Abstract

A new computing method for discrete-signal sinc interpolation suitable for use in image and signal processing and the synthesis of holograms is described. It is shown to be superior to the commonly used zero-padding interpolation method in terms of interpolation accuracy, flexibility, and computational complexity.

© 1997 Optical Society of America

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References

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  1. T. Smith, M. S. Smith, S. T. Nichols, “Efficient sinc function interpolation technique for center padded data,” IEEE Trans. Acoust. Speech Signal Process. 38, 1512–1517 (1990).
    [CrossRef]
  2. J. D. Markel, “FFT prunning,” IEEE Trans. Audio Electron. AU-19, 305–311 (1971).
    [CrossRef]
  3. L. P. Yaroslavsky, Digital Picture Processing. An Introduction (Springer-Verlag, Berlin, 1985).
    [CrossRef]
  4. V. Kober, M. Unser, L. P. Yaroslavsky, “Spline and sinc signal interpolations in image geometrical transforms,” in Fifth International Workshop on Digital Image Processing and Computer Graphics, N. A. Kuznetsov, V. A. Soifer, eds., Proc. SPIE2363, 152–161 (1994).

1990 (1)

T. Smith, M. S. Smith, S. T. Nichols, “Efficient sinc function interpolation technique for center padded data,” IEEE Trans. Acoust. Speech Signal Process. 38, 1512–1517 (1990).
[CrossRef]

1971 (1)

J. D. Markel, “FFT prunning,” IEEE Trans. Audio Electron. AU-19, 305–311 (1971).
[CrossRef]

Kober, V.

V. Kober, M. Unser, L. P. Yaroslavsky, “Spline and sinc signal interpolations in image geometrical transforms,” in Fifth International Workshop on Digital Image Processing and Computer Graphics, N. A. Kuznetsov, V. A. Soifer, eds., Proc. SPIE2363, 152–161 (1994).

Markel, J. D.

J. D. Markel, “FFT prunning,” IEEE Trans. Audio Electron. AU-19, 305–311 (1971).
[CrossRef]

Nichols, S. T.

T. Smith, M. S. Smith, S. T. Nichols, “Efficient sinc function interpolation technique for center padded data,” IEEE Trans. Acoust. Speech Signal Process. 38, 1512–1517 (1990).
[CrossRef]

Smith, M. S.

T. Smith, M. S. Smith, S. T. Nichols, “Efficient sinc function interpolation technique for center padded data,” IEEE Trans. Acoust. Speech Signal Process. 38, 1512–1517 (1990).
[CrossRef]

Smith, T.

T. Smith, M. S. Smith, S. T. Nichols, “Efficient sinc function interpolation technique for center padded data,” IEEE Trans. Acoust. Speech Signal Process. 38, 1512–1517 (1990).
[CrossRef]

Unser, M.

V. Kober, M. Unser, L. P. Yaroslavsky, “Spline and sinc signal interpolations in image geometrical transforms,” in Fifth International Workshop on Digital Image Processing and Computer Graphics, N. A. Kuznetsov, V. A. Soifer, eds., Proc. SPIE2363, 152–161 (1994).

Yaroslavsky, L. P.

V. Kober, M. Unser, L. P. Yaroslavsky, “Spline and sinc signal interpolations in image geometrical transforms,” in Fifth International Workshop on Digital Image Processing and Computer Graphics, N. A. Kuznetsov, V. A. Soifer, eds., Proc. SPIE2363, 152–161 (1994).

L. P. Yaroslavsky, Digital Picture Processing. An Introduction (Springer-Verlag, Berlin, 1985).
[CrossRef]

IEEE Trans. Acoust. Speech Signal Process. (1)

T. Smith, M. S. Smith, S. T. Nichols, “Efficient sinc function interpolation technique for center padded data,” IEEE Trans. Acoust. Speech Signal Process. 38, 1512–1517 (1990).
[CrossRef]

IEEE Trans. Audio Electron. (1)

J. D. Markel, “FFT prunning,” IEEE Trans. Audio Electron. AU-19, 305–311 (1971).
[CrossRef]

Other (2)

L. P. Yaroslavsky, Digital Picture Processing. An Introduction (Springer-Verlag, Berlin, 1985).
[CrossRef]

V. Kober, M. Unser, L. P. Yaroslavsky, “Spline and sinc signal interpolations in image geometrical transforms,” in Fifth International Workshop on Digital Image Processing and Computer Graphics, N. A. Kuznetsov, V. A. Soifer, eds., Proc. SPIE2363, 152–161 (1994).

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Figures (4)

Fig. 1
Fig. 1

Interpolation functions for different versions of the discrete sinc interpolation.

Fig. 2
Fig. 2

(a) General principle and (b) an implementation of an algorithm for the discrete sinc interpolation. ISDFT, inverse SDFT.

Fig. 3
Fig. 3

Modified algorithm for the discrete sinc interpolation.

Fig. 4
Fig. 4

Examples of 5/3-, 5/2-, and 5–fold expansions of an image fragment.

Equations (9)

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ax=n=-ansinπx/Δx-nπx/Δx-n=n=-an sincπx/Δx-n.
ax=n=0N-1 ansinπMx/Δx-n/NN sinπx/Δx-n/N=n=0N-1 an sincdM; N; πx/Δx-n,
sincd± 1; N; x=sincdN-1; N; x+sincdN+1; N; x/2.
αru,ν=1Nn=0N-1an exp± i2πnνNexpi2πn+urN,
ãnu/p,ν/q=1Nr=0M-1αru,ν exp-i2πrpN×exp-i2πnr+qN=k=0N-1 ak expi2πkν+M-12/N×sincdM; N; k-n+u-p×exp-i2πnq+M-12×expi2πM-1Nu-p,
an0/p,ν/q=k=0N-1 ak sincdM; N; k-n-p×exp-iπM-1N p.
sincdN; N; x=sinπxN sinπx/N,
Qopsep=ONxNyLx+1log Nx+LxLy+1log Ny
Qopinsep=ONxNyLxLy+1log NxNy,

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