 Classical Interpolation 395

Swiss Federal Institute of 2.1 Interpolation Constraint

Technology—Lausanne 3 Generalized Interpolation 396

3.1 Determination of the Coefficients • 3.2 Reconciliation

4 Terminology and Other Pitfalls 397

5 Artifacts 397

5.1 Resampling • 5.2 Ringing • 5.3 Aliasing • 5.4 Blocking • 5.5 Blurring

6 Desirable Properties 400

6.1 Separability • 6.2 Symmetry • 6.3 Partition of Unity

7 Approximation Theory 402

7.1 Strang-Fix Equivalence • 7.2 Reproduction of the Polynomials • 7.3 Regularity •

7.4 Approximation Kernel Example

8 Specific Examples 405

8.1 Nearest-Neighbor • 8.2 Linear • 8.3 B-splines • 8.4 o-Moms • 8.5 Schaum's Functions • 8.6 Keys' Function • 8.7 Sinc • 8.8 Dirichlet Apodization • 8.9 Hanning Apodization

9 Cost-Performance Analysis 410

10 Experiments 411

10.1 Nearest-Neighbor and Linear Interpolation • 10.2 Cubic Interpolation • 10.3 Sinc-Based Interpolation • 10.4 Discussion

11 Conclusion 414

Appendix 415

A.1 Fourier Transform and Fourier Series • A.2 Partition of Unity • A.3 Recursive Filtering

References 418

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